FIRST YEAR ENGINEERING - sginstitute.in · 3 First Year Engineering Course Common to All Branches Semester II: Physics Group Sr. No. Subject Teaching / Week (Hours/Week) Examination

1

FIRST YEAR ENGINEERING

Structure and Syllabus

(From the Academic Year 2013-2014)

(Course common to all branches except Architecture and Textile Engineering)

INSTRUCTIONS:

There are two groups in each semester:

1. Physics Group and

2. Chemistry Group

Allotment of groups to students:

a) Semester I: 50% students from each college will be admitted to Physics Group and remaining 50%

will be admitted to Chemistry Group. The concerned College will decide the number and names of the students

to be admitted in physics and chemistry groups and inform the same to the University.

b) Semester II: The students for Physics group in semester-I will be admitted to Chemistry Group in

semester-II. The students for Chemistry Group in semester-I will be admitted to Physics Group in semester-II.

2

First Year Engineering Course Common to All Branches

Semester I: Physics Group

Sr.

No.

Subject Teaching / Week

(Hours/Week)

Examination Scheme

(Marks)

L P T Total Theory TW Total

1 Engineering Physics 03 02 05 100 25 125

2 Engineering

Mathematics-I

03 01 04 100 25 125

3 Basic Electrical

Engineering

03 02 05 100 25 125

4 Basic Civil

Engineering

03 02 05 100 25 125

5 Engineering Graphics# 03 02 05 100# 25 125

6 Professional

Communication-I

01 02 03 -- 25 50

7 Workshop Practice-I 01 02 03 -- 25 50

Total 17 12 01 30 500 200 700 #Theory paper of 4 hours duration


Semester I: Chemistry Group

Sr.

No. Subject Teaching / Week

(Hours/Week)

Examination Scheme

(Marks)


1 Engineering Chemistry 03 02 05 100 25 125

2 Engineering

Mathematics-I

03 01 04 100 25 125

3 Fundamentals of

Electronics and

Computer $

03 02 05 100 25 125

4 Applied

Mechanics

03 02 05 100 25 125

5 Basic Mechanical

Engineering

03 02 05 100# 25 125

6 Professional

Communication-II

01 02 03 -- 25 50

7 Workshop Practice-II 01 02 03 -- 25 50

Total 17 12 01 30 500 200 700 $ should be taught by single faculty ONLY

3


Semester II: Physics Group

Sr.

No.


(Hours/Week)

Examination Scheme

(Marks)


1 Engineering Physics 03 02 05 100 25 125

2 Engineering

Mathematics-II

03 01 04 100 25 125

3 Basic Electrical

Engineering

03 02 05 100 25 125

4 Basic Civil

Engineering

03 02 05 100 25 125


6 Professional

Communication-I

01 02 03 -- 25 50


Total 17 12 01 30 500 200 700 #Theory paper of 4 hours duration


Semester II: Chemistry Group

Sr.

No.


(Hours/Week)

Examination Scheme

(Marks)


1 Engineering Chemistry 03 02 05 100 25 125

2 Engineering

Mathematics-II

03 01 04 100 25 125

3 Basic Electrical

Engineering

03 02 05 100 25 125

4 Basic Civil

Engineering

03 02 05 100 25 125


6 Professional

Communication-I

01 02 03 -- 25 50


Total 17 12 01 30 500 200 700 $ should be taught by single faculty ONLY

4

INDEX

Sr.

No.

Subject Page No.

1 Engineering Physics 5

2 Engineering Mathematics I 17

3 Basic Electrical Engineering 54

4 Basic Civil Engineering 66

5 Engineering Graphics 77

6 Professional communication I 91

7 Workshop Practice I --

8 Engineering Chemistry 95

9 Fundamental of Electronics and Computer Programming 110

10 Applied Mechanics 124

11 Basic Mechanical Engineering 145

12 Engineering Mathematics II 156

13 Workshop Practice II --

14 Professional communication II 185

5

FE Engineering Semester I & II

Engineering Physics

Course Engineering Physics Course Code 40901

Examination

Scheme

Theory Term Work POE Total

Max. Marks 100 25 25 150

Contact

Hours/ week

3 6 -- 9

Prepared by Date

Prerequisites Atomic Structure, energy levels, concept of diffraction, polarization and

interference, total internal reflection, Rayleigh‟s criterion, concept of quanta,

nature of light, scattering of light.

Course Outcomes

At the end of the course the students should be able to:

CO1 Understand the concepts of diffraction, polarization and apply the knowledge

gained, for practicals.

CO2 study the basics of laser and fibre optics and to acknowledge the role of laser and

optical fibers in various fields

CO3 Know the origin of nuclear fission and nuclear fusion and study reactors.

CO4 To differentiate various crystal systems and to study the X-ray diffraction by

crystal.

CO5 Deal with the concepts of Quantum mechanics and solve numericals.

CO6 Generate awareness of newly introduced nanotechnology and to study synthesis,

properties and applications of nanomaterials.

Mapping of COs with POs

POs COs

a b c d E f G h i j k l

CO1 √ √ √

CO2 √ √ √

CO3 √ √ √ √

CO4 √ √ √ √

CO5 √

CO6 √ √

6

Course Contents

Unit No. Title No. of

Hours

Section I

1. Diffraction and Polarization 07

2. Laser and Fibre Optics 07

3 Nuclear Energy 07

Section II

4. Crystallography 07

5.. Quantum Physics 07

6. Nano Physics 07

Reference Books:

Sr. No. Title of Book Author Publisher/Edition Topics

1 Solid State Physics : Structure

& Electron Related Properties

S. O. Pillai Eastern Ltd,

New Age International Ltd.

Unit 4,

Unit 5

2 Introduction to Solid State

Physics

Charles Kittle,

Wiley India Pvt.

Ltd.(8thEdtion).

Wiley India Pvt.

Ltd.

Unit 4

3 Engineering Physics B. K. Pandey and S.

Chaturvedi Cengage

Learning-2012

All units

4 Modern Physics B. L. Theraja S. Chand &

Company Ltd.,

Delhi

Unit 6

5 Nanotechnology Pandey Cengage

Publication

Unit 5

6 Optics Subramanyam &

Brij Lal S. Chand &

Company (P.) Ltd.

Unit 1

and 2

7

Scheme of Marks

Section Unit No. Title Marks

I 1 Diffraction and Polarization 17

2 Laser and Fibre Optics 17

3 Nuclear Energy 16

II 4 Crystallography 17

5 Quantum Physics 17

6 Nano Physics 16

Course Unitization

Section

Unit Course Outcomes No. of Questions

in

No. Title CAT-I CAT-II

I 1 Diffraction and

Polarization

Understand the concepts of diffraction,

polarization and apply the knowledge

gained, for practicals.

1

2 Laser and Fibre

Optics

study the basics of laser and fibre optics

and to acknowledge the role of laser and

optical fibers in various fields

1

3 Nuclear Energy Know the origin of nuclear fission and

nuclear fusion and study reactors.

1

II 4 Crystallography To differentiate various crystal systems

and to study the X-ray diffraction by

crystal.

1

5 Quantum

Physics

Deal with the concepts of Quantum

mechanics and solve numericals.

1

6 Nano Physics Generate awareness of newly introduced

nanotechnology and to study synthesis,

properties and applications of

nanomaterials.

1

8

Unit wise Lesson Plan

Section I

Unit No 1 Unit Title Diffraction and Polarization Planned

Hrs.

07

Unit Outcomes: Understand the concepts of diffraction, polarization and apply the

knowledge gained, for practicals.

At the end of this unit the students should be able to:

UO1 Explain basic concepts of light, diffraction, resolving power and

polarization.

CO1

UO2 Differentiate between O-ray and e-ray as well as positive crystal and

negative crystal.

CO1

UO3 Derive grating equation and resolving power of diffraction grating. CO1

UO4 Realize the use Laurentz half shade polarimeter for determination of

specific rotation

CO1

UO5 Solve numericals of grating equation and specific rotation. CO1

Lesson schedule

Class

No.

Details to be covered

1 Diffraction: Introduction, , , ,

2 diffraction grating - construction, theory

3 resolving power, resolving power of plane transmission grating,

4 numerical of grating equation

5 Polarization: Introduction, double refraction, Huygens‟ theory (positive and negative

crystals)

6 optical activity, Laurent‟s half shade polarimeter

7 Numerical of specific rotation, Photo-elasticity

Unit No

2 Unit Title LASER and Fiber Optics Planned

Hrs.

07

Unit Outcomes: study the basics of laser and fibre optics and to acknowledge the role

of laser and optical fibers in various fields


UO1 Understand the concept of atom, different atomic energy levels. Understand

the role of quantum mechanics in atomic model.

CO1

UO2 Relate Quantum Mechanics used in Bohr‟s postulates with the stability of

atom and also with the energy emission by an atom.

CO1

UO3 Explain the transitions takes place between energy levels. CO1

UO4 Describe the stimulated absorption, spontaneous and stimulated emission.

Ultimately to study the LASER emission.

CO1

UO5 Explain conditions for lasing action. To list different characteristics of laser. CO1

UO6 Study different types of laser and study Ruby laser (Solid State Laser) in CO1

9

detail (construction, working and energy level diagram).

UO7 Acknowledge the structure of an optical fiber and describe total internal

reflection in the core of fiber.

CO1

UO8 Differentiate between single mode and multi mode fiber. Study multimode

fiber in detail with the help of diagram.

CO1

UO9 Acknowledge the applications of optical fiber and laser in day today life. CO1

UO10 Solve numerical of numerical aperture. CO1

Lesson schedule

Class

No.


1 Absorption, spontaneous emission, stimulated emission,

2 Lasing action, pumping energy, population inversion

3 Types of laser, characteristics of laser, Ruby laser, construction, working with energy

level diagram.

4 applications of laser (industrial & medical), Holography (construction, reconstruction,

and applications).

5 Principle, structure of optical fibre, propagation of light, acceptance angle and

acceptance cone (no derivation),

6 numerical aperture (no derivation), types of optical fibre,

7 Applications (medical, military, entertainment, communication, optical fiber sensors),

advantages of optical fibres.

Unit No

3 Unit Title Nuclear Energy Planned

Hrs.

07

Unit Outcomes: Know the origin of nuclear fission and nuclear fusion and study

reactors.


UO1 Identify the basic principles of the mass-energy equivalence concept. CO2

UO2 Define and calculate the mass defect and the binding energy of the nucleus. CO2

UO3 Define nuclear fission and chain reaction. CO2

UO4 Understand how the binding energy curve leads to nuclear fission and

nuclear fusion.

CO2

UO5 Have a basic understanding of the construction nuclear reactor (fission and

fusion).

CO2

UO6 Have a basic understanding of conditions for fusion reactor. CO2

UO7 Be able to calculate energy generated in fission of 1 kg of U235 in joule,

KWh, and calorie.

CO2

UO8 Be able to perform simple criticality calculations for efficiency of nuclear

reactor, nuclear power and fission rate.

CO2

Lesson schedule

10

Class

No.


1 Introduction, structure of nucleus, 1a.m.u.relation with energy, .

2 Binding energy, binding energy curve, energy released by 1 Kg. of U-235

3 Chain reaction, its types, multiplication factor

4 nuclear reactor and their classification, essentials of nuclear reactor

5 numericals for energy released by Uranium

6 Nuclear fusion (p-p chain, c-n cycle),

7 conditions for fusion reaction, fusion reactor.

Review Questions

Q1 Distinguish between positive & negative crystals CO1

Q2 Explain the theory of plane diffraction grating & obtain grating equation

6 marks

CO1

Q3 Write a note on „ Laurent‟s half shade polarimeter‟ CO1

Q4 Define resolving power & obtain expression for it. CO1

Q5 Define double refraction & Find the angular separations between two sodium

lines, whose wavelength are 5890A0 & 5898A0 respectively for the plane

diffraction grating with 1800 lines/inch in first order spectrum.

CO1

Q6 Explain optical activity & State the formula for specific rotation CO1

Q7 Diffraction grating used at normal incidence gives the line of wavelength λ1

= 6000A0 in certain order superimposed on another line λ2 =4500 A0 of the

next higher order. if the angle of diffraction is 300, calculate The number of

lines in 1 cm of grating.

CO1

Q1 Distinguish between positive & negative crystals CO2

Q2 Explain the theory of plane diffraction grating & obtain grating equation

6 marks

CO2

Q3 Write a note on „ Laurent‟s half shade polarimeter‟ CO2

Q4 Define resolving power & obtain expression for it. 5 marks CO2

Q5 Define double refraction & Find The angular separations between two

sodium lines, whose wavelength are 5890A0 & 5898A0 respectively for the

plane diffraction grating with 1800 lines/inch in first order spectrum.

CO2

Q1 Define, Chain reaction and critical size CO3

Q2 Discuss the classification of nuclear reactor. CO3

Q3 Distinguish between fission and fusion. CO3

Q4 Discuss the requirements of thermonuclear fusion power reactor CO3

Q5 Explain thermonuclear reactions according to sun and st CO3

Q6 Describe fusion power reactor with neat diagram CO3

Q7 Define nuclear fission. Calculate the energy released by 1 kg.of U235 in kwh CO3

Q8 A city requires 5000 MWh electric energy per day. This is to be obtained by

nuclear reactor of efficiency 30% . Calculate the mass of U235 needed for

one day operation of nuclear reactor. Assume the energy released per fission

of U235 is 200MeV.

CO3

Q9 A railway engine develops an average power of 1000 kW during a ten hour

run from one station to another. If the engine is driven by an atomic power

CO3

11

plant of 20% efficiency, How much U-235 would be consumed on the run?

Each U- 235 atom on fission releases 200MeV of energy.

Section II

Unit No

4 Unit Title Crystallography Planned

Hrs.

07

Unit Outcomes: To differentiate various crystal systems and to study the X-ray

diffraction by crystal.


UO1 Define crystal structure, Unit cell, lattice point, and space lattice. CO4

UO2 Familiar with crystal systems to develop the relationships between axial

length and interfacial angles.

CO4

UO3 Understand the characteristics of sc, fcc and bcc lattice with the help of

suitable diagrams.

CO4

UO4 Understand the fundamentals of how crystals relates with the diffraction. CO4

UO5 Calculate the density, lattice constant of crystal CO4

UO6 Determine the crystal structure by knowing number of atoms per unit cell. CO4

UO7 Revise basics of X-ray properties using Laue spot and relate it with

diffraction by crystals. Derive Bragg's law for diffraction with usual

diagram.

CO4

UO8 Describe real application of Bragg‟s law in Braggs X-ray spectrometer. CO4

UO9 To solve numerical problems on Braggs law. CO4

Lesson schedule

Class

No.


1 Introduction matter, states of matter, Unit cell,

2 properties of unit cell i..e (number of atoms per unit cell, coordination number, atomic

radius, packing fraction) for BCC, FCC and SC structure

3 Fourteen Bravais lattices, symmetry elements in cube

4 relation between density and lattice constant, relation between interplaner distance and

lattice constant, numericals for both relations

5 Miller indices - procedure, features and sketches for different planes.

6 X-ray diffraction, Bragg's law,

7 Bragg's x-ray spectrometer, numericals for Bragg‟s law

Section II

Unit No

5 Unit Title Quantum Physics Planned

Hrs.

05

Unit Outcomes: Deal with the concepts of Quantum mechanics and solve numericals.


UO1 Distinguish Classical mechanics from Quantum mechanics and provides a

general scheme for understanding a vast range of physical phenomena.

CO5

UO2 Basic understanding of the key concepts of elementary quantum

mechanics,.

CO5

12

UO3 Be able to deal with conceptually rich and technically difficult theoretical

problems.

CO5

UO4 Know how to use the theory to discuss quantum phenomena quantitatively. CO5

Lesson schedule

Class

No.


1 Introduction to quantum mechanics. Wave-particle duality,

2 De- Broglie Hypothesis. Determination of wavelength of matter waves.

3 Properties of matter waves. Compton Effect.

4 Derivation of Compton shift.

5 Numericals for Compton shift and de-Broglie‟s wavelength.

Unit No

6

Unit Title NanoPhysics Planned

Hrs.

07

Unit Outcomes: Generate awareness of newly introduced nanotechnology and to study

synthesis, properties and applications of nanomaterials.


UO1 Study scale of structure of material and study fundamentals of

nanomaterials.

CO6

UO2 Provide understanding of nanostructure properties and applications. CO6

UO3 The definition of nanotechnology, including the nanoscale and property

changes.

CO6

UO4 Characterization Techniques for nanostructured materials. CO6

UO5 Relevant applications, products or technologies. CO6

UO6 Explain structure & working of different instruments used in

nanotechnology.

CO6

UO7 Synthesis, processing and manufacturing of nanocomponents and

nanosystems.

CO6

Lesson schedule

Class

No.


1 Basic concepts – nanoscale, nanomatrerials. Introduction to nanotechnology.

2 Production techniques for nanomaterials- top down approach.

3 Production techniques for nanomaterials- bottom up approach, properties and

applications of nanomaterials.

4 Properties and applications of nanomaterials.

5 Characterization tools Scanning Tunneling Microscopy.

6 Characterization tools Atomic Force Microscopy.

7 Introduction to CNT, Properties and applications.

Review Questions

Q1 Explain seven systems of crystals in terms of relations of intercepts &

interfacial angles. List the name of 14 bravais lattices.

CO4

13

Q2 Define packing factor & calculate the values of packing factor for S.C. ,

BCC, FCC lattices

CO4

Q3 What are Miller indices? Explain the procedure to find Miller indices &

obtain the properties of Miller indices.

CO4

Q4 Show that for cubic lattice, the lattice constant is given by a3 = nA /þN,

where the symbols have usual meaning

CO4

Q5 Explain Element of symmetry in cubic lattice. s CO4

Q6 State Bragg‟s law. Describe the construction & working of Braggs

spectrometer used for crystal analysis.

CO4

Q7 Derive Bragg‟s relation. CO4

Q8 A beam of x-ray of wavelength 0.842 Å is incident on a crystal at a

glancing angle of 80 35‟ when the 1st order Bragg‟s reflection occurs.

Calculate the glancing angle for 3rd order reflection.

CO4

Q9 Lead is face centered cubic with an atomic radius of r=1.746A0. Find the

spacing of (200) (220) (111) planes.

CO4

Q10 Obtain the Miller indices for the plane making intercepts of 1 A0,2 A0,3

A0 along x, y & z axes.

CO4

Q11 State the De- Broglie‟s hypothesis of matter wave. CO5

Q12 Derive an expression for wavelength of matter wave in terms of kinetic

energy of particle.

CO5

Q13 State the properties of matter wave. CO5

Q14 State & explain Heisenberg uncertainty principle. CO5

Q15 What is Compton Effect? Derive an expression for Compton shift. CO5

Q16 Explain in brief production techniques used in nanomaterial. CO6

Q17 Discuss in brief construction & working of STM. CO6

Q18 Write the properties &application of nanomaterial. CO6

Q19 Explain two types of CNT & state any four application. CO6

Q20 Explain in brief AFM. CO6

14

Model Question Paper

Course Title : Engineering Physics Max.

Marks

Duration 3hrs. 100

Instructions:

1. Figures to the right indicate full marks.

2. Use of electronic calculator is allowed.

Section-I

Marks

1 a Explain the theory of plane diffraction grating & obtain grating

equation.

6

b Explain the construction & working of Laurent‟s half shade

polarimeter.

6

c What is double refraction? Distinguish between positive & negative

crystal.

5

d Define resolving power? Hence determine resolving power in second

order for a light of wavelength 5000 A0 which falls on a grating

normally. Two adjacent principle maxima occur at sinθ1=0.2 &

sinθ2=0.3 respectively. Also calculate the grating element (Given: The

width of grating surface is 2.5).

5

2 a Explain the construction & working of ruby laser. 6

b Explain the terms, a) Population inversion b) Pumping energy

c) Stimulated emission 6

c Explain the construction of optical fibre & explain propagation of light

through fibre. 5

d What are the advantages of optical fibre communication system over

conventional method of communication? Hence determine numerical

aperture of optical fibre if refractive index of core & cladding is 1.60

& 1.57 respectively.

5

3 a Explain the essentials of nuclear fission reactor. 6

b Calculate the power output of a nuclear reactor which consumes 25

gm of U235

per day. Assume 5% reactor efficiency& energy released

per fission of U235

is 200MeV.

5

c Explain the conditions of fusion reactor. 5

d Explain nuclear chain reaction and Critical size. 5

Section-II

Marks

4 a Explain seven systems of crystals in terms of relations of intercepts &


6

b Explain Element of symmetry in cubic lattice. 6

c What are Miller indices? Obtain the Miller indices for the plane

making intercepts of 1 A0,2 A

0,3 A

0 along x, y & z axes.

5

15

d State & derive Bragg‟s law of X-ray diffraction. 5

5 a What is Compton Effect? Derive expression for Compton shift. 6

b State the hypothesis of matter wave. Hence obtain relation for

wavelength of matter wave in terms of kinetic energy.

6

c State & explain Heisenberg‟s uncertainty principle. 5

d State the properties of matter wave. 5

6 a Explain in brief two production techniques used in synthesis of

nanomaterials.

6

b Discuss in brief the construction & working of scanning tunneling

microscope. 5

c What are carbon nanotubes (CNT‟s). State it‟s any three applications. 5

d State different properties of nanomaterials. 5

Assignments

List of experiments/assignments to meet the requirements of the syllabus:

1. Calculation of divergence of LASER beam.

2. Determination of wavelength of LASER using diffraction grating.

3. Diffraction grating using mercury vapor lamp.

4. Polarimeter.

5. Verification of inverse square law of intensity of light.

6. Measurement of band gap energy.

7. Study of crystal structure.

8. Study of symmetry elements of cube.

9. Determination of „d‟(interplaner distance) using XRD pattern.

10. Study of Planes with the help of models related Miller Indices.

Assignment No. 1

Assignment Title Diffraction and polarization CO1

Batch I Explain the theory of plane diffraction grating & obtain grating equation.

What is double refraction? Write difference between O-ray and e-ray.

Batch II Explain the construction & working of Laurent‟s half shade polarimeter.

What is the difference between positive and negative crystal?

Batch III Explain the theory of plane diffraction grating & obtain grating equation.

Explain the construction & working of Laurent‟s half shade polarimeter.

Assignment No. 2

Assignment Title Laser and Fiber Optics CO2

Batch I Define spontaneous absorption, spontaneous emission and stimulated

emission.

Explain fiber optics communication system

16

Batch II Explain construction and working of Ruby laser.

What are different types of optical fiber?

Batch III Write different applications of laser.

What are advantages of optical fiber?

Assignment No.3

Assignment Title Nuclear energy CO3

Batch I Calculate energy released by 1gm of U235.

Batch II Calculate energy released by 1kg of U235.

Batch III Calculate energy released by 20kg of U235.

Assignment No.4

Assignment Title Crystallography CO4

Batch I Explain seven systems of crystals in terms of relations of intercepts &


Batch II Explain Element of symmetry in cubic lattice.

Batch III What are Miller indices? Write procedure to determine miller

indices.Obtain the Miller indices for the plane making intercepts of 1 A0,2

A0,3 A

0 along x, y & z axes.

Assignment No.5

Assignment Title Quantum Physics CO5

Batch I What is Compton Effect? Derive expression for Compton shift.

Batch II State the hypothesis of matter wave. Hence obtain relation for wavelength

of matter wave in terms of kinetic energy.

Batch III State & explain Heisenberg‟s uncertainty principle.

State properties of matter waves.

Assignment No.6

Assignment Title Nanophysics CO6

Batch I Explain in brief two production techniques used in synthesis of

nanomaterials.

Batch II Discuss in brief the construction & working of scanning tunneling

microscope.

Batch III What are carbon nanotubes (CNT‟s). State it‟s any three applications.

List of additional assignments /experiments

Experiment No. 1

Experiment Title Least Count of Instruments

17

FE Engineering Semester I

Engineering Mathematics I

Course Engineering Mathematics I Course Code BH102

Examination

Scheme


Max. Marks 100 25 -- 25 125

Contact

Hours/ week

3 1 -- 4

Prepared by Ms. Patil P. V. Date 30.04.2014

Prerequisites Algebra of matrices

Basic knowledge of Complex numbers and algebra

Basic knowledge of limits

Basic knowledge of derivatives and its applications

Basic knowledge of partial derivative

Course Outcomes


CO1 To find the rank of the matrix & to solve simultaneous linear equations by

matrix method.

CO2 To find Eigen values & Eigen vectors

CO3 Use of De Moivres theorem, roots of complex numbers, meaning of circular

functions, hyperbolic functions & inverse hyperbolic functions.

CO4 To obtain expansions of functions at x=o & x=a Also to evaluate indeterminate

forms

CO5 Partial differentiation: - meaning, Euler‟s theorem, applications of partial

differentiation

CO6 To solve simultaneous linear equations by different numerical techniques.


POs

COs


CO1 √

CO2 √ √

CO3

CO4 √

CO5 √ √

CO6 √

18

Course Contents


Hours

Section I

1. Matrices and solution of linear system equations

1.Rank of matrix: definition, normal form and Echelon form

2. Consistency of linear system equations

3. System of linear homogeneous equations

4. System of linear Non-homogeneous equations

5

2. Eigen Values and Eigen vectors

1. Linear dependence and independence of vectors

2. Eigen Values

3. Properties of Eigen Values

4. Eigen vectors

5. Properties of Eigen vectors

6. Cayley-Hamilton's theorem (Without proof)

7. Inverse and higher powers of matrix by using Cayley-Hamilton's

theorem

8

3. Complex Numbers

1. De Moivre's Theorem (Without proof)

2. Roots of complex numbers by using De Moivre's Theorem

3. Expansion of sinnθ and cosnθ in powers of sinθ and /or cosθ.

4. Circular functions of a complex variable - definitions

5. Hyperbolic Functions, Relation between Circular & Hyperbolic

functions

6. Inverse Hyperbolic Functions

7. Separation into real and imaginary parts

8

Section II

4. Expansion of Functions and Indeterminate forms:

1. Maclaurin's theorem

2. Standard expansions 8

3. Taylor's theorem

4. Expansion of function in power series by using

i) Standard series method,

ii) Differentiation and integration method,

iii) Substitution method

5. Indeterminate forms and L' Hospital's rule

7

5. Partial Differentiation:

1. Partial derivatives: Introduction

2. Total derivatives

3. Differentiation of implicit function

4. Euler's theorem on homogeneous function of two variables

5. Change of variables

6. Jacobian, Properties of Jacobian, Jacobian of Implicit function,

7. Errors and Approximation

8

19

8. Maxima and Minima of functions of two variables

6. Numerical Solution of linear simultaneous equations:

1. Gauss elimination method

2. Gauss-Jordan method

3. Jacobi‟s iteration method

4. Gauss-Seidel iteration method

5. Determination of Eigen values by iteration

6

Reference Books:


1 Higher Engineering Mathematics Dr. B. S. Grewal Khanna

Publishers,

Delhi.

All

2 A text book of Applied

Mathematics, Vol.-I,II,III

P. N. Wartikar & J.

N. Wartikar

Pune Vidyarthi

Griha

Prakashan, Pune.

All

3 Advanced Engineering

Mathematics

Erwin Kreyszig Wiley India Pvt.

Ltd.

All

4 A textbook of Engineering

Mathematics Volume I

Peter V. O‟Neil

and Santosh K.

Sengar

Cengage

Learning

All

5 Mathematical methods of

Science and Engineering

Kanti B. Datta Cengage

Learning

6

6 Numerical Methods Dr. B. S. Grewal Khanna

Publishers,

Delhi.

6


Mathematics

N. P. Bali, Iyengar Laxmi

Publications (P)

Ltd., New Delhi

All

8. Higher Engineering Mathematics H.K. Das and Er.

Rajnish Varma

Chand Technical

publication

All

20

Scheme of Marks


I 1 Matrices and solution of linear system equations 15

2 Eigen Values and Eigen vectors 15

3 Complex Numbers 20

II 1 Expansion of Functions and Indeterminate forms 15

2 Partial Differentiation 20

3 Numerical Solution of linear simultaneous equations 15

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in


I 1 Matrices and solution of

linear system equations

CO1 Q.1

(15 Marks)

2 Eigen Values and Eigen

vectors

CO2 Q.2

(15 Marks)

3 Complex Numbers CO3 Q.1

(15 Marks)

II 1 Expansion of Functions

and Indeterminate forms

CO4 Q.2

(15 Marks)

2 Partial Differentiation CO5

3 Numerical Solution of

linear simultaneous

equations

CO6

21


Section I

Unit

No

1 Unit Title Matrix and solution of linear system

of equation

Planned Hrs. 7

Unit Outcomes


UO1 find rank of a matrix by given three different methods CO1

UO2 Study of consistent and Inconsistent equations

UO3 Solve homogenous and non- homogenous system of linear equations by using rank

Lesson schedule

Class

No.


1 Introduction, Algebra of matrices and Types of Matrices

2 Definition of Rank and Rank of a matrix by normal form

3 Rank and Inverse of a matrix by PAQ form

4 Rank of a matrix by echelon form

5 Consistent and Inconsistent equations

6 Solution of non- homogenous equations

7 Solution of homogenous equations

8 University Examples

Review Questions

Q1 Reduce the following matrices to normal form and hence find its rank

1)

4 5 6 7

9 10 11 12

10 11 12 13

18 19 20 21

2)

1 2 1 0

2 4 3 0

1 0 1 8

3)

5 2 4 1 6

2 1 1 2 2

4 1 0 5 10

1 2 5 8 6

4)

2 3 1 2

1 1 2 4

3 1 3 2

6 3 0 8

5)

2 3 1 1 3

1 1 2 4 6

3 1 3 2 5

6 3 0 7 2

6)

6 1 3 8

4 2 6 1

10 3 9 7

16 4 12 15

UO1

Q2 Reduce the following matrices to PAQ form and hence find its rank

1)

1 1 1

1 1 1

3 1 1

2)

2 1 3 6

3 3 1 2

1 1 1 2

3)

1 2 3 1

2 1 3 1

1 0 1 1

0 1 1 1

4)

1 1 2

1 2 3

0 1 1

Q 3 Test for consistency and if possible solve them

(a) 2 3 4 11x y z , 5 7 15x y z , 3 11 13 25x y z

(b) 2 4, 2 2 7,3 2 1x z x y z x y

UO2,

UO3

22

(c) 2 3 1,3 2 3, 4 5 1x y z x y z x y z

(d) 2,2 2 1,3 4 9x y z x y z x y z

(e) 3,3 2 2,2 4 7 7x y z x y z x y z

(f) 2 3,3 2 1,2 2 3 2,x y z x y z x y z 1x y z

(g) 2 3 9, 2 3 6,3 2 8x y z x y z x y z

(h) 2 3, 2 4, 2x y z x y z x z

Q4 Investigate for what values of λ and µ the equation

6, 2 3 10, 2x y z x y z x y z

Have (i) no solution (ii) a unique solution (iii) Infinite solution

UO2,

UO3

Q5 For what value of the equations 1x y z ; 2 4x y z ;

24 5 10x y z have a solution and solve them for the value of

Q6 Find the value of k for which the system has non-zero/non-trivial solution & hence

find solution for each value of k for

3 0,4 2 3 0,2 4 0x y kz x y z kx y kz

Q7 Solve

1. 3 2 0, 2 3 0, 4 5 0x y z x y z x y z

2. 2 3 0, 2 3 0, 4 5 4 0, 2 0x y z x y z x y z x y z

3. 3 5 0, 5 3 6 0, 2 0, 5 0x y z x y z x y z x y z

4. 2 0, 2 3 0, 3 4 0,3 4 7 0x y z x y z x y z x y z

Unit

No

2 Unit Title Eigen Values & Eigen Vectors Planned Hrs. 08

Unit Outcomes


UO1 Check dependency and independency of vectors CO2

UO2 Find Eigen values and Eigen vectors for given matrix

UO3 Solve examples on Cayley Hamilton‟s Theorem and use it to find Inverse and

higher powers of matrices

Lesson schedule

Class

No.


1 Introduction of vectors

2 Dependency and independency of vectors

3 Introduction to Eigen values and its properties

4 Examples on Eigen Values

5 Introduction to Eigen vectors and its properties

6 Examples to find Eigen values and its corresponding Eigen vectors

7 Introduction to Cayley Hamilton‟s Theorem

8 Examples on Cayley Hamilton‟s Theorem

23

Review Questions

Q1 Define linear dependence & independence of vectors. Examine the linear

dependence of vectors and find relation between then, if possible.

1. [1, 0, 2, 1]; [3, 1, 2, 1]; [4, 6, 2, -4]; [-6, 0, -3, -4]

2. [3,2,7], [2,4,1], [1,-2,6]

3. [1, 1, 3], [1, 3, -3], [-2, -4, -4], [-9, -25, 9]

4. [1, 2, -1, 0], [1, 3, 1, 2], [4, 2, 1,0], [6, 1, 0, 1]

UO1

Q2 Show that the vectors

[2, 3, -1, -1]; [1, -1, -2, -4]; [3, 1, 3, -2]; [6, 3, 0, -7] form a linearly dependent set.

Also express one of these as linear combination of others

Q3

If 1 2 3, , are Eigen values of matrix

1 4

0 2 6

0 0

3

5

Find (a) 1 2 3

(b) 1 2 3

UO2

Q4 Find the Eigen values and Eigen vectors for the following matrices

(a)

2 2 3

1 6

2

2

1 0

(b)

1 1 3

1 5 1

3 1 1

(c)

8 6 2

6 7 4

2 4 3

(d)

6 2 2

2 3 1

2 1 3

Q5 Find the Eigen values and Eigen vectors for the greatest Eigen value for the matrix

A=

4 2 2

5 3

2 4

2

1

Hence find Eigen values of -2A3 , And Adj of A

Q6

For Eigen values for A-1, A5, -3A where A=

2 2

1 3

6

2 3 1

2

Q7 State Cayley- Hamilton theorem and find A-1 and A4 , where

i) A=

7 2 2

6

6

1 2

2 1

ii) A=

3 2 4

4 3

2 4 3

2

UO3

Q8 Find characteristic equation for A and find the matrix expression represented by

8 7 6 5 4 3 25 7 3 5 8 2A A A A A A A A I ,where A= 0 1 0

2 1 1

1 1 2

UO3

24

Q9

Find the characteristic equation of the matrix

8 8 2

4 3 2

3 4 1

A and show that the

matrix A satisfies its characteristic equation

UO3

Unit

No

3 Unit Title Complex Numbers Planned

Hrs.

9

Unit Outcomes


UO1 Simplify and find roots of complex number by using De Moivre‟s Theorem CO3

UO2 Expand sinnѳ, cosnѳ and tannѳ in powers of sinѳ, cosѳ and tanѳ

UO3 Find relation and difference between circular and hyperbolic functions

UO4 Solve examples by using hyperbolic and inverse hyperbolic functions

UO5 Separate real and imaginary parts of a given complex number

Lesson schedule

Class

No.


1 Introduction of complex number, modulus, Argument and Algebra of complex numbers

2 Statement of De Moivers theorem and examples

3 Roots of comlex number by using De Moivers theorem

4 Expansion of sinnѳ, cosnѳ and tannѳ in powers of sinѳ, cosѳ and tanѳ

5 Definition of circular function in complex variable

6 Introduction of Hyperbolic functions and its properties

7 Relation between circular and hyperbolic functions

8 Inverse Hyperbolic functions

9 Separation of real and imaginary parts

Review Questions

Q1 Simplify

1.

7 5

12 6

cos2 sin 2 cos3 sin3


i i

i i

2.

2 3

9 5

cos5 sin5 cos7 sin 7

cos 4 sin 4 cos sin

i i

i i

3. 1 sin cos

1 sin cos

ni

i

UO1

Q2 Show that

1. 1 cos sin

cos sin1 cos sin

ni

n i ni

UO2,

UO3

25

2. 8 8

81 3 1 3 2i i

3. 5 3sin 632cos 32cos 6cos

sin

4. 3 5

2 4

5tan 10 tan tantan 5

1 10 tan 5tan

Q3 Express cos7 and sin 6 in terms of powers of cos and sin UO2

Q4 Solve

1. 4 3 2 1 0x x x x

2. 9 5 4 1 0x x x

3. 6 0x i

4. 7 4 3 1 0x x x

5.

61

11

x

x

6. 5 51 32( 1)x x

UO1

Q5 Find the continued product of all the values of

3/4

1 3

2 2i

UO1

Q6 Find all the values of

1. 1/5

1 2. 1/5

1 i

UO1

Q7 Find nth root of unity and show that

1. Roots are in geometric progression

2. Sum of the all roots is zero

3. Product of all roots is 1

1n

UO1

Q8 Find the common roots of 4 1 0x and

6 0x i UO1

Q9 Solve the equation 7cosh 8sinh 1x x for real values of x UO3

Q10 Prove that

1.

31 tanh

cosh 6 sinh 61 tanh

xx x

x

2. 7 1sinh sinh 7 7sinh5 21sinh3 35sinh

64x x x x x

3. 1 2sinh log( 1)z z z

4. 1 2cosh log( 1)z z z

5. 1 1 1

tanh log2 1

zz

z

UO4

26

6. 1 1

2sinh tanh

1

xx

x

7. 1 1tanh (sin ) cosh (sec )

8. 1 1coth log

2

x x a

a x a

9. 1sech sin log cot2

Q11 If

x xtan tanh

2 2, prove that 1. sinh tanu x 2. cosh secu x

UO4

Q12 Separate into real and imaginary parts

1. ii 2.

i

i 3. tanh x iy 4. 1tan ie 5.

1 3cos

4

i

UO5

Q13 If cos( ) (cos sin )i r i then prove that

1 sin( )log

2 sin( )

UO4

UO5

Q14 If sin( ) tan seci i , prove that cos 2 cosh 2 3

Q15 If tan( ) sin( )i x iy , prove that

tan sin 2

tanh sinh 2

x

y

Q16 If cos

4u iv ec ix , prove that

2 2 2 2 2( ) 2( )u v u v

Q17 If tan

6x iy i , prove that

2 2 21

3

xx y

Q18 If 1 1 1cosh cosh ( ) coshx iy x iy a then prove that

2 2 22( 1) 2( 1) 1a x a y a

Q19 If tan( )i i and x,y are real prove that x is indeterminate and y is infinite

Section II

Unit

No

4 Unit Title Expansion of functions Planned

Hrs.

9

Unit Outcomes


UO1 Expand given function by using Maclaurin‟s series, Taylor‟s series, some standard

expansions, derivative and integration method and substitution method

CO4

UO2 Find limits of indeterminate forms by L‟ Hopital‟s Method

Lesson schedule

Class

No.


1 Introduction, Expansion by using Maclaurins series

2 Standard expansions by using Maclaurins series

27

3 Expansions by using standard expansions

4 Expansions by using derivative and integration method

5 Expansion by using substitution method

6 Expansions by using Taylor‟s Method

7

8 Examples on Indeterminate forms

9

Review Questions

Q1 Expand in powers of x

1. tanx

2. log(1+ex)

3. exsecx

4. 2

1 1 1tan

x

x

5. log tan4

x

6. 3 4 517 6 2 3( 2) ( 2) ( 2)x x x x in powers of x by Taylor‟s

theorem

7. tan x in powers of 4

x

8. log(1 sin )x by Maclaurin‟s series

9. 1x

x

e by using standard expansions

10. 5 4 3 2 1x x x x x in powers of 1x and hence find (11/10)f

11. 3 22 7 1x x x in powers x-2

UO1

Q2 Prove that

1. 2 4 6

logsec .....2 12 45

x x xx

2. 4

2 2 2sec 1 .....

3

xx x

3. 2 3 4

cos 111 ....

2 3 24

x x x x xe x

4. 3 4

2 5(1 ) 1 .....

2 6

x x xx x

5. 2 3

1/ 5log[log(1 ) ] .....

2 24 8

x x x xx

6. 2 3

log(1 ) ....2 3

x x xe x x

UO1

28

Q3 If

3 2 32 1x xy y x then prove that 2

1 ....3

xy x

UO1

Q4 If

2 3 4

....2 3 4

y y yx y then prove that

2 3

.....2! 3!

x xy x

UO1

Q5 Using Taylor‟s Theorem

1. 25.15 2. 0tan(46 36') 3.

0sin(30 30') 4. 0cos 41

UO1

Q6 Evaluate

1. limx o

3 3

5 3

sin 2 sinx x

x x

2. limx o

2

2

sin

1

xe x x x

x xlog x

3. log(2 )cot( 1)1

lim x xx

4. limx

1

1 1 12 3 5

3

xx x x

5. limx o

tan3

sin 2

x

x

6. lim

y x

x y

x y

x yx o

7. limx o

1

2

112

x xx e e

x

8. limx o

2

2

sin

1

xe x x x

x xlog x

9. limx a

7tan2

2ax

a

10. limx

1

1 1 12 3 5

3

xx x x

11. limx o

tan3

sin 2

x

x

12. 0

limx

2

1

tan xx

x

UO2

29

13. limx a

1

2 2

sin

sin

a x

a x

a x

14. limx a

cot( )

log 2

x ax

a

Q7 If lim

x o 3

sin 2 sinx p x

x is finite; find the value of p and limit

UO2

Unit

No

5 Unit Title Partial Differentiation Planned

Hrs.

12

Unit Outcomes


UO1 Take partial derivative of a given function (Implicit or Explicit) CO5

UO2 Solve examples by using Euler‟s Theorem and it‟s corollaries

UO3 Solve examples by using Jacobian and its properties

Lesson schedule

Class

No.


1 Introduction to partial differentiation

2 Total derivative

3 Differentiation of implicit function

4 Statement of Euler‟s theorem and examples

5 Statement of corollaries of Euler‟s theorem and examples

6 Change of variable

7 Introduction of Jacobian

8 Properties of Jacobians

9 Jacobians of Implicit functions

10 Exapmles on errors and approximations

11 Examples on Maxima and Minima

Review Questions

Q1 If 2 2 2 2 2 2sin( ) sin( ) sin( )u x y y z z x then prove that

1 1 10

u u u

x x y y z z

UO1

Q2 If

2 1 2 1tan tany x

u x yx y

; then prove that 2 2u u

x y y x

UO1

Q3 If ( , ) ,

u

vz x y and x uv y then prove that

UO1

30

1 1

2 2

z z z

x v u u v ,

2

2 2

z v z v z

y u u v

Q4 If

122 2 2u x y z prove that

2 2 2

2 2 20

u u u

x y z

UO1

Q5 If 0ux vy and 1

u v

x y; prove that

2 2

2 2y x

u v x y

x y x y

UO1

Q6

If 2 2

1tan1

xyu

x y ; prove that

2

32

1

2 21

u

x yx y

UO1

Q7 If ( )ax byz e f ax by then show that 2

z zb a abz

x y

UO1

Q8

If

1 12 2

1 13 3

1cosx y

u ec

x y

; prove that i) 1

tan12

u ux y u

x y

ii) 2 2 2 2

2 22 2

tan 13 tan2

12 12 12

u u u u ux xy y

x yx y

UO2

Q9 If 2 1 2 1sin sin

y xu x y

x y; prove that

(i) u u

x yx y

(ii) 2 2 2

2 22 2

2u u u

x xy yx yx y

UO2

Q10

If 18 8 8

2 3sin

x y zu

x y z; then find

u u ux y z

x y z

UO2

Q11 If

1sinx y

x yu ; prove that

u x u

y y x

UO2

Q12

If 2 2

logx y

ux y

; find 2 2 2

2 22 2

2u u u

x xy yx yx y

and u u

x yx y

UO2

Q13

If 2

2

yu

x;

2 2

2

x yv

x then find

,

,

u v

x y

UO3

Q14

If 2 3

11

x xy

x,

1 32

2

x xy

x &

1 23

3

x xy

x; find

, ,1 2 3

1 2 3, ,

y y y

x x x

UO3

31

Q15 If sin cosx r , sin siny r , cosz r then find

, ,

, ,

r

x y z

UO3

Q16 Verify

' 1JJ , if, sin cosx , sin siny UO3

Q17 If x vw , y wu , z uv and u = sin cosr , sin sinv r ,

cosw r find , ,

, ,

x y z

r

UO3

Q18

If

3 3 3u v w x y z , 2 2 2 3 3 3u v w x y z ,

2 2 2u v w x y z

Show that , ,

, ,

u v w

x y z=

x y y z z x

u v v w w u

UO3

UO3

Q19 If u xyz , v =

2 2 2x y z , w x y z show that x

u=

1

x y x z

UO3

Q20 The diameter and altitude of a can in the shape of a right circular cylinder are

measured as 4 cm & 6 cm respectively. The possible error in each measurement is

0.1 cm. Find approximately the error in the values computed for the volume and

lateral surface.

UO3

Q21 If a body‟s weight in air is A and that of in water W, its specific gravity is given by

AS

A W. If A = 20 kg & W = 10 kg and percentage error in A and W is 3, find

percentage error in S.

UO3

Q22 If

1102 3, ,f x y z x y z find the approximate value of , ,f x y z when

x = 1.99, y = 3.01, z = 0.98

UO3

Q23 Show that the function

3 3, 63 12f x y x y x y xy is maximum at

(-7, -7) and minimum at (3, 3).

UO3

Unit

No

6 Unit Title Numerical Solution of linear

simultaneous equations

Planned

Hrs.

06

32

Unit Outcomes


UO1 Solve system of simultaneous linear equations by using Gauss elimination method,

Gauss Jordon method, Jacobi‟s method, Gauss seidel iteration method

CO6

UO2 Determine eigen values by iterative method

Lesson schedule

Class

No.


1 Introduction of all the methods

2 Examples on Gauess elimination method

3 Examples on Gauess Jordon method

4 Examples on Jacobi‟s method

5 Examples on Gauess seidal method

6 Determination eigen values by iterative method

Review Questions

Q1

1. Solve by using Gauss Elimination Method

1. x 0.5y 0.3333z 1,0.5x 0.3333y+0.25z 0,0.3333x 0.25y 0.2z=0

2. 1 2 3 4 1 2 3 4 1 2 3 4x 2x 3x 9x 5,3x 10x 4x 2x 7,11x 5x 9x 2x 13,

1 2 3 42x +3x 7x 6x =11

3. 3 2 5,2 3 1,3 2 6x y z x y z x y z

4. 2 3 10,2 3 3 1,3 2 4 3 2,x y z t x y z t x y z t 2 2 3 7x y z t

5. 2 3 14,4 5 7 35,3 3 4 21x y z x y z x y z

6. 5 2 142, 3 30,2 3 5x y z x y z x y z

UO1

Q2 2. Solve the equations by Gauss Jordan Method

1) 10 2y z 9,2x 20y 2z 44, 2x 3y 10z 22x

2) 1 2 3 1 2 3 1 2 35x x x 142, x 3x x 30, 2x x 3x 5

3) 5,2 3 10,3 2 2 3x y z x y z x y z

4) 9,2 3 4 13,3 4 5 40x y z x y z x y z

5) 2 3 1, 4 5 25,3 4 2x y z x y z x y z

6) 2 6 22,3 4 26,6 19x y z x y z x y z

UO1

Q3 3. Use Jacobi‟s Iteration Method to solve the following equations

1) 20x y 2z 17,3x 20y – z 18,2x - 3y 20z 25

2) 1 2 3 4 1 2 3 4 1 2 3 42x 12x x 4x 13,13x 5x 3x x 18,2x x 3x 9x 31,

1 2 3 43x 4x 10x x 29

3) 2x - 3y + 20z 25,20x y – 2z 17,3x+20y-z -18

4) 15x +2y + z 18,2x 20y – 3z 19,3x-6y+25z 22

5) 4x +y +3 z 17, x 5y+z 14,2x-y+8z 12

6) 27x +6y- z 85, x y+54z 110,6x+15y+2z 72

7) 5x -y+ z 10,2x 4y 12, x+5y+5z 1

UO1

33

Q4 4. Using Gauss Seidel Iteration Method solve the following equations

1) 3x + 2y = 4.5, 2x + 3y – z = 5, - y + 2z = - 0.5 Iterate four times using the initial

approximation x=0.4, y=1.6, z=0.4 by fixing three decimal places in calculator.

2) 27x + 6y – z = 85, 6x + 15y + 2z = 72, x + y + 54z = 110 by fixing five decimal

places in calculator

3) 1 2 3 1 2 3 1 2 310x x x 12,2x 10x +x 13,2x 2x +10x 14

4) 28x +4y- z 32,2x 17y+4z 35, x+3y+10z 24 (up to 4th iteration)

5) 4x -2y- z 40, x-6y+2z 28, x-2y+12z 86 (up to 4th iteration)

6) 25x+2y+ z 69,2x+10y+z 63, x+y+z 43 (up to 4th iteration)

7) 1 2 3 1 2 3 1 2 33x 0.1x 0.2x 7.85,0.1x 7x -0.3x -19.3,0.3x 0.2x +10x 71.4,

UO1

Q5 5. Find the largest Eigen value and the corresponding Eigen vector of the following

matrices

1)

1 3 2

4 4 1

6 3 5

by using initial Eigen vector as

1

1

1

X

2)

1 3 1

3 2 4

1 4 10

by taking initial Eigen Vector as

0

0

1

up to Fifth iteration

3)

5 0 1

0 2 0

1 0 5


1

0

0

up to Fifth iteration

4)

2 2 2

2 / 3 5 / 3 5 / 3

1 5 / 2 11/ 2

5)

2 1 0

1 2 1

0 1 2

UO2

Q6 Find the dominant Eigen value and the corresponding Eigen vector of

A=

1 6 0

1 2 0

0 0 3

. Find also the least Eigen value and hence the third Eigen value by

power method

UO2

Q7

Find the numerically largest Eigen value of the matrix A=

25 1 2

1 3 0

2 0 4

By power method. Also find the corresponding Eigen vector

UO2

Q8 Find the dominant Eigen value and the corresponding Eigen vector of UO2

34

A=

10 2 1

2 10 1

2 1 10

taking initial Eigen Vector as

1

0

0

by power method


Course Title : Engineering Mathematics I Max.

Marks

Duration 3 hours 100

Instructions:

All questions are compulsory

Figures to the right indicates full marks

Use of non-programmable calculator is allowed

Section-I

Marks

1 Attempt any three 15

a Reduce the following matrix to normal form and hence find its rank

0 1 3 1

1 0 1 1

3 1 0 2

1 1 2 0

5

b Test for consistency and if possible solve

1 2 3 1 2 3 1 2 32 1, 3 2 2 2, 7 2 3 5x x x x x x x x x

5

c Investigate for what values of and the system of equations

6, 2 3 10, 2x y z x y z x y z have infinite number of

solutions

5

d Solve the following system of equations

2 0, 2 3 0, 3 4 0, 3 4 7 0x y z x y z x y z x y z

5


a Examine the following set of vectors for linearly dependent or

independent if dependent find the relation

1 2 32,3,4, 2 , ( 1, 2, 2,1) , 1,1,2, 1T TTX X X

5

b Find the Eigen values and the Eigen vector corresponding to smallest 5

35

Eigen value only

1 3

1 5 1

3 1

1

1

A

c

Find the characteristic equation of the matrix

8 8 2

4 3 2

3 4 1

A and

show that the matrix A satisfies its characteristic equation

5

d

Determine the Eigen values of the matrix

7 2 0

2 6 2

0 2 5

A and

hence determine the Eigen values of 1A and

4A

5

3 Attempt any four 20

a Find all the values of

3/4

1 3i and show that their product is 8 5

b Prove that 2 4 6sin 7

7 56sin 112sin 64sinsin

5

c If 5sinh cosh 5x x find tanh x 5

d If sin( ) (cos sin )i r i then prove that

2 1cosh 2 cos 2

2r

5

e If tan( )x iy i where x, y are real prove that x is indeterminate and

y is infinite.

5

Section-II

Marks


a Expand sinx xe in powers of x up to 4x 5

b Prove that

3 51

2

2sin 2 .....

1 3 5

x x xn x

x

5

c Express 23 2 5x x in terms of 2x by using Taylor‟s theorem 5

d Evaluate

1

1 log1lim

x

x xx

5


a If 3 3 3log( 3 )u x y z xyz then prove that

3u u u

x y z x y z

5

36

b If

1/2 1/21

1/3 1/3cos

x yu ec

x ythen show that

2 2 2 22 2

2 2

tan 13 tan2

12 12 12

u u u u ux xy y

x x y y

5

c If 2 2 1/2( , ) (50 )f x y x y , find the approximate value of

(3,4) (2.9,4.1)f f by theory of approximation

5

d For the transformations ( ), ( )x a v u y b u v and

2 2cos 2 , sin 2u r v r find ( , )

( , )

x y

r

5

e Divide 120 into three parts so that the sum of their product taken two

at a time shall be maximum 5

6 Attempt any four 15

a Solve by Gauss Elimination method

3 4 5 18, 2 8 13, 5 2 7 20x y z x y z x y z

5

b Find the solution of the following system of equations using Jacobi‟s

iterative method (5 Iteration)

8 3 2 20, 4 11 33, 6 3 12 35x y z x y z x y z

5

c Solve using Gauss- Siedel method, the following system of equations

28 4 32, 3 10 24, 2 17 4 35x y z x y z x y z Correct to 3

places decimals

5

d Determine the largest Eigen value by Iteration method of the matrix

1 2

3 4A

5

Assignments

List of experiments/assignments to meet the requirements of the syllabus

Assignment No. 1

Assignment

Title

Matrices and solution of linear system equations CO1

Batch I 1. Reduce the following matrices to Canonical(Normal) form and hence find

rank

(a)

5 2 4 1 6

2 1 1 2 2

4 1 0 5 10

1 2 5 8 6

(b)

1 2 3 0

2 4 3 2

3 2 1 3

6 8 7 5

2. Find nonsingular matrices P & Q s.t. PAQ is in the normal form also find rank

of A, where

37

(a) A=

1 1 1

1 1 1

3 1 1

(b)A=

3 2 1 5

5 1 4 2

1 4 11 19


of A and 1A , where A=

2 1 3

3 1 2

1 2 3

4. Reduce the following matrices to echelon form and find rank

(a)

2 1 1

3 1 1

4 1 2

1 1 1

(b)

2 1 3 4

0 3 4 1

2 3 7 4

2 5 11 6

5. Test for consistency and if possible solve them

(i) 6, 2 5, 3 8, 2 2 3 7x y z x y z x y z x y z ,

(j) 1 2 3 1 2 3 1 2 32 1, 3 2 2 2, 7 2 3 5x x x x x x x x x

(k) 2 6 11 0, 6 20 6 3 0, 6 18 1 0x y x y z y z

6. Solve

(a) 3 5 0, 5 3 6 0, 2 0, 5 0x y z x y z x y z x y z

(b) 2 3 0, 2 3 0, 4 5 4 0, 2 0x y z x y z x y z x y z

7. Discuss the solution for all values of k where equations are

2 3 (3 4) 0, 4 (4 2) 0,x ky k z x k y k z

2 1 (3 4) 0x k y k z

Batch II 1. Reduce the following matrices to Canonical(Normal) form and hence find

rank

(a)

2 1 1 3 8

1 1 1 1 2

3 2 1 0 6

0 4 3 2 8

(b)

1 2 3 0

2 4 3 2

3 2 1 3

6 8 7 5


of A, where A=

3 2 1 5

5 1 4 2

1 4 11 19


38

of A and 1A , where A= 3

3 3 4

2 4

0 1 1


1.

1 2 1 4

2 4 3 4

1 2 3 4

1 2 6 7

2.

2 1 3 6

3 3 1 2

1 1 1 2


a) 2 3, 3 2 1, 2 2 3 2, 1 0x y z x y z x y z x y z ,

b) 1 3 1 2 3 1 22 4, 2 2 7, 3 2 1x x x x x x x

c) 6, 2 5, 3 8,2 2 3 7x y z x y z x y z x y z

6. Solve

a) 2 0, 3 2 0, 4 5 0x y z x y z x y z

b) 2 0, 2 3 0, 3 4 0, 3 4 7 0x y z x y z x y z x y z

7. Find the value of k for which the system has non-zero solution & hence find

solution for each value of k for

3 0,4 2 3 0,2 4 0x y kz x y z kx y kz

8. Find the value of k for which the equations 3 4 3, 2 3 2 0, 6 5 3 0x y z x y z x y kz have infinite

number of solutions and hence find the solution

Batch III 1. Define Rank and reduce the following matrices to Canonical(Normal) form

and hence find rank

1.

1 1 2 3

4 1 0 2

0 3 1 4

0 1 0 2

2.

4 5 6 7

9 10 11 12

10 11 12 13

18 19 20 21


of A, where A is

1.

1 1 2 1

4 2 1 2

2 2 2 0

2.

1 1 1

1 1 1

3 1 1


39

1.

1 2 1 3

3 1 2 1

2 2 3 2

1 1 1 1

2.

1 2 3 2

1 1 3 5

2 3 4 5


1. 2 3 1, 3 6 3 2, 6 6 3 5y z x y z x y z

2. 3 2 0, 2 3 0, 4 5 0x y z x y z x y z

3. 6, 2 5, 3 8,2 2 3 7x y z x y z x y z x y z

5. Solve

1) 2 3 0, 2 3 0, 4 5 4 0, 2 0x y z x y z x y z x y z

2) 2 1, 2 2 2 2, 2 4 1, 5 5x y z u x y z u x y z u u

6. Show that if 5 the system of the equations

3 4 3, 2 3 2,6 5 3x y z x y z x y zhas a unique

solution. If 5 , show that the equations are consistent and have infinite

solutions. Determine the solution in each case.

7. Investigate for what values of λ and µ the equation

6, 2 3 10, 2x y z x y z x y z

have (i) no solution (ii) a unique solution (iii) Infinite solution

8. Determine the value of k for which the system has non-zero solution and find

the solution for each value of k for

3 0, 4 2 3 0,2 4 0x y kz x y z kx y kz

Assignment No. 2

Assignment

Title

Eigen Values and Eigen Vectors CO2

Batch I 1. Define linear dependence & independence of vectors. Examine the linear

dependence of vectors [1, 0, 2, 1]; [3, 1, 2, 1]; [4, 6, 2, -4]; [-6, 0, -3, -4] and

find relation between then, if possible.

2. Check whether the following vectors are L. I. or L. D.

[3,2,7], [2,4,1], [1,-2,6]

3. If 1 2 3, , are Eigen values of matrix

1 4

0 2 6

0 0

3

5

Find (a) 1 2 3

(b) 1 2 3

4. Find the Eigen values and Eigen vectors for the following matrices

40

(a) A=

1 3

1 5

3 1

1

1

1

(b) A=

2 2 3

1 6

2

2

1 0

5. State Cayley- Hamilton theorem and find A-1

and A4

, where

i) A=

7 2 2

6

6

1 2

2 1

ii) A=

3 2 4

4 3

2 4 3

2

6. Find characteristic equation for A and find the matrix expression

represented by 8 7 6 5 4 3 25 7 3 5 8 2A A A A A A A A I ,

7. where A= 0 1 0

2 1 1

1 1 2

8. For Eigen values for A-1

, A3, -9A where A=

1 1

2

2

1 1 2

1 1

Batch II 1. Define linear dependence & independence of vectors. Examine the linear

dependence of vectors [1, 0, 2, 1]; [3, 1, 2, 1]; [4, 6, 2, -4]; [-6, 0, -3, -4] and

find relation between then, if possible.

2. Check whether the following vectors are L. I. or L. D.

[1,1,1,3], [1,2,3,4], [2,3,4,9]


1 4

0 2 6

0 0

3

5

Find (a) 1 2 3

(b) 1 2 3

4. Find the Eigen values and Eigen vectors for the following matrices

(a) A=

1 3

1 5

3 1

1

1

1

(b) A=

2 2 3

1 6

2

2

1 0

5. State Cayley- Hamilton theorem and find A-1

and A4

, where

i) A=

7 2 2

6

6

1 2

2 1

ii) A=

3 2 4

4 3

2 4 3

2

6. Find characteristic equation for A and find the matrix expression represented

41

by 8 7 6 5 4 3 25 7 3 5 8 2A A A A A A A A I ,

where A= 0 1 0

2 1 1

1 1 2

7. For Eigen values for A-1

, A5, -3A where A=

2 2

1 3

6

2 3 1

2

Batch III 1. Define linear dependence & independence of vectors. Show that the vectors

[2, 3, -1, -1]; [1, -1, -2, -4]; [3, 1, 3, -2]; [6, 3, 0, -7] form a linearly

dependent set. Also express one of these as linear combination of others

2. Check whether the following vectors are L. I. or L. D. If dependent find

relation between them

A. [1, 1, 3], [1, 3, -3], [-2, -4, -4], [-9, -25, 9]\

B. [1, 2, -1, 0], [1, 3, 1, 2], [4, 2, 1,0], [6, 1, 0, 1]


1 4

0 2 6

0 0

3

5

Find (a) 1 2

(b) 1 2 3

4. Find the Eigen values and Eigen vectors for the greatest Eigen value for the

matrix A=

4 2 2

5 3

2 4

2

1

Hence find Eigen values of -2A3 , And Adj of A

5. Find Eigen values and Eigen vectors for A=

8 6 2

6 7 4

2 4 3

6. State and verify Cayley- Hamilton theorem and hence find A-1 and A4 ,

where A=

1 1 3

1 3 3

2 4 4

7. Find characteristic equation for A and use it to find the matrix expression

represented by 6 5 4 3 24 126 9 2A A A A A A I ,

42

where A=

10 5

2 3 4

3 5 7

3

Assignment No. 3

Assignment

Title

Complex Numbers CO3

Batch I i. 1. Simplify

7 5

12 6



i i

i i

ii. 2. Show that 1 cos sin

cos sin1 cos sin

ni

n i ni

iii. 3. Find all the values of

3/4

1 3

2 2i show that their product is 1

iv. 4. Solve 4 3 2 1 0x x x x

v. 5. Solve 9 5 4 1 0x x x

vi. 6. Solve for x and note all five roots

51

321

x

x

vii. 7. Prove that 2 4 6sin 7

7 56sin 112sin 64sinsin

viii. 8. If cos cos cos 0, sin sin sin 0 then show that

cos 2 cos 2 cos 2 0, sin 2 sin 2 sin 2 0

Batch II ix. 1. Simplify

2 3

9 5

cos5 sin5 cos7 sin 7

cos4 sin 4 cos sin

i i

i i

x. 2. Show that 8 8

81 3 1 3 2i i

xi. 3. Find the continued product of all the values of

3/4

1 3

2 2i

xii. 4. Solve

61

11

x

x

43

xiii. 5. Solve 5 51 32( 1)x x

xiv. 6. Solve for x and note all roots 9 5 4 1 0x x x

xv. 7. Prove that

3 5

2 4


1 10 tan 5tan

xvi. 8. If cos cos cos 0, sin sin sin 0 then show that

cos 2 cos 2 cos 2 0, sin 2 sin 2 sin 2 0

Batch III xvii. Simplify

1 sin cos

1 sin cos

ni

i

xviii. 2. Show that

3 5

2 4


1 10 tan 5tan

xix. 3. Find the continued product of all the values of

3/4

1 3

2 2i

xx. 4. Solve 6 0x i

xxi. 5. Solve 7 4 3 1 0x x x

xxii. 6. Solve for x and note all five roots

51

321

x

x

xxiii. 7. Prove that 100 100 511 1 2i i

xxiv. 8. Find nth root of unity and show that

1. Roots are in geometric progression

2. Sum of the all roots is zero

3. Product of all roots is

11

n

Assignment No. 4

Assignment

Title

Complex Numbers CO3

Batch I 1) If 1 3z i and n is an integer, then show that 2 22 2 0n n n nz z if n is

not multiple of 3

2) Define cosh & sinhx x . Also prove that 2 2cosh sinh 1x x

3) Prove 1 2cosh log( 1)x x x

44

4) If cos (cos sin )i R i then prove that 1 sin( )

log2 sin( )

5) If tan6

i x iy then prove that 2 2 2

13

xx y

6) If tan ii e then prove that 1

log tan2 4 2 4 2

nand

7) Separate into real and imaginary parts of i) 1tan ie

8) Prove that 1 1tanh (sin ) cosh (sec )

Batch II 1. Solve the equation 7cosh 8sinh 1x x for real values of x

2. Prove that 1 2cosh log( 1)z z z

3. Ifx x

tan tanh2 2

, prove that 1. sinh tanu x 2. cosh secu x

4. Separate into real and imaginary parts

i

i

5. If tan6

x iy i , prove that 2 2 2

13

xx y

6. If sin( ) tan seci i , prove that cos 2 cosh 2 3

7. Prove that 1sech sin log cot

2

Batch III 1. Prove that

31 tanh

cosh 6 sinh 61 tanh

xx x

x

2. Prove that 1 1

2sinh tanh

1

xx

x

3. Prove that 1 1tanh (sin ) cosh (sec )

4. Separate into real and imaginary parts 1 3

cos4

i

5. f cos( ) (cos sin )i r i then prove that 1 sin( )

log2 sin( )

6. If cos4

u iv ec ix , prove that 2 2 2 2 2( ) 2( )u v u v

7. If 1 1 1cosh cosh ( ) coshx iy x iy a then prove that

2 2 22( 1) 2( 1) 1a x a y a

Assignment No. 5

45

Assignment

Title

Expansion of Functions and Indeterminate forms CO4

Batch I

1. Prove that 2 3 5 71 1 11tan

2 3 5 7

x x x xx

x

2. Expand 5 4 3 25 6 7 8 9x x x x x in powers of ( x - 1)

3. Expand 1

log log 1 xx up to 3x

4. If 3 2 32 1x xy y x then expand y in ascending powers of x

5. Find approximate value of tan43 correct up to four places of decimals

6. Obtain expansion of sinxe x in powers of x up to 6x

7. Using Taylor‟s theorem expand 4 3

2 3 2 4( 2) 3x x x in of x

8. Evaluate limx o

1

2

112

x xx e e

x

9. If limx o 3

sin 2 sinx p x


10. Find (i) limx a

7tan2

2ax

a (ii) lim

x

1

1 1 12 3 5

3

xx x x

Batch II 1. Expand loge x in powers of (x-1) and hence evaluate log 1.1e correct up to

four decimal places

2. Prove that 2 3

log(1 )2 3

x x xe x x

3. Prove that If 3 2 32 1x xy y x then expand y in ascending powers of x

4. Find approximate value of 30'sin30 correct up to four places of decimals

5. Obtain expansion of sin xe in powers of x up to

4x

6. Using Maclaurin‟s series prove that

42 2 3sin ...........

6

x xe x x x

46

7. Using Taylor‟s theorem expand 3 4 517 6( 2) 3( 2) ( 2) ( 2)x x x x in

powers of x

8. Evaluate following limits

1. limx o

2

2

sin

1

xe x x x

x xlog x 2. log(2 )cot( 1)

1lim x xx

3. limx a

tan2

2

xax

a 4. lim

x o

2 2(1 )

log(1 )

xe x

x x

Batch III 1. Prove that

2 3 5 71 1....

2 3 5 7

11tanx x x x

n xx

2. Expand loge x in powers of (x-1) and hence evaluate log 1.1e correct up to

four decimal places

3. Prove that 2 3

log(1 )2 3

x x xe x x

4. Prove that 3

21 5

.....2 24 8

log log 1x xx xx

5. Find approximate value of 30'sin30 correct up to four places of decimals

6. Using Maclaurin‟s series prove that

42 2 3sin ...........

6

x xe x x x

7. Using Taylor‟s theorem expand 3 4 57 ( 2) 3( 2) ( 2) ( 2)x x x x in

powers of x

8. Evaluate following limits

1)0

limx

2

1

tan xx

x 2) lim

x a

1

2 2

sin

sin

a x

a x

a x 3) lim

x a

cot( )

log 2

x ax

a

9. If limx o 3

sin 2 sinx p x


47

Assignment No. 6

Assignment

Title

Partial Differentiation CO5

Batch I 1. If 2 1 2 1tan tan

y xu x y

x y; then prove that

2 2u u

x y y x

2. If z = (x, y) and x = uv, u

yv

then prove that

1 1

2 2

z z z

x v u u v And

2

2 2

z v z v z

y u u v

3. If 122 2 2u x y z ; prove that

2 2 2

2 2 20

u u u

x y z

4. If 0ux vy and 1u v

x y; prove that

2 2

2 2y x

u v x y

x y x y

5. If

1 12 2

1 13 3

1cosx y

u ec

x y

; prove that (i)1

tan12

u ux y u

x y

(ii) 2 2 2 2

2 22 2

tan 13 tan2

12 12 12

u u u u ux xy y

x yx y

6. If 2 1 2 1sin siny x

u x yx y

; then find

(i) u u

x yx y

(ii) 2 2 2

2 22 2

2u u u

x xy yx yx y

7. If 18 8 8

2 3sin

x y zu

x y z; find

u u ux y z

x y z

8. If 2 2

logx y

ux y

; find 2 2 2

2 22 2

2u u u

x xy yx yx y

&u u

x yx y

Batch II 1. If

2 1 2 1tan tany x

u x yx y

; then Find 2u

x y

48

2. If z = (u, v) and ,x yu e v e then prove that

2 2z

u v

zuv

x y

3. If cosh sinh , sinh coshx u v y u v and z is function of x and y

then prove that

2 2 2 2

2 2 2 2

z z z z

x y u v

4. If 1sin

x y

x yu ; prove that

u x u

y y x

5. If 2 2

2 2cos

x y

x yu ; then prove

2 2 2 2cot cos 2 cos2 222 2 4

u u u u u ec ux xy y

x yx y

6. If log( sin sin )x y y xu ; then show that 2 2u u

x y y x

7. If ( ) ( )z f x at x at ; Then Prove that 2

2

2 20

2

z za

xt

Batch III 1. If 2 1 2 1tan tan

y xu x y

x y; then prove that

2 2u u

x y y x

2. If z = (x, y) and x = uv, u

yv

then prove that

1 1

2 2

z z z

x v u u v And

2

2 2

z v z v z

y u u v

3. If 1

2 2 2u

x y z; Evaluate

2 2 2

2 2 2

u u u

x y z

4. If 0ux vy and 1u v

x y; prove that

2 2

2 2y x

u v x y

x y x y

5. If 2 2

1tan1

xyu

x y then show that

2

32

1

2 21

u

x yx y

6. 2 2 2 2 2 2sin( ) sin( ) sin( )u x y y z z x prove that

1 1 10

u u u

x x y y z z

49

7. If

1 12 2

1 13 3

1cosx y

u ec

x y

; prove that (i)1

tan12

u ux y u

x y (ii)

2 2 2 22 2

2 2

tan 13 tan2

12 12 12

u u u u ux xy y

x yx y

8. If 2 1 2 1sin siny x

u x yx y

; then find(i) u u

x yx y

(ii) 2 2 2

2 22 2

2u u u

x xy yx yx y

9. If 2 2

logx y

ux y

; find 2 2 2

2 22 2

2u u u

x xy yx yx y

&u u

x yx y

Assignment No. 7

Assignment

Title

Partial Differentiation CO5

Batch I 1. If

2

2

yu

x;

2 2

2

x yv

x then find

,

,

u v

x y

2. If sin cosx r , sin siny r , cosz r then find , ,

, ,

r

x y z

3. Verify ' 1JJ , if, sin cosx , sin siny

4. If 3 3 3u v w x y z ,

2 2 2 3 3 3u v w x y z

2 2 2u v w x y z

Show that , ,

, ,

u v w

x y z=

x y y z z x

u v v w w u

5. The diameter and altitude of a can in the shape of a right circular cylinder are

measured as 4 cm & 6 cm respectively. The possible error in each

measurement is 0.1 cm. Find approximately the error in the values computed

for the volume and lateral surface.

6. If a body‟s weight in air is A and that of in water W, its specific gravity is

50

given byA

SA W

. If A = 20 kg & W = 10 kg and percentage error in A

and W is 3, find percentage error in S.

7. If 1102 3, ,f x y z x y z find the approximate value of , ,f x y z when x

= 1.99, y = 3.01, z = 0.98

8. Show that the function 3 3, 63 12f x y x y x y xy is maximum

at (-7, -7) and minimum at (3, 3).

Batch II

1. If 2 3

11

x xy

x,

1 32

2

x xy

x &

1 23

3

x xy

x; find

, ,1 2 3

1 2 3, ,

y y y

x x x

2. If x vw , y wu , z uv and u = sin cosr , sin sinv r ,

cosw r find , ,

, ,

x y z

r

3. Show that the function 3 3, 63 12f x y x y x y xy is maximum

at (-7, -7) and minimum at (3, 3).

4. The H. P. required to proper a steamer varies as the cube of velocity and the

square of length. If there is 3% increase in velocity and 4% increase length,

find % error in H.P.

5. The diameter and the altitude of a can in the shape of right circular cylinder

are measured as 4cm and 6cm resp. The maximum possible error in each

measurement is 0.1cm find approximately the maximum possible errors in the

values computed for volume and lateral surface

6. If 2 2 2 2 2 2, ,x v w y u w z v u prove that

' 1JJ

Batch III 1) If

2

2

yu

x;

2 2

2

x yv

x then find

,

,

u v

x y

2) If 2 3

11

x xy

x,

1 32

2

x xy

x &

1 23

3

x xy

x; find

, ,1 2 3

1 2 3, ,

y y y

x x x

51

3)If sin cosx r , sin siny r , cosz r then find , ,

, ,

r

x y z

4) Verify ' 1JJ , if,

x y z u,

y z v, z w

5) If x vw , y wu

, z uv and u = sin cosr , sin sinv r ,

cosw r find , ,

, ,

x y z

r

6) If 3 3 3u v w x y z ,

2 2 2 3 3 3u v w x y z ,

2 2 2u v w x y z Show that , ,

, ,

u v w

x y z=

x y y z z x

u v v w w u

7) The diameter and altitude of a can in the shape of a right circular cylinder are

measured as 4 cm & 6 cm respectively. The possible error in each measurement

is 0.1 cm. Find approximately the error in the values computed for the volume

and lateral surface.

Assignment No. 8

Assignment

Title

Numerical Solution of linear simultaneous equations CO6

Batch I 1. Solve by using Gauss Elimination Method

1) x + 0.5y + 0.3333z = 1, 0.5x + 0.3333y + 0.25z = 0,

0.3333x + 0.25y+ 0.2z=0

2) x1 - 2x2 + 3x3 + 9x4= 5, 3x1 + 10x2 + 4x3 + 2x4= 7, 11x1 +5x2 +9x3 +2x4=13,

2x1 +3x2 +7x3 +6x4=11

2. Solve the equations by Gauss Jordan Method

1. 10x + 2y + z = 9, 2x + 20y - 2z = - 44, -2x + 3y + 10z = 22

2. 5x1 - x2 - 2x3 =142, x1 - 3x2 - x3 = - 30, 2x1 - x2 - 3x3 = 5

3. Use Jacobi‟s Iteration Method to solve the following equations

1. 20x + y - 2z = 17, 3x + 20y – z = - 18, 2x - 3y + 20z = 25

2. 2x1 + 12x2 + x3 -4x4= 13, 13x1 + 5x2 -3x3 + x4= 18, 2x1 + x2 -3x3 + 9x4= 31,

3x1 - 4x2 + 10x3 + x4=29

4. Using Gauss Seidel Iteration Method solve the following equations

1. 3x + 2y = 4.5, 2x + 3y – z = 5, - y + 2z = - 0.5 Iterate four times using the

initial approximation x=0.4, y=1.6, z=0.4 by fixing three decimal places in

calculator.

2. 27x + 6y – z = 85, 6x + 15y + 2z = 72, x + y + 54z = 110 by fixing five

decimal places in calculator

5. Find the largest Eigen value and the corresponding Eigen vector of the

following matrices

52

1.

1 3 2

4 4 1

6 3 5


1

1

1

X

2.

1 3 1

3 2 4

1 4 10


0

0

1

up to 5th

iteration

Batch II 1. Solve by using Gauss Elimination Method

a. 2 3 10,2 3 3 1,3 2 4 3 2,x y z t x y z t x y z t

2 2 3 7x y z t

b. 5 2 142, 3 30,2 3 5x y z x y z x y z


a) 9,2 3 4 13,3 4 5 40x y z x y z x y z

b) 2 6 22,3 4 26,6 19x y z x y z x y z


a. 2x - 3y + 20z 25,20x y – 2z 17,3x+20y-z -18

b. 15x +2y + z 18,2x 20y – 3z 19,3x-6y+25z 22

4. Find the largest Eigen value and the corresponding Eigen vector for

I.

1 3 2

4 4 1

6 3 5


1

1

1

X

II.

1 3 1

3 2 4

1 4 10


0

0

1

up to 5th iteration


a. 4x -2y- z 40, x-6y+2z 28, x-2y+12z 86 (up to 4th iteration)

b. 1 2 3 1 2 3 1 2 310x x x 12,2x 10x +x 13,2x 2x +10x 14

Batch III 1. Solve by using Gauss Elimination Method

a. 2 3 14,4 5 7 35,3 3 4 21x y z x y z x y z

b. 5 2 142, 3 30,2 3 5x y z x y z x y z


a. 2 3 1, 4 5 25,3 4 2x y z x y z x y z

b. 2 6 22,3 4 26,6 19x y z x y z x y z


a. 5x -y+ z 10,2x 4y 12, x+5y+5z 1

b. 4x +y +3 z 17, x 5y+z 14,2x-y+8z 12


a. 25x+2y+ z 69,2x+10y+z 63, x+y+z 43 (up to 4th iteration)

53

b. 1 2 3 1 2 3 1 2 33x 0.1x 0.2x 7.85,0.1x 7x -0.3x -19.3,0.3x 0.2x +10x 71.4,

5. Find the largest Eigen value and the corresponding Eigen vector of the

following matrices

a.

1 3 2

4 4 1

6 3 5


1

1

1

X

b.

1 3 1

3 2 4

1 4 10


0

0

1

up to 5th iteration

List of Tutorials

T1 To find the rank of the matrix.

T2 Solve simultaneous linear equations

T3 Find Eigen values & Eigen vectors

T4 Examples on DeMoivres theorem, roots of complex numbers

T5 Examples on, hyperbolic functions & inverse hyperbolic functions

T6 Examples on, expansions of functions at x=o & x=a

T7 Evaluation of indeterminate forms

T8 Examples on Partial differentiation, Euler‟s theorem & corollaries

T9 Applications of partial differentiation

T10 Numerical Solution of linear simultaneous equations

List of open ended experiments/assignments

1. Solve above given assignments by using Scilab software and compare your answers

54


Basic Electrical Engineering

Class FE (Shivaji University, Kolhapur) Semester I & II

Course Basic Electrical Engineering Course Code 41413

Examination

Scheme Theory Term Work POE Total

Max. Marks 100 25 -- 125

Contact

Hours/ week 3 2 -- 5

Prepared by Mr.S.S.Godhade, Mr. P.D. More,

Ms. P.R.Desai, Ms. S.S.Patil Date 05/05/2014

Course Objectives: To provide the students with an introductory and broad treatment of the

field of electrical engineering.

Prerequisites

Basic parameters in electrical circuit, ohm‟s law, Properties of series and parallel

connections, Knowledge about magnet, magnetic materials and their types and

properties, Faraday‟s laws of electromagnetic Induction, Concept of phasors,

Flemming‟s right hand and left hand rules.

Course Outcomes


CO1 To Recite the fundamental concepts of magnetic circuits

CO2 Analyses basic DC & AC circuits.

CO3 To Discuss the fundamentals of R, L & C circuits.

CO4 To Illustrate various house wiring methods and compare different electrical

lamps.

CO5 To illustrate basic concepts of the 3 phase AC circuits.

CO6 To explain the working of transformer Justify different types of tests performed

on transformers.

CO7 List the different types of electrical AC machines and explain the working of

single phase alternator.

CO8 To train students to make connections of single phase transformer & single

phase IM.


POs

COs a b c d E f G h i j k

CO1 √ √

CO2

CO3 √ √ √

CO4 √ √

CO5 √ √ √

CO6 √

CO7 √

CO8 √ √

55

Course Contents

Unit

No. Title

No. of

Hours

Section I

1

D C Circuits:

A) Analysis of D.C. circuits: Kirchhoff‟s laws, mesh and node analysis,

Energy conversions between electrical, mechanical, thermal quantities.

B) Magnetic circuits: Series magnetic circuits.

08

2

Single phase AC Circuits: Generation of sinusoidal voltage, R.M.S. &

Average value, form factor, phasor representation of A.C. quantities,

impedance, admittance, R-L,R-C, R-L-C series and parallel circuits powers,

p.f., power factor improvement by capacitor method.

08

3

Earthing and Lamps: Necessity of Earthing, Earthing methods, Fuse,

MCB, Fluorescent tube, CFL, mercury vapour lamp, LED lamp, single line

diagram of electrical system, study of energy meter.

05

Section II

4

Three phase A.C. Circuits: Introduction to 3 phase supply and its

necessity, Generation of three phase A.C. voltage, balanced three phase

system, relation between line and phase quantities

08

5

A.C. Machines:

A) Single phase Transformer: Construction, operating principle, Types,

emf equation, Ratios of voltage and current, operation on no load and with

load, power losses, efficiency, All day efficiency, voltage regulation,

applications, autotransformer.

B) Single phase alternator: Construction, types, operating principle, emf

equation,

alternator on load, Voltage regulation, (Theoretical treatment)

08

6 Single phase A.C. motor: Construction, operating principle, T-N

characteristics, applications of induction motor and universal motor. 05

Text Books:

Sr.

No. Title of Book Author Publisher/Edition Topics

1 Basic Electrical Engineering Shingare Shingare Engg. Academy 1 to 6

2 Basic Electrical Engineering B.H. Deshmukh Nirali Publication. 1 to 6

3 Basic Electrical Engineering J.S.Katre Tech-Max Publication. 1 to 6

4 A Text Book of Electrical

Technology (Vol.-I & II) B. L. Theraja S. Chand Publication 1 & 6

5 Fundamentals of Electrical

Tech. V. K. Mehta S. Chand Publications. 1 to 4

6 Fundamentals of Electrical

Engg.

Ashfaq

Hussein Dhanapat Rai Publication 1 to 4

56

Scheme of Marks


I

1 D C Circuits: A) Analysis of D.C. circuits

B) Magnetic circuits 16

2 Single phase AC Circuits 16

3 Earthing and Lamps 18

II

5 Three phase A.C. Circuits 16

6 A.C. Machines: A) Single phase Transformer

B) Single phase alternator 16

7 Single phase A.C. motor 18

Course Unitization

Section

Course

Outcomes

No. of Questions

in

No. Unit Title CAT-I CAT-II

I

1 D C Circuits: A) Analysis of D.C. circuits

B) Magnetic circuits CO1

6 (Q. 1

to Q. 3)

2 Single phase AC Circuits CO2

3 Earthing and Lamps CO3

II

4 Three phase A.C. Circuits CO5

6 (Q. 1

to Q. 3) 5

A.C.Machines: A)Singlephase Transformer

B) Single phase alternator CO6

6 Single phase A.C. motor CO7


Section I

Unit No 1 Unit Title DC Circuits Planned

Hrs. 08

Unit Outcomes: At the end of this unit the students should be able to

UO 1. Define different basic electrical quantities.

2. Explain and apply Kirchhoff‟s Laws (KVL and KCL).

3. Paraphrase concept of magnetic circuits.

4. Define MMF, reluctance magnetic flux, flux density.

5. Outline the concepts of B-H curve, magnetic leakage & fringing.

6. Solve Numerical on series magnetic circuit.

CO 1,

CO 2

57

Lesson schedule

Class

No.


1 Introduction to the subject & syllabus

2 Definition of EMF, current, resistance, power, energy and factors affecting on

resistance

3 Series parallel circuits, division of current in two parallel branches

4 Kirchhoff‟s Laws – KCL, KVL. ,Numerical based on mesh and node analysis

5 Concept of magnetic circuit, MMF, reluctance magnetic flux, flux density

6 Magnetic field strength, Comparison between electrical and magnetic circuits

7 B-H curve, magnetic leakage & fringing

8 Simple examples on series magnetic circuit

Review Questions

Q1 State and explain Kirchhoff‟s laws. CO1

Q2 Define the terms and state their units

a) Magnetic flux b) Magnetic flux density

c) Magnetic field strength d) MMF

CO1

Q3 Compare Electric and Magnetic circuits stating their similarities and

dissimilarities.

CO1

Q4 Explain series Magnetic Circuit with the help of neat diagram. CO2

Q5 Explain Magnetic leakage and fringing. CO2

Q6 Explain B-H Curve for material. CO2

Q7 Derive the derivation Flux = MMF/Reluctance. CO2

Unit

No 2 Unit Title Single phase AC Circuits

Planned

Hrs. 08


UO

1. Define Faraday's laws of electromagnetic induction, Lenz‟s law &

Fleming's right hand rule.

2. Concept of statically induced EMF & dynamically induced EMF.

3. Explain generation of single phase alternating EMF.

4. Derive the value of average value and RMS value.

5. Analysis of purely R, L, C and R-L, R-C, R-L-C circuits.

6. Explain the concept of power factor & its significance, pf improvement

methods.

CO2,

CO3

Lesson schedule

Class

No.


1 Faraday's laws of electromagnetic induction, Lenz's law, dynamically induced EMF

2 Fleming's right hand rule, statically induced EMF-self & mutually induced EMF,

Concept of self and mutual inductance

58

3 Generation of single phase alternating EMF

4 Definition of Cycle, frequency, time period, amplitude, average value and RMS

value

5 Concept of Form factor, peak factor, phase, phase difference, phasor representation

6 Analysis of purely resistive, inductive and capacitive circuits

7 Analysis of R-L, R-C circuits, R-L-C circuits

8 Concept of power factor and its significance, Power factor improvement methods.

Review Questions

Q1 State and explain Faradays laws of electromagnetic induction. CO3

Q2 Explain importance of RMS value & derive the equation to calculate RMS

value of sinusoidal a.c. quantity (graphically & analytically).

CO3

Q3 Explain generation of single phase alternating emf & derive the expression for

its magnitude.

CO3

Q4 Define the following terms:

(a) Peak factor (b) Form Factor (c) Instantaneous value (d) Phase

difference

CO3

Q5 Show that when sinusoidal a.c. is applied across pure inductance current

flowing through inductance lags behind voltage by 90°.

CO3

Q6 With neat circuit diagram & phasor diagram explain RLC series circuit. CO3

Q7 Explain the term power factor in a.c. circuit & explain a method to improve pf CO3

Q8 With neat circuit diagram & phasor diagram explain RLC parallel circuit. CO3

Unit

No 3 Unit Title Earthing and Lamps

Planned

Hrs. 05


UO

1. Concept of earthing & earthing methods.

2. Construction and working of different electrical lamps.

3. Explain single line diagram of electrical system and their stages.

4. Construction and working of 1 phase energy meter.

CO4

Lesson schedule

Class

No.


1 Necessity of earthing and earthing methods- plate & pipe earthing

2 Function of MCB, fuse and types

3 Construction and working of fluorescent lamp, CFL, LED and mercury vapour lamp

4 Single line diagram of electrical system

5 Study of single phase energy meter.

Review Questions

Q1 Explain why earthing is necessary and various methods of earthing with neat

diagram.

CO4

Q2 Define fuse. What is the function of fuse? CO4

Q3 Discuss various stages in electrical power system with single line diagram. CO4

59

Q4 Explain working operation of 1 phase energy meter with neat diagram. CO4

Assignments

Assignment No. 1

Assignment

Title Topic – 1 & 2

CO1 &

CO2

Batch I State and explain Kirchhoff‟s laws.

Batch II

An electrically driven pump lifts of water per minute through a height of

12 m. Efficiencies of motor and pump are 70 % and 80 % respectively. Calculate-

A) Current drawn by motor if at works on 400 V supply.

B) Energy consumption in KWH and cost of the energy at the rate of 75

paise/KWH, if pump operates 2 hrs per day for 30 days. Assume of

water weight 1000 kg.

OR

A mild steel ring has a mean circumference of 500 mm and a uniform cross

sectional area of . An air gap of 1 mm is cut in the ring. Determine

current required in the coil of 500 turns wound over the ring, to produce a flux of

147µ Weber in the air gap. Neglect fringing and assume relative permeability of

iron as 1200.

Batch III Show that average power consumed by pure capacitance is zero when it is

supplied with a.c. supply. Draw voltage current & power waveform.

Batch IV Explain the term power factor in a.c. circuit, its significance. Explain power

factor improvement by using capacitor methods.

Assignment No. 2

Assignment


CO3 &

CO4

Batch I

Find the current flowing through a purely inductive circuit containing a voltage

source, V= 325 Sin (100 πt) and an inductance L= 2H.

OR

For a series R-C circuit consisting of a resistance of 50 Ω and a capacitor of 100

µF, calculate the following if the supply voltage is 230 V, 50 Hz.

i. Impedance of the circuit.

ii. Current through the circuit.

iii. Power factor.

iv. Power consumed.

Batch II Explain why earthing is necessary. Write a short note on plate earthing.

Batch III Discuss construction and working of single phase energy meter.

Batch IV

Write a short note (any three)

i. HRC fuse

ii. MCB

iii. LED lamp

60

iv. Mercury vapour lamp

Section II

Unit

No 4 Unit Title Three phase A.C. Circuits

Planned

Hrs. 08


UO

1. Differentiate between single phase and three phase supply

systems.Explain Generation of three phase A.C. voltage.

2. Deduce the relationship between line and phase values for star and delta

connection.

3. Distinguish between balanced and unbalanced load.

CO5

Lesson schedule

Class

No.


1 Introduction to 3 phase supply and its necessity ,advantages

2 Meaning of phase sequence, Generation of three phase A.C. voltage,

3 obtaining relationship between line and phase values for balanced star and delta

connection

4 To study balanced star and delta connected source

5 Balanced star connected load

6 Balanced delta connected load

7 Numerical based on line and phase quantities

8 Numerical based on star and delta connection

Review Questions

Q1 State the advantages of 3phase supply. CO5

Q2 Explain generation of three phase A.C. voltage in brief. CO5

Q3 Derive the relationship between line and phase quantities in Star connection. CO5

Q4 Derive the relationship between line and phase quantities in delta

connection.

CO5

Q5 Explain star connection in 3phase circuit and state their advantages. CO5

Q6 Explain delta connection in 3phase circuit and state their advantages. CO5

Q7 Explain the measurement of power by using two-wattmeter method. Derive

the expression for active power.

CO5

Unit

No 5 Unit Title A.C. Machines

Planned

Hrs. 08


UO 1. List types of transformers. CO6,

61

2. Deduce EMF equation of transformer.

3. Recall Losses in transformer, efficiency and voltage regulation

4. Perform O.C. / S.C. Test for transformer.

5. Explain the Construction and operating principle for alternator.

6. Deduce EMF equation of alternator.

CO7

Lesson schedule

Class

No.


a) Single phase transformers

1 To study the Construction and operating principle for single phase transformer

2 Types of transformer , emf equation

3 Transformation ratio, working of transformer at no load and with load.

4 Losses in transformer, efficiency and voltage regulation

5 Direct loading method for efficiency and regulation

6 O.C. / S.C. Test for transformer

b) Single phase alternator

7 To study the Construction and operating principle for alternator

8 Emf equation ,working of alternator on load, voltage regulation

Review Questions

Q1 How parameters, losses, efficiency & regulation are determined by O.C. &

S.C. test of transformer.

CO6

Q2 With a neat diagram explain direct loading method for finding efficiency &

regulation of transformer.

CO6

Q3 For ideal transformer prove that (N2/N1): (E2/E1): (I1/I2): K CO6

Q4 Derive e.m.f. equation of transformer. CO6

Q5 Explain the working principal of transformer & compare core & shell type

transformer.

CO6

Q6 Explain transformer at no load. CO6

Q7 How eddy current losses are minimized? CO6

Q8 Explain transformer at load with neat circuit & vector diagram. CO6

Q9 Define: a) Efficiency b) Regulation Up c) Regulation Down CO6

Q10 Give the condition for maximum efficiency. CO6

Q11 Define all day efficiency. CO6

Q12 Explain in brief the application of single phase transformer. CO6

Q13 Explain construction of auto transformer. CO6

Q14 Write a short note on auto transformer. CO6

62

Q15 Explain construction & working principal of alternator. CO7

Q16 Explain types & application of alternator. CO7

Q17 Derive the e.m.f. equitation of alternator. CO7

Q18 Derive the equivalent circuit of alternator. CO7

Q19 Define voltage regulation & explain in brief performance of alternator. CO7

Q20 Explain polarity test & ratio test for single phase transformer. CO6

Unit

No 6 Unit Title Single phase A.C. motor

Planned

Hrs. 05


UO

1. List types of single phase motors.

2. Discriminate between the single phase induction and universal motor.

3. Analyze Torque / speed characteristics of single phase A C Motor.

4. Outline the applications of single phase induction motors and universal motor.

CO8

Lesson schedule

Class

No.


1 To study the construction and operating principle

2 Types of single phase motors

3 Difference between the single phase induction and universal motor

4 Torque / speed characteristics

5 Applications of single phase induction motors and universal motor

Review Questions

Q1 Explain construction & working principle of universal motor. CO8

Q2 Describe the construction & working of split phase induction motor. CO8

Q3 Explain construction & working principle of single phase induction motor. CO8

Q4 With the help of neat diagram explain working of

a. capacitor start capacitor run motor

b. shaded pole motor

CO8

Q5 Why single phase induction motor is not self starting? How it is made self

start?

CO8

Q6 State various applications of single phase induction motors. CO8

Q7 Explain Torque Speed characteristics of single phase induction motor. CO8

Q8 Define: a. Torque b. Slip c. Synchronous speed CO8

63

Assignments

Assignment No. 3

Assignment


CO5, CO6 &

CO7

Batch I Explain generation of three phases A.C Voltage in brief and State the advantages

of 3phase supply.

OR

Derive relation between line and phase quantities in delta connected load.

Batch II A balanced star connected load is supplied from a symmetrical 3-phase 400 V,

50Hz system. The current I in each phase is 30Amp and lags 30˚ behind the

phase voltage. Find-

i) phase voltage ii) resistance and reactance per phase iii) load inductance per

phase

Batch III A three phase delta connected load draws a current of 20 A at a lagging power

factor of 0.8 from a 400V, 50 Hz supply. Calculate-

i. Resistance of each phase

ii. Inductance of each phase

iii. Power consumed.

Batch IV A 100 KVA, 230V/2200V, 50Hz single phase transformer has 50 turns on the

secondary winding. Assuming an ideal transformer. Calculate-

i. Number of primary turns.

ii. Maximum value of flux in core.

iii. Primary full load current.

iv. Secondary full load current.

OR

Explain construction of 1 phase alternator in brief. State the applications of

alternator.

Assignment No. 4

Assignment


CO7 &

CO8

Batch I Explain working principle of single phase transformer & state different losses

produced in transformer.

Batch II Explain working principle of single phase transformer & state different losses


OR

Explain construction & working principal of alternator.

Batch III Why single phase I.M. is not self starting? How it is made to self start.

Batch IV Write a short note on

i) Universal motor

ii) Shaded pole induction motor

iii) Permanent split capacitor motor

64


Course Title :Basic Electrical Engineering

Time: 3 Hrs. Marks: 100

Instructions:

1. All questions are compulsory.

2. Figure to the right indicate full marks.

3. Assume suitable data wherever necessary

4. Draw neat sketches wherever necessary.

Section-I Marks

Q 1 Answer any TWO

a State and explain Kirchhoff‟s current law & voltage law. 08

b Compare Electric & Magnetic circuits stating their similarities &

dissimilarities. 08

c A mild steel ring has a mean circumference of 500 mm and a uniform cross

sectional area of . An air gap of 1 mm is cut in the ring. Determine

current required in the coil of 500 turns wound over the ring, to produce a flux

of 147µ Weber in the air gap. Neglect fringing and assume relative

permeability of iron as 1200.

08

Q 2 Answer any TWO

a Explain generation of single phase AC voltage in brief. 08

b A voltage of 220V at 50Hz is applied across a non inductive resistor connected

in series with a condenser the current in circuit is 2.5A the power loss in

resistor is 100W & that in the condenser is negligible calculate resistance and

capacitance.

08

c A series combination of R and C is further connected in series with a variable

pure inductor and put across 200V, 50Hz supply. The maximum current

obtainable is 0.314A and voltage across C is 300V find the circuit constants

08

Q 3 Answer the following

a Discuss various stages in electrical power system with single line diagram. 08

b Write a short note on (any two)

i) Plate earthing

ii) Fluorescent lamp

iii) Mercury vapour lamp

10

Section-II Marks

Q 4 Answer any TWO

a Explain working principle of single phase transformer. State different losses


08

b A 100 KVA, 230V/2200V, 50Hz single phase transformer has 50 turns on the

secondary winding. Assume an ideal transformer. Calculate-

i. Number of primary turns.

ii. Maximum value of flux in core.

08

65

iii. Primary full load current.

iv. Secondary full load current.

c Explain construction of single phase alternator in brief. State the applications

of single phase alternator. 08

Q 5 Answer any TWO

a Derive relation between line & phase quantities in delta connected load. 08

b A balanced star connected load is supplied from a symmetrical 3-phase 400

volts, 50Hz system. The current I in each phase is 30Amp and lags 30˚ behind

the phase voltage. Calculate - i) phase voltage ii) resistance and reactance per

phase iii) load inductance per phase.

08

c A three phase delta connected load draws a current of 20 A at a lagging power

factor of 0.8 from a 400V, 50 Hz supply. Calculate-

i. Resistance of each phase

ii. Inductance of each phase

iii. Power consumed.

08

Q 6 Answer the following

a Why single phase I.M. is not self starting? How it is made to self start. 08

b Write a short note on (any two)

i. Universal motor

ii. Shaded pole induction motor

iii. Permanent split capacitor motor

10

66


Basic Civil Engineering

Course BASIC CIVIL ENGINEERING Course Code

Examination

Scheme


Max. Marks 100 25 -- 125

Contact

Hours/ week

3 2 -- 5

Prepared by Mr. Patil S. B. Date- 06/05/2014

Pre-requisites NIL

Course Outcomes


CO1 Explain relevance of Civil engineering to other branches of engineering.

CO2 Explain functions of different building components.

CO3 Explain uses, properties & types of various building materials.

CO4 Explain linear & angular measurements using principles of surveying.

CO5 Explain vertical measurements using principle of leveling & determine the area

of irregular figure.

CO6 Explain component of water supply scheme, road & railway track.


POs

COs

a b c d E f G h i j k

CO1 √ √ √ √ √

CO2 √ √ √ √

CO3 √ √ √

CO4 √ √ √

CO5 √

CO6 √ √ √ √ √ √ √

67

Course Contents

Unit

No. Title

No. of

Hours

Section I

1. Relevance of Civil Engineering and Building Planning

Introduction, branches of civil engineering, application of civil engineering in

other allied fields.

Principles of planning, introduction to Bye-Laws regarding building line, height

of building, open space requirements, F.S.I., setbacks, ventilation, Sanitation as

per municipal corporation area requirement.

07

2. Components of Building

Sub-structure

Types of soil and rocks as foundation strata, concept of bearing capacity, types of

foundations i.e. shallow and deep and their suitability. Shallow foundation such

as wall foundation, isolated foundation, deep foundation such as pile foundation.

Super-structure - Elements of super-structures and their functions.

07

3. Building Materials and Design

Use and properties of the following materials :

Concrete – ingredients and grades, plain and reinforced cement concrete and

ready mix concrete, bricks, steel, aluminum, plastic, timber, roofing materials

etc.

Introduction to types of loads, load bearing and framed structures.

06

Section II

4. Linear and Angular Measurements

Principles of surveying

Classification of surveys

Chain Surveying

Introduction to metric chain and tapes, error in chaining, nominal scale and R.F.,

ranging, chaining and offsetting, index plan, location sketch and recording of

field book. Chain and compass survey

Meridian, bearing and its types, system of bearing, Types of compass: prismatic

and surveyor's compass. Calculation of included angles, correction for local

attraction.

07

5. Leveling

Terms used in leveling, use of Dumpy level and Auto Level, temporary

adjustments. Methods of reduction of levels, types of leveling, Contours,

characteristics of contours, use of contour maps.

Introduction and use of EDM's with special reference to Total Station.

Measurement of area by planimeter – mechanical and digital.

07

6. Introduction to Transportation, Environmental and Irrigation Engineering

Components of rigid and flexible pavement, components of railway track (Broad

Gauge)

Components of water supply scheme (flow diagram)

Types of Dams (Earthen and Gravity Dam)

06

68

Reference Books:


1. A Text Book of Building

Construction

S.P. Arora, S.P.

Bindra

DhanpatRai

Publications

1 & 2

2. Basic Civil Engineering G. K. Hiraskar DhanpatRai

Publications

All

3. Engineering Materials R.K.Rajput S. Chand 3

4. Surveying N. Basak Tata Mc-Graw

Hill Publication

4 &5

Scheme of Marks


I 1 Relevance of Civil Engineering and Building Planning 20

2 Components of Building Sub-structure 26

3 Building Materials and Design 17

II 4 Linear and Angular Measurements 16

5 Leveling 20

6 Introduction to Transportation, Environmental and

Irrigation Engineering

21

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in


I

1 Relevance of Civil Engineering and

Building Planning

CO1 2

2 Components of Building Sub-

structure

CO2 2

3 Building Materials and Design CO3 2

II

4 Linear and Angular Measurements CO4 2

5 Leveling CO5 2

6 Introduction to Transportation,

Environmental and Irrigation

Engineering

CO6 2

69


Section I

Unit

No

1 Unit

Title Relevance of civil engineering &

building planning

Planned Hrs. 7

Unit Outcomes


UO1 Explain relevance of Civil engineering to other branches of engineering. CO1

Lesson schedule

Class

No.


1 Introduction to basic civil engineering

2 Introduction & various branches of civil engineering

3 Application of civil engineering to other field & role of civil engg.

4 Introduction to building planning & principles of planning.

5 Principles of planning.

6 Orientation of building & selection of site

7 Building bye laws, municipal corporation area requirement.

Review Questions

Q1 Describe in brief various branches of civil engg. Indicating their importance. CO1

Q2 The subject basic civil engg. Is of vital importance to all the branches of engg.”

Comment on this statement.

CO1

Q3 Explain role of civil engineering in various construction activities. CO1

Q4 Explain about general scope of civil engineering in today‟s world. CO1

Q5 Define engineering. State the application of civil engineering in industrial, public

and residential building.

CO1

Q6 List out principles of planning and explain any 3 with figure. CO1

Q7 What is orientation of building?

Q8 Give the I.S. recommendation for (i) size of habitable room (ii) size of W.C. (iii)

height of building

Q9 What do you mean by planning? What are the objects of building planning?

Q10 Write a note on built up area.

Q11 Which are the site selection criteria for the building?

Q12 Explain how planning of residential building differs from that of an industrial

building.

Unit

No

2 Unit

title Components of building. Planned Hrs. 6

70

Unit Outcomes


UO1 Explain functions of different building components. CO2

Lesson schedule

Class

No.


1 Types of soil and rocks

2 Concept of bearing capacity and settlement of foundation.

3 Shallow foundation, deep foundation.

4 Suitability of foundation.

5 Elements of super structure and their function.

6 Elements of sub structure and difference between sub structure and super structure.

Review Questions

Q1 What is foundation and what are the different types of foundation. CO2

Q2 Explain with neat sketch different elements of building. CO2

Q3 Distinguish between i) ultimate and safe bearing capacity.

ii) Sub structure and super structure iii) shallow foundation and deep foundation.

CO2

Q4 Explain load transfer action or mechanism in R.C.C framed structure. CO2

Q5 Why does foundation settle? What are its effects on structure? CO2

Q6 Which are the different methods of determining bearing capacity of soil? Explain

any one method.

Q7 How bearing capacity of soil can be improved?

Q8 Explain with neat sketch types of settlement.

Q9 Explain the basis on which you will select foundation for a particular situation.

Unit

No

3 Unit

Title Building materials and design

Planned

Hrs.

5

Unit Outcomes


UO1 Explain uses, properties & types of various building materials. CO3

Lesson schedule

Class

No.


1 Types of loads, concept of strength and stability.

2 Types and grades of concrete, characteristics and advantages of brick and steel.

71

3 Factors of safety and requirements of general safety of building.

4 Properties and uses of aluminum and plastic.

5 Classification and properties of timber and roofing material.

Review Questions

Q1 What do you mean by strength and stability of building? CO3

Q2 Which are the different types of loads acting on building? CO3

Q3 Write a short note on general safety of building. CO3

Q4 What is factor of safety? CO3

Q5 Explain R.C.C., P.C.C., and R.M.C. CO3

Q6 Compare merits and demerits of timber and steel as building material. CO3

Q7 Write the uses of plastic and aluminum in building construction. CO3

Q8 Explain the characteristics of good building stone. CO3

Q9 How to recognize good brick? CO3

Q10 What is mean by seasoning of timber? CO3

Section II

Unit

No

4 Unit

Title Linear and angular measurement Planned Hrs. 9

Unit Outcomes


UO1 Explain linear & angular measurements using principles of surveying. CO4

Lesson schedule

Class

No.


1 Principle of surveying & classification of surveying.

2 Chain survey & its instruments.

3 Errors in chaining, scale & R.F.

4 Ranging & offsetting.

5 Problems based on errors in chaining.

6 Compass survey.

7 Types of compass & concept of local attraction.

8 Problems based on W.C.B.

9 Problems based on R.B.

72

Review Questions

Q1 Define surveying. On which objects& purposes survey work can be done? CO4

Q2 Classify surveying on the basis of instruments used. Explain the principles on

surveying works.

Q3 Describe errors in chaining.

Q4 Two stations A & B are not intervisible due to rising ground between them.

Explain with neat sketch how the line AB can be ranged.

Q5 What is scale? What is R. F.?

Q6 What is an offset? What are the types of offset? Instruments used for offsetting?

Q7 Distinguish between plane survey & geodetic survey.

Q8 A chain was tested & found to be exactly 20 m long, while starting to measure the

length of a survey line. After measuring a distance of 1245m & was noticed that

the chain had become 85mm too long. Find the correct length of survey line.

Q9 Draw neat sketch showing graduations of surveyor compass & prismatic compass.

Q10 Explain how surveyor compass differ from prismatic compass. What are the

temporary adjustments of compass?

Q11 Explain the following bearing systems (i) W.C.B. (ii) Q.B.

Q12 Explain in detail meridians. What are the F.B. & B.B. of line?

Q13 The following F.B. & B.B. were observed in running a compass traverse. Draw

the traverse, correct for local attraction, calculate included angles.

Line F.B. B.B.

AB 440 30

‟ 226

030

‟

BC 124030

‟ 303

015

‟

CD 1810

10

DA 2890 30

‟ 108

045

‟

Unit

No

5 Unit

Title Leveling

Planned

Hrs.

9

Unit Outcomes


UO1 Explain vertical measurements using principle of leveling & determine the area of

irregular figure.

CO5

Lesson schedule

Class Details to be covered

73

No.

1 Various terms used in leveling

2 Introduction to dumpy level and its parts

3 Uses and different adjustment of dumpy level.

4 Types of leveling and methods of reduction level.

5 Calculation of RL by rise and fall method.

6 Calculation of RL by HI method..

7 Characteristics and uses of contour map

8 Introduction to EDM and total station

9 Measurement of area of irregular shape figure

Review Questions

Q1 Draw neat sketch to explain various surfaces & lines associated with leveling.

CO5

Q2 Explain temporary adjustments for a level.

Q3 What do you mean by reduction of levels? Explain any one method in brief.

Q4 Draw a neat sketch of dumpy level and name all of its parts. Explain the function

of important parts.

Q5 Define contour. What are various uses of a contour map?

Q6 Write a note on inverted staff reading.

Q7 Write a short note on characteristics of contours.

Q8 Explain the terms: 1) T.B.M. 2. R.L. 3. C.P. 4. Line of collimation 5. Axis of

bubble tube

Q9 Enlist any three fundamental lines of a dumpy level and state their relation.

Q10 Distinguish between rise and fall method and HI method.

Q11 Enlist different uses of EDM

Q12 Write a note on auto level.

Q13 Write a short not on area measuring instrument.

Q14 The following staff readings were taken on a continuously sloping ground with a

help of dumpy level and 4 m leveling staff at 20 m interval. The 1st reading was taken on starting point of road having R.L. 350.00m.

0.540, 1.245, 2.375, 3.885, 1.245, 2.560, 3.780, 0.875, 1.625, 2.960.

Q15 The following staff readings were observed successively with a level.

1.23, 1.900, 3.535, 2.170 and 2.135.

The instrument was shifted to a new position after 3rd reading, last reading was

taken on an inverted staff held at bottom of slab. First reading was taken on a BM

of RL 250m. Enter the above data in level book page and complete it by HI

74

method with usual check.

Q16 Find the unknown things in then problem.

case area IR FR N Anchor point

1 - 3.375 8.92 +1 outside

2 25 cm2

6.19 8.23 -1 inside

Unit

No

6 Unit

Title Introduction to Transportation,

Environmental and Irrigation

Engineering

Planned Hrs. 7

Unit Outcomes


UO1 Explain component of water supply scheme, road & railway track. CO6

Lesson schedule

Class

No.


1 Various components of pavement

2 Components of railway track.

3 Components of water supply scheme.

4 Types of dam.

Review Questions

Q1 Write note on classification of roads.

CO6

Q2 Draw the section showing various components of road in cutting. And explain each

part.

Q1 Which are the components of water supply scheme?

Q2 What are the types of dam?


Course Title : Basic Civil Engineering.

Duration-

3 Hrs.

Max. Marks

100

Instructions:

1 All Questions are compulsory.

2 Figures to the right indicate full marks.

3 Use of non programmable calculator is allowed

4 Mention any data assumed wherever necessary.

75

Section-I

Marks

1 Attempt any four questions from following

a Write note on: Roominess of building 4

b Enlist various principles of planning and explain „Grouping‟ in detail. 4

c Write note on modes of transportation. 4

d Explain the byelaw which controls „height of building‟. 4

e Write note on: Instruments for measuring distances. 4

2 a Give classification of shallow foundation. Explain simple wall footing. 9

b Along with neat sketch explain various elements of substructure. 8

3 A Attempt any three questions from following

a Write uses of Bricks in building material. 4

b Write note on ingredients of concrete. 4

c Enlist various components of building superstructure. 4

d Which are the properties of steel? 4

B Write uses of timber in building material. 5

Section-II

Marks

4 a Define the terms: surveying, fore bearing 3

b Write note on W.C.B and Q.B. 3

c Explain Meridians in compass surveying. 3

d The distance between two points measured by a 20m chain was 1340m and

when measured by a 30m chain was 1345m. If 30m chain was two links too

short, find out whether the 20m chain was of correct length or not. If not

then find the error in it. or

7

d The following bearings were observed in a closed traverse

line AB BC CD DE

FB 45˚45‟ 96˚55‟ 29˚45‟ 324˚48‟

BB 226˚10‟ 277˚5‟ 209˚10‟ 144˚48‟

At what station do you suspect local attraction? Calculate correct bearings

7


a Define contour and contour interval. 3

b Enlist various types of leveling and explain any one. 3

c Draw contours for valley and hill. 3

d Explain the principle of EDM. 3

B The following readings were observed with a dumpy level and a 4 m

leveling staff on a continuous falling ground.

i)1.780, ii)2.770, iii)3.750, iv)0.580, v)2.170, vi)2.250, vii)3.875, viii)1.310,

ix)1.580, x)2.525. first reading was observed on the B.M.,R.L.132.110.

Calculate the R.L. by any method.

8


76

a Write note on rigid pavement. 4

b Write note on types of dam. 4

c Along with neat sketch show various components of railway track 4

d Draw a labeled diagram of cross section of road in cutting. 4

B Explain layout of water supply system. 5

Practical:


Assignment Title

All Batches 1. Plotting the outlines of building by chaining, ranging and offsetting.

2. Plotting of closed traverse by prismatic compass.

3. Plotting of closed traverse by surveyor's compass

4. Reduction of levels by rise and fall method.

5. Reduction of levels by collimation plane method.

6. Measurement of area by mechanical planimeter.

7. Measurement of area by digital planimeter.

8. Use of total station for various measurements.

9. Layout and setting out of small residential building.

10. Site visit to study various construction processes

Report to be submitted on any under construction site

77


Engineering Graphics

Course Engineering Graphics Course Code 59180

Examination

Scheme


Max. Marks 100 - - 100

Contact

Hours/ week

3 6 -- 9

Prepared by Ajay P.Dhawan Date 08/05/2014

Prerequisites Knowledge of Steel Rule, Set-squares & Protractor.

Course Outcomes


CO1 Discuss and demonstrate the importance of Engineering Graphics in

Engineering & draw the different curves.

CO2 Draw Horizontal line, Vertical line & solve the planes examples using rotational

method.

CO3 create thinking to learn methods of projections

CO4 Draw FV,TV & SV of the object.

CO5 Draw isometric object from FV,TV & SV

CO6 Construct the objects by developing surfaces of solids and knowledge of cutting

planes.


POs

COs


CO1 √ √

CO2 √ √

CO3 √

CO4 √

CO5 √

CO6 √

78

Course Contents


Hours

SECTION I

1. Unit1: Fundamentals of Engineering Graphics& Engineering

Curves

A) Fundamentals of Engineering Graphics:

Introduction to Drawing instruments and their uses. Layout of drawing

sheets, different types of lines used in drawing practice, Dimensioning

system as per BIS (Theoretical treatment only)

B) Engineering curves:

Construction of regular polygons (up to hexagon). Construction of

Ellipse, Parabola, Hyperbola, Involutes,

Archimedian spiral and Cycloid only. .

06

2. Unit 2: Projections of lines & Planes

A) Projections of lines:

Introduction to First angle and third angle methods of projection.

Projections of points on regular reference planes. Projections of

horizontal, frontal and Profile lines on regular and auxiliary reference

planes. Projection of oblique lines it‟s True length and angle with

reference planes by rotation and auxiliary plane method. Concept of

grade and bearing of line, Point View of a line, Projections of

intersecting lines, Parallel lines, perpendicular lines and skew line. (Use

coordinate system only)

B) Projections of planes:

Projections on regular and on auxiliary reference planes. Types of

planes (horizontal, frontal, oblique and Profile planes ). Edge view and

True shape of a Plane. Angles made by the plane with Principle

reference planes. Projections of plane figures inclined to both the

planes. (Circle and regular polygon) (Use coordinate system

10

3 UNIT 3 Projections of solids: Projections of Prisms, Pyramids, Cylinder and Cones inclined to both

reference planes (Excluding frustum and sphere)

5

SECTION II

4 Unit 4: Orthographic Projections :

Orthographic views: lines used, Selection of views, spacing of views,

dimensioning and sections. Drawing required views from given pictorial

views (Conversion of pictorial view into

orthographic view) including sectional orthographic view

7

5 Unit 5: Isometric projections

Isometric projections: Introduction to isometric, Isometric scale,

Isometric projections and Isometric views / drawings. Circles in

isometric view. Isometric views of simple solids and objects

7

6 Unit 6:Sections of solids & Development of surfaces

A) Sections of solids:

7

79

Prisms, Pyramids, Cylinders and Cones (Simple positions and inclined

to one plane and parallel to other)

B) Development of plane and curved surfaces:

Prisms, Pyramids, Cylinders and Cones along with cutting plane

Reference Books:


01 Engineering Drawing N.D. Bhatt Charotar publishing House All

02 Engineering Graphics K.Venugopal and

V.Prabhu Raja

New Age International (P)

Ltd

All

Scheme of Marks


I 1 Fundamentals of Engineering Graphics& Engineering

Curves

12

2 Projections of lines & Planes 25

3 Projections of solids 13

II 4 Orthographic Projections 24

5 Isometric projections 13

6 Sections of solids & Development of surfaces 13

Course Unitization

Sectio

n

Unit Course

Outcomes

No. of Questions in

No Title CAT-I CAT-II

I 1 Fundamentals of

Engineering Graphics&

Engineering Curves

CO1 Q1

2 Projections of lines & Planes CO2 Q2 & Q3

II 4 Orthographic projections CO4

Q1

5 Isometric projections CO5 Q2

80


Section I

Unit

No

1 Unit Title Fundamentals of Engineering Graphics&

Engineering Curves

Planned

Hrs.

06

Unit Outcomes


UO1 Learn drawing standard SP46, Give dimensioning to drawing.. CO1

UO2 Draw Ellipse, Parabola& Hyperbola CO1

UO3 Draw Cycloid,Archemidean Spiral CO1

Lesson schedule

Class

No.


1 Introduction & Draw circle, pentagon and hexagon

2 Ellipse-arc of Circle method

3 Ellipse-Concentric circle method, Oblong or rectangle method, Parabola-Rectangle &

Tangent method .

4 Hyperbola-Rectangle method, Focus & Directrix method for ellipse, hyperbola &parabola.

5 Involute., Cycloid

6 Archemedeain spiral

Review Questions

Q1 Two fixed points A and B are 100 mm apart. Trace the complete path of a point

P moving in such a way that, the sum of its distances from A & B is always the

same and equal to 130 mm. Name the curve. Draw another curve parallel to and

20mm away from this curve.

CO1

Q2 A circle of 60 mm diameter rolls on a straight line without slipping. In the initial

position, the diameter AB of circle is parallel to the line on which it rolls. Draw

loci of the points A and B of diameter AB for one revolution of the circle.

CO1

Unit

No

2 Unit Title Projections of lines & Planes

Planned

Hrs.

10

Unit Outcomes


UO1 learn Frontal line ,Horizontal line, Oblique line CO2

UO2 Familiarize with the terms Grade and Bearing, Iillustrate theory of Parallel,

perpendicular, intersecting & Skew lines.

CO2

UO3 Learn angle made by plane with FRP and HRP CO2

Lesson schedule

Class

No.


81

7 1. Parallel line, Horizontal line, Frontal line,Oblique line .

8 Problems on Oblique line Grade ,Bearing.

9 Problems on Parallel lines, perpendicular Lines.

10 Problems on Intersecting lines & Skew lines

11 Planes inclined to HRP.

12 Planes inclined to FRP.

13 Examples of circle & semicircle.

14 Examples of pentagonal Plate

15 Examples of Hexagonal Plate

16 Examples of pentagonal & Hexagonal Plate

Review Questions

Q1 Draw the projection of a line AB if the grade of line is 45% at A and bearing is

S600E. Top view length 60 mm .End point A is 20 mm above HRP and 20 mm in

front of FRP.

CO2

Q2 Find out the angle made by the plane ABC with FRP. Take A(10,10,85)

B(30,45,105),C(65,30,70).

CO2

Q3 The coordinates of points ABC are A(10,20,80),B(50,40,90),C(40,10,120). Find

perimeter of triangle ABC

CO2

Q4 A thin circular plate of 50 mm diameter is resting on point A on its rim,with the

surface of the plate inclined at 450 to the HP and the diameter through A inclined

at 300 to the VP.Draw the projection of the circular plate.

CO2

Unit

No 3 Unit Title Projections of solids Planned

Hrs. 5

Unit Outcomes


UO1 Describe various features of cone. CO3

UO2 Differentiate between parameters of Prism & pyramid. CO3

UO3 Draw the projection of solids by rotational method CO3

Lesson schedule

Class

No.


17 Projection of cone

18 Projection of pentagonal Pyramid.

19 Projection of Hexagonal Pyramid.

20 Projection of Pentagonal & Hexagonal prism

21 Projection of cylinder

Review Questions

Q1 A pentagonal prism is resting on one of the corners of its base on the HP. The

longer edge containing that corner is inclined at 450 to the HP. The axis of the

prism makes an angle of 300 to the VP. Draw the projections of the solid. Take

CO3

82

the side of base 45 mm and height 70 mm.

Q2 A hexagonal pyramid, base 25 mm side and axis 55 mm long, has of its slant

edge on the ground. A plane containing that edge and axis is perpendicular to the

HP and inclined at 450 to the VP .Draw its projections when the apex is nearer the

VP than the base.

CO3

Unit

No

4 Unit Title Orthographic Projections Planned

Hrs.

07

Unit Outcomes


UO1 Describe First angle projection system. CO4

UO2 . Learn Third angle projection system. CO4

UO3 Draw FV, TV and LHSV, RHSV of the object CO4

UO4 Give dimensions to object CO4

Lesson schedule

Class

No.


22 First angle projection system & Third angle projection system

23 Simple objects of Orthographic.

24 Conversion of pictorial views in to orthographic views of simple objects.

25 Conversion of pictorial views in to orthographic views of simple objects.

26 conversion of pictorial views in to orthographic views



Review Questions

Q1 1. A pictorial view of a block is shown.

CO4

83

Draw the following views.

a) Front View in the direction X

b) Top view

c) Right hand side view

Unit

No

5 Unit Title Isometric projections Planned

Hrs.

7

Unit Outcomes


UO1 Read Isometric scale. CO5

UO2 Draw isometric view. CO5

Lesson schedule

Class

No.


29 Isometric views & Isometric projection.

30 Isometric views of simple solids and objects

31 Isometric views of simple solids and objects

32 Isometric views of solids and objects.




Review Questions

Q1 Draw isometric drawing of the object show in its front and L.H view. Take “O” as

origin.

CO5

84

Unit

No 6 Unit Title Sections of solids & Development of

surfaces

Planned

Hrs. 07

Unit Outcomes


UO1 Explain horizontal Section plane. CO6

UO2 Explain Vertical Section plane, Draw the development of the surfaces of cone,

prism, cylinder &pyramid

CO6

Lesson schedule

Class

No.

36 Section of cone,Section of Pyramid.

37 Section of Prism, Section of cylinder.

38 Parallel method of Development for Cylinder

39 Parallel method of Development for prism.

40 Radial method of development for cone.

41 Radial method of development for Pentagonal pyramid

42 Radial method of development for Hexagonal pyramid.

Review Questions

Q1 A cone of diameter of base 50 mm and axis 60 mm long is resting on its base on

H.P. A Horizontal cutting plane cuts the apex 25 mm from the top.Draw true

shape & develops the remaining part of the cone.

CO6


Subject: Engineering Graphics

Section I & II

Maximum Marks: 100

Instructions: All Questions are Compulsory

Section I

1

(a)

A point P moves such that its distances from two fixed points A & B which are 90

mm apart remains constant, when P is at equal distance from A & B its distance

from each one is 75 mm .draw the path traced by the point P. Draw normal and

tangent to the curve.

06

(b)

A circle of 50 mm diameter rolls on a straight line without slipping .In the initial

position ,consider the diameter of the circle which is parallel to the line on which it

rolls .Draw the path traced by the outer extreme point on the above diameter for

06

85

one revolution of the circle. Draw normal and tangent to the curve.

(b)

OR

Draw two convolutions of an Archimedean spiral ,given the maximum radius of

100 mm and minimum radius of 28 mm .Draw normal and tangent to the curve at a

point 45 mm from the pole

06

2

(a)

Solve Any Three

A line CD makes 700 with AB .D is on the line AB. Draw front & top view of line

CD. Take A(10,10,80) B(50,45,80) C(35,55,105)

04

(b) Complete the projections of line AB. FV length=60 mm, Bearing w.r.t A=S60E,

Grade 50 % w.r.t A. Take point A 15 mm from both the planes. 04

(c) Draw projections of line PQ (30 mm long) which is perpendicular to AB.Q is on

AB. A(10,10,70) B(55,45,100) P(20,y,100) 04

(d) Find angle with HRP & true shape of plane PQR. Take P(10,40,90) Q(25,10,115)

R(60,50,80) 04

3 (a) A pentagonal of 40 mm side is resting on one of its corner on the VP. The edge

opposite to that corner makes an angle of 300 to the HP. The surface of the

pentagon is inclined at 450 to the VP. Draw the projection of the pentagon.

13

4 (a) Draw projection of a cone with base 40 mm diameter and axis 50 mm long when it

is resting on VP in such a way that apex is 35 mm away from VP and towards

observer. The FV axis makes angle of 400 with HP.

12

Section II

5 (a) A pictorial view of a machine block is shown.

Draw the following views.

(a)An elevation (FV) along the direction of an arrow F

24

86

(b)Sectional end view from left on the section plane X-X

(c)Plan (Top view)

6 (a) Draw isometric drawing of the object show in its front and top view. Take “O” as

origin.

13

7 (a) A cylinder of 50 mm diameter and 70 mm long is resting on H.P. It is cut by a

section plane, inclined 45° to HP and passing through a point on axis which is 25

mm from top end. Draw sectional front view, top view and true shape of section &

develop the lateral surface.

13

Assignments


Assignment No. 1

Assignment

Title

Engineering Curves CO1

Batch I (i)Two fixed points A and B are 100 mm apart. Trace the complete path of a point

P moving in such a way that, the sum of its distances from A & B is always the

same and equal to 30 mm. Name the curve. Draw another curve parallel to and

20mm away from this curve.

(ii) A fixed point is 60 mm from a fixed straight line. Draw the locus of a point P

moving in such a way that it is equidistant from fixed point & the fixed straight

line.

Batch II (i)A circle of 60 mm diameter rolls on a straight line without slipping. In the

initial position, the diameter AB of circle is parallel to the line on which it rolls.

Draw loci of the points A and B of diameter AB for one revolution of the circle

(ii) Draw a circle with diameter AB equal to 60 mm. Draw a line 140 mm long

and tangent to the circle. Trace the path of A, when the line AC rolls on the circle

without slipping

87

Batch III (i)Two straight lines OA and OB make an angle of 750 between them. P is point

40 mm from OB. Draw a hyperbola through P with OA and OB as asymptotes,

making at least 10 points.

(ii) Draw the curves when the distance of the the focus from the directrix is 50

mm & eccentricities are 3/2,1,2/3.Also draw tangent & normal to the curve.

Assignment No. 2

Assignment

Title

Projections of Lines & Planes CO2

Batch I (i)Find out the angle made by the plane ABC with FRP.Take

A(10,10,85),B(30,45,105),C(65,30,70).Find true Shape and perimeter of ABC.

(ii) Complete the projection of MN 30 mm long is perpendicular to AB.N lies on

AB. Take A(10,30,50),M(25,y,65),B(50,10,60).

(iii) A pentagonal plate ABCDE with 40 mm long side has its side AB on the HP

and is inclined at 200 to VP. Corner D of the plate is in the VP and 45 mm above

the HP. Draw the projection of the pentagonal plate.

Batch II (i) A pentagonal of 40 mm side is resting on one of its corner on the VP. The edge

opposite to that corner makes an angle of 300 to the HP. The surface of the

pentagon is inclined at 450 to the VP. Draw the projection of the pentagon

(ii) .”C” is the midpoint of the line PQ measuring 40 mm and parallel to RS.

Complete the projections. R(20,20,110), S(80,50,90),C(50,20,115)

(iii) Complete the projection line MN. End M is 40 mm above the HRP and 35

mm in front of FRP. Bearing w.r.t M is N450E , grade w.r.t M is 60%.TL=60 mm

Batch III (i)A regular hexagonal plate ABCDEF has corner A in the VP. Diagonal AD

makes an angle of 450 to the VP. The top view of the diagonal makes an angle of

600 to the HP. Draw the projection of the hexagonal plane using change of

position method.

(ii) Complete the projection of line PQ 30 mm long and perpendicular to AB. Q

lies on AB.A(10,30,50),B(50,10,60),P(20,y,65).

(iii) Complete the projection of AB.Take Point A 60 mm from both the planes.

Bearing S450W w.r.t A FV makes 30

0 to HRP.TL=60 mm.

Assignment No. 3

Assignment

Title

Projection of Solids CO3

Batch I (i)An equilateral triangular prism of side of base 25 and axis 50 long is resting on

an edge of its base on HP.The face containing that edge is inclined at 300 to

HP.Draw the projections of the prism ,when the edge on which the prism rests, is

inclined at 600 with VP

(ii)A pentagonal prism is resting on one of the corners of its base on the HP.The

longer edge containing that corner is inclined at 450 to the HP.The axis of the

prism makes an angle of 300 to the VP.Draw the projections of the solid. Take the

side of base 45 mm and height 70 mm

88

Batch II (i)A square pyramid, base 25 mm side and axis 55 mm long, has one of its slant

edges on the ground. A plane containing that edge and the axis is perpendicular to

the HP and inclined at 450 to the VP.Draw its projections when the apex is nearer

the VP than the base.

(ii A square pyramid of base 35 side and axis 50 long is resting on one of its

triangular faces on HP with the edge of the base containing that face inclined at

450 to VP. Draw the projections of the pyramid.)

Batch III (i)Draw projection of a cone with base 40 mm dia. And axis 50 mm long when it

is resting on VP in such a way that apex is 35 mm away from VP and towards

observer. The FV axis makes angle of 400 with HP.

(ii) Draw the top view and front view of a right circular cylinder base dia. 35 mm

and axis 65 mm long when it is resting on its circular rim in such a way that its

axis makes an angle of 300 with HP and the top view of its axis is inclined at

angle of 450 to VP.

Assignment No. 4

Assignment

Title

Orthographic Projection CO4

Batch I

89

Batch II

Batch III

Assignment No. 5

Assignment

Title

Isometric Projection CO5

Batch I

90

Batch II

Batch III

Assignment No. 6

Assignment

Title

Sections of solids & Development of surfaces CO6

Batch I (i) A hexagonal prism with side of base 30 mm and axis 70 mm long rests on

comer of its base on H.P It is cut by a section plane inclined 30° to H.P. and

passing through a point on axis, which is 20 mm from top end. Draw sectional

true shape of section & develop the lateral surface.

Batch II (i) A cone with 60 mm base diameter and 70 mm height rests with its base on

ground .It is cut by auxiliary plane making 600 to HP and 10 mm away from the

axis of cone .Draw the true shape of section & develop the lateral surface.

Batch III (i) A hexagonal pyramid, base 25 mm side and axis 60 mm long rests on one of

its side on H.P. It is cut by section plane, inclined 30° to H.P. intersects the axis at

25 mm from the apex of the pyramid, removing the apex. Draw front view, top

view and true shape of section & develop the lateral surface .

91

FE Engineering Semester I

Professional Communication I

Course Professional Communication - I Course Code 40901

Examination

Scheme


Max. Marks 25 25

Contact

Hours/ week

1 2 -- 3

Prepared by Mr. B. B. Pujari Date 2/05/2014

Prerequisites Basic English Grammar

Course Outcomes


CO1 understand the nature and importance of communication, types, barriers and

filters

CO2 construct grammatically correct sentences and understand LSRW skills

CO3 understand Phonetics, English sound systems, phonetic transcription, stress and

intonation

CO4 Learn the importance and techniques of oral communication

CO5 Learn professional correspondence, its importance, language and styles


POs COs


CO1 √

CO2 √

CO3 √ √

CO4 √

CO5 √ √

Course Contents


Hours

1. Understanding Communication 02

2. Grammar and Vocabulary 03

3 Phonetics 03

4. Developing Oral Skills 02

5.. Professional Correspondence 04

92

Reference Books:


1 Speaking Accurately K.C. Nambiar, Cambridge

University Press

New Delhi

Unit 3,

Unit 4

2 Communication Skills Handbook Jane Summers,

Brette Smith Wiley India

Pvt.Ltd

All units

3 Communication Skills

Handbook: How to succeed in

written and oral communication

Jane Summers,

Brette Smith Wiley India

Pvt.Ltd.

Unit 1

4 Handbook for Technical

Writing

David A.

McMurrey,

Joanne Buckley,

David A.

McMurrey, Joanne Buckley, Cengage

Unit 5

5 Write Right Syed Abdur

Rahim Unit 1&2

6 English Grammar for Today Geoffrey Leech

Margaret Deucher Palgrave Unit2

7 A Communicative Grammar of

English

Geoffrey Leech

Jan Svartvik Pearson Unit2

Course Unitization

Secti

-on

Unit Course Outcomes No. of Questions

in


I 1 Understanding

Communication

understand the nature and importance of

communication, types, barriers and filters 1

2 Grammar and

Vocabulary

construct grammatically correct

sentences and understand LSRW skills 1

3 Phonetics understand Phonetics, English sound

systems, phonetic transcription, stress

and intonation

1

I 4 Developing

Oral Skills

know about the importance and

techniques of oral communication

1

5 Professional

Correspondence

know about Professional correspondence,

its importance, language and styles 1

93


Section I

Unit No

1

Unit Title Understanding Communication Planned

Hrs.

02

Unit Outcomes: To know the nature and process of communication; and various types

of communication


UO1 explain nature and importance of communication CO1

UO2 understand the process of communication CO1

UO3 Know barriers of communication CO1

UO4 know filters of communication CO1

Lesson schedule

Class

No.


1 Communication : introduction, nature, importance and process

2 Types of communication: Verbal and Non-verbal

Understanding barriers and filters of communication

Unit No

2

Unit Title Grammar and Vocabulary Planned

Hrs.

03

Unit Outcomes: to study language skills-LSRW, tenses, sentence structures and

various types of sentences


UO1 know forms of tenses CO2

UO2 understand language skills-LSRW CO2

UO3 know sentence structures and different types of sentences CO2

UO4 recognize and understand confusing word pairs CO2

Lesson schedule

Class

No.


1 English grammar; forms of tenses

2 confused word pairs, types of sentences

3 Four language skills LSRW

Unit No

3

Unit Title Phonetics Planned

Hrs.

03

Unit Outcomes: To understand phonetics, English sounds – vowels, consonants,

diphthongs, Phonetic transcription, stress and intonation


UO1 understand phonetics and its importance CO3

UO2 know the phonetic alphabets CO3

UO3 Understand use of stress sounds and effective use of intonation CO3

94

Lesson schedule

Class

No.


1 Understanding phonetics

2 Phonetic alphabets

3 Transcription ,stress and intonation

Unit No

4

Unit Title Professional correspondence Planned

Hrs.

04

Unit Outcomes: To know about professional correspondence ; importance, language

and style and various formats

At the end of this unit the students should be able to

UO1 know the importance of professional correspondence and language, style

and formats (British and American)

CO4

UO2 Letter writing - simple application letter, inquiry and replay to inquiry,

placing an order , complaint and its adjustment letter and email writing

CO4

Lesson schedule

Class

No.


1 Know the importance of professional correspondence and language, style and formats

(British and American)

2 Letter writing -simple application letter , letter of inquiry and replay to inquiry

3 placing an order, complaint and adjustment letter

4 email writing

Assignments

List of experiments/assignments to meet the requirements of the syllabus:

1.Elocution

2.Vocabulary building

3.Phonetic Alphabets (Listen & repeat)

4.Pronunciation

5.Fluency Tips

6.Extempore

7.Teamwork- story making

8.Effective reading (newspaper articles)

9.Active listening (memorizing)

10.Grammar activities

11.Letter writing Activities

12.Situational conversation

95

Course Plan

Course Workshop Practice-I Course Code

Examination

Scheme


Max. Marks 25 -- 25

Contact

Hours/ week

2 -- 2

Prepared by S. V. Dhanal Date

Prerequisites Fundamentals of computer and electronics

Course Outcomes


CO1 identify hardware components of a typical computer system.

CO2 assemble and Disassemble the PC.

CO3 handle and operate peripheral devices like printer, scanner, pen

drives, CD-ROM, Multimedia Devices, UPS etc.

CO4 identify and study of communication elements like Single pair

Wires (phone lines), multi-pair wires (UTP), fibre-optic cables, printer data

cables, connectors.

CO5 troubleshoot and Maintain PC

a) POST (power on self test) b) Virus c) Power related problems.

CO6 Demonstration of multimedia features – running and handling of audio and

video clips, use of CD Read / Write operations etc.

CO7 To demonstrate and use of electrical and electronics hand and power tools.

CO8 To make Carpentry joints such as butt joint, dovetail

96


POs

COs

a b c d E F G H i j k l

CO1

CO2 √

CO3 √

CO4 √

CO5 √

CO6 √

Course Contents


Hours

Section A

1. A) Computers:

1. Introduction and identification of hardware components of a typical

computer system.

2. Assembling and Disassembling the PC.

3. Handling and operating peripheral devices like printer, scanner, pen


4. Identification and study of communication elements like Single pair

wires (phone lines), multi-pair wires (UTP), fibre-optic cables, printer

data cables, connectors- RJ-45, RJ-9, RJ-11, USB, 9-Pin and 25-Pin

serial and parallel connectors; converters- serial to USB, 9-Pin to 25-

Pin, Vice-Versa and others.

5. Troubleshooting and Maintenance of PC


6. Demonstration of multimedia features – running and handling of

audio and video clips, use of CD Read / Write operations etc.

2 B) Electronics :

1. Demonstration and use of electrical and electronics hand and power

tools.

2. Measurement of resistor and capacitor, measurement of voltage and

frequency using oscilloscope.

3. Assembly of Electronic components on the printed circuit board

(PCB)

4. Demonstration and performance measurement of any two electronic

components / devices –

a. Diodes b. Transistor. c. Logic gates.

3 C ) -1 Carpentry involving dovetail / butt joint su

ch as a tray, frame etc.

97

Reference Books:

Sr. No. Title of Book Author Publisher/Edition Units

1 The complete PC upgrade and

maintenance guide -- BPB.

Publications.

Mark Minasi,


Section I

Unit No 1 Unit Title Planne

d Hrs.

Unit Outcomes


UO1 identify hardware components of a typical computer system. CO1

UO2 assemble and Disassemble the PC.

CO2

Lesson schedule

Unit No 1 Unit Title Computers Planne

d Hrs.

Unit Outcomes


UO1 handle and operate peripheral devices like printer, scanner, pen


CO3

UO2 identify and study of communication elements like Single pair

Wires (phone lines), multi-pair wires (UTP), fibre-optic cables, printer data

cables, connectors.

CO4

Unit No 2 Unit Title Computers Planne

d Hrs.

Unit Outcomes


UO1 troubleshoot and Maintain PC


CO5

UO2 Demonstration of multimedia features – running and handling of audio and

video clips, use of CD Read / Write operations etc.

CO6

Unit 2 Electronics

98

UO1 To demonstrate and use of electrical and electronics hand and power tools.

CO7

Unit 3 Carpentry involving dovetail / butt joint

UO1 To make carpentry joints CO8


Engineering Chemistry

Course Engineering Chemistry Course Code 59183

Examination

Scheme


Max. Marks 100 25 -- 125

Contact

Hours/ week

3 2 -- 5

Prepared by Ms P K Damate Date 29/04/2014

Prerequisites This course requires the student to know applications of the basic concepts of

organic, inorganic, physical and analytical chemistry and to integrate pure

chemistry principles with engineering applications.

Course Outcomes


CO1 Understand water quality parameters and advanced water purification

techniques.

CO2 Understand basics of instrumental methods of chemical analysis and their

applications.

CO3 Understand the synthesis and applications of advanced materials.

CO4 Understand qualities of good fuel such as calorific value and its determination.

CO5 Understand basic chemistry behind corrosion of metals and various corrosion

prevention methods.

CO6 Understand properties and applications of metallic materials and concepts of

green chemistry.

99


POs

COs


CO1 √ √ √ √ √ √ √ √ √

CO2 √ √ √ √ √ √ √ √

CO3 √ √ √ √ √ √

CO4 √ √ √ √ √ √ √ √ √

CO5 √ √ √ √ √ √ √ √

CO6 √ √ √ √ √ √ √ √

Course Contents


Hours

Section I

1. Unit 1: Water

Introduction, impurities in natural water, water quality parameters total

solids, acidity, alkalinity, chlorides, and dissolved oxygen (definition,

causes, significance), hardness of water (causes, types, units of

hardness), ill effects of hard water in steam generation in boilers,

numerical on hardness, treatment of hard water (ion exchange and

reverse osmosis).

7

2. Unit 2: Instrumental methods of chemical analysis

Introduction, advantages and disadvantages of instrumental methods.

A) pH-metry:

Introduction, pH measurement using glass electrode, applications of pH-

metry.

B) Spectrometry:

Introduction, Laws of spectrometry (Lamberts and Beer-Lambert‟s law),

Single beam spectrophotometer (schematic, working and applications).

C) Chromatography:

Introduction, types, gas-liquid chromatography (GLC), basic principle,

Instrumentation and applications.

7

3. Unit 3: Advanced materials

A) Polymers:

Introduction, plastics, thermosoftening and thermosetting plastics,

industrially important plastics like phenol formaldehyde, urea

formaldehyde and epoxy resins, conducting polymers (doping,

conjugation, conductivity), examples and applications, biodegradable

plastics.

B) Nanomaterials:

Introduction, synthesis and applications.

C) Composite materials:

Introduction, constituents, types of composites, advantages,

7

100

composition, properties and uses of fiber reinforced plastics (FRP) and

glass reinforced plastic (GRP)

Section II

4. Unit 4: Fuels

Introduction, classification, calorific value, definition, units (calorie,

kcal, joules, kilojoules), characteristics of good fuels, comparison

between solid, liquid and gaseous fuels, types of calorific value (higher

and lower), Bomb calorimeter and Boy‟s calorimeter. Numerical on

Bomb and Boy‟s calorimeter. Fuel cells: Introduction, classification,

advantages, limitations and applications.

7

5. Unit.5: Corrosion:

Introduction, causes, classification, atmospheric corrosion(oxidation

corrosion), electrochemical corrosion (hydrogen evolution and oxygen

absorption mechanism), factors affecting rate of corrosion. Prevention

of corrosion by proper design and material selection, hot dipping

(galvanizing and tinning), cathodic protection, metal spraying and

electroplating.

7

6 Unit 6: Metallic materials & Green Chemistry (7)

A) Metallic materials: Introduction, alloy definition and classification,

purposes of making alloys. Ferrous alloys: Plain carbon steels (mild,

medium and high), stainless steels. Nonferrous alloys: Copper alloy

(Brass), Nickel alloy (Nichrome), Aluminum alloy (Duralumin and

Alnico), Tin alloy (Solder metal).

B) Green Chemistry:Definition, goals of green chemistry,significance,

basic components of green chemistry research, industrial applications.

7

Reference Books:

Sr. No. Title of Book Author Publisher/Edition Topics*

1 Engineering Chemistry Jain and Jain Dhanpat Rai

Publishing

Company Ltd.,

New Delhi.

1,3,5

2. A Textbook of


S. S. Dara and S. S.

Umare, S. Chand

Company Ltd.,

New Delhi.

1,5

3. A Textbook of


C. P. Murthy, C. V.

Agarwal and A. Naidu

BS Publications,

Hyderabad.

1

4. Instrumental Methods of

Chemical Analysis

Chatwal and Anand Himalaya

Publishing House,

New Delhi

2

5. Engineering Chemistry Dr. A. K. Pahari, Dr. B.

S. Chauhan

Laxmi

Publications (P)

Ltd, New Delhi.

3,4,5,6

101

6. A text Book of


Shashi Chawla, Dhanpat

Rai

Shashi Chawla,

Dhanpat Rai & Co.

(Pvt.) Ltd,

Delhi.

1,3,5

7. Engineering Chemistry Renu Bapna and Renu

Gupta

MacMillan

Publishers (India)

Ltd, Delhi

4

8. Industrial Chemistry B. K. Sharma GOEL Publishing

House

All

9. Principles of

Nanotechnology

Phani Kumar SciTech

Publications

1

* Indicates the unit number as per SUK syllabus.

Scheme of Marks

Section Unit No. Title Marks*

I 1. Water 35

2. Instrumental methods of chemical analysis 19

3. Advanced materials 20

II 4. Fuels 23

5. Corrosion 34

6. Metallic materials & Green Chemistry 19

*Marks weightage as per SUK Exam Dec.2013 question paper pattern.

Course Unitization

Sec

Unit Course Outcomes No. of Questions in

No. Title CAT-I CAT-II Prelim

I 1. Water

To study the impurities in

natural water, water quality

parameters, treatment of hard

water and solve numerical.

Three

questions

with sub

questions

-- Four

questions

with sub

questions

2. Instrumen

tal

methods of

chemical

analysis

To study the basics of

instrumental methods of

chemical analysis and to

acknowledge the use of pH-

metry, spectrometry and

chromatography in various

fields.

3. Advanced

materials

To understand the basic --

Three

questions

102

concepts of formation and

applications of advanced

material

with sub

questions

II 4. Fuels To know and identify good

quality fuels by using basic

chemistry and solve numerical

problem

Four

questions

with sub

questions

5. Corrosion To learn basic chemistry behind

corrosion and its various

prevention methods.

--

6. Metallic

materials

& Green

Chemistry

To understand properties and

applications of metallic

materials and generate

awareness of newly introduced

green chemistry.


Section I

Unit No 1 Unit Title Water Planned

Hrs.

7

Unit Outcomes


UO1 Understand water quality parameters and advanced water purification

techniques.

CO1

Lesson schedule:

Class No. Details to be covered

1 Introduction of water as universal solvent

2 Water sources and water quality parameters.

3 Total solids and acidity of water.

4 Alkalinity and chlorides

5 Dissolved oxygen

6 Hardness of water

103

7 Numerical problems

Review Questions

Q1 Write a note on impurities present in water? CO1

Q2 Explain alkalinity of water sample CO1

Q3 Discuss the experimental determination of hard water. CO1

Q4 What are the different troubles caused by the use of hard water in boilers? CO1

Q5 Discuss in short ill effects of hard water. CO1

Q6 Find out temporary, permanent and total hardness in water sample with

following impurities

i)Ca(HCO3)2= 81 ppm ii) MgCO3 =84 ppm iii) CaCl2=22.2 ppm

iv) MaSO4 = 60 ppm v)KCl=30 ppm (Does not contribute to hardness).

CO1

Unit No 2 Unit Title Instrumental Methods of Chemical

Analysis

Planned

Hrs.

7

Unit Outcomes CO2


UO2 Understand basics of instrumental methods of chemical analysis and their

applications.

Lesson schedule:


1 Introduction, advantages and disadvantages of instrumental methods

2 Study of pH-metry

3 Applications of pH-metry

4 Introduction of spectrometry and study of laws of spectrometry

5 Single beam spectrophotometer

6 Introduction to chromatography

7 Instumentation and applications of GLC

Review Questions CO2

Q1 Give the advantages and disadvantages of instrumental methods. CO2

Q2 Define pH. Explain the construction and working of glass electrode. CO2

Q3 State Lambert‟s law. Derive the equation for Lambert‟s law. CO2

Q4 Discuss the applications of pH-metry. CO2

Q5 Explain the working of single beam spectrophotometer and their functions. CO2

Q6 Give classification of chromatographic technique. CO2

Q7 Give principle and technique of gas liquid chromatography. CO2

Unit No 3 Unit Title Advanced material Planned

Hrs.

7

Unit Outcomes


UO3 Understand the synthesis and applications of advanced materials. CO3

104

Lesson schedule


1 Introduction to polymer and plastic

2 Types of plastic

3 Urea-formaldehyde resin and phenol formaldehyde resin

4 Conducting polymers

5 Biodegradable polymers

6 Nanomaterials

7 Composite materials

Review Questions

Q1 Define polymer and monomer. Classify the polymers on the basis of

structure.

CO3

Q2 Distinguish between thermoplastic and thermosetting plastic. CO3

Q3 Write a note on phenol formaldehyde resin. CO3

Q4 Explain preparation. Properties and applications of urea formaldehyde resin. CO3

Q5 Discuss the biodegradable polymers. CO3

Q6 Write a note on conducting polymers. CO3

Q7 Explain the preparation, properties and uses of epoxy resin. CO3

Q8 Discuss the synthesis methods of nonmaterial CO3

Q9 Explain the properties of FRP. Discuss manufacturing methods of FRP. CO3

Section II

Unit No 4 Unit Title Fuel Planned

Hrs.

7

Unit Outcomes


UO4 Understand qualities of good fuel such as calorific value and its

determination.

CO4

Lesson schedule


1 Introduction and classification of fuels

2 Calorific value

3 Characteristics of fuels

4 Comparison between solid, liquid and gaseous fuels

5 Bomb calorimeter and boys calorimeter


7 Fuel cell

Review Questions

Q1 Define fuel. Explain characteristics of good fuel. CO4

Q2 Define calorific value of fuel. How calorific value is determined using Boy‟s

calorimetric method?

CO4

105

Q3 Explain construction and working of Bomb calorimeter. How is the gross

calorific value calculated?

CO4

Q4 Write a note on fuel cell. CO4

Q5 Define fuel. Explain characteristics of good fuel. CO4

Q6 Define calorific value of fuel. How calorific value is determined using Boy‟s

calorimetric method?

CO4

Q7 Explain construction and working of Bomb calorimeter. How is the gross

calorific value calculated?

CO4

Q8 Following observations were recorded in a bomb calorimeter experiment.

Calculate the gross and net calorific value of the fuel contains 5.7 hydrogen.

Weight of empty crucible= 3.175 gm

Weight of crucible +fuel= 4.085 gm

Mass of water in calorimeter = 2500 gm

Water equivalent of calorimeter = 470 gm

Observed rise in temperature = 2.410C

Cooling correction = 0.0350C

Fuse wire correction= 11.5 Cal

CO4

Unit No 5 Unit Title Corrosion Planned

Hrs.

7

Unit Outcomes


UO5 Understand basic chemistry behind corrosion of metals and various

corrosion prevention methods.

CO5

Lesson schedule


1 Introduction of corrosion

2 Causes and classification of corrosion

3 Atmospheric corrosion

4 Electrochemical corrosion

5 Factors affecting on rate of corrosion

6 Methods of Prevention of corrosion

Review Questions

Q1 Define corrosion. Give classification of corrosion. CO5

Q2 Define corrosion. Explain the mechanism of hydrogen evolution in

electrochemical corrosion.

CO5

Q3 Define corrosion. Explain the mechanism of oxygen absorption in


CO5

Q4 Discuss factors affecting on rate of corrosion. CO5

Q5 What is Cathodic Protection? Explain cathodic protection as a method to

prevent corrosion.

CO5

106

Q6 Explain electroplating process. CO5

Q7 Write a note on metal spraying. CO5

Q8 Explain prevention method of metal from corrosion by proper design. CO5

Unit No 6 Unit Title Metallic materials and green chemistry Planned

Hrs.

7

Unit Outcomes


UO6 Understand properties and applications of metallic materials and concepts of

green chemistry.

CO6

Lesson schedule:


1 Introduction , alloy definition and classification

2 Purposes of making alloy

3 Ferrous alloys

4 Nonferrous alloys

5 Stain less steel alloy and tin alloy

6 Goals and significance of green chemistry.

Review Questions

Q1 Explain purposes of making alloy. CO6

Q2 Write a note on stainless steel. CO6

Q3 Write composition and uses of Nichrome. CO6

Q4 Enlist different goals of Green chemistry. CO6

Q5 Write properties and uses of Mild carbon steel. CO6

Q6 Write composition, properties and uses of brass. CO6

Q7 Write a note on Tin alloy. CO6

Q8 Write composition, properties and uses of bronze. CO6


Course Title : Engineering Chemistry Max.

Marks

Duration 3 hrs. 100

Instructions:

1. Figures right to the indicate full marks.

2. Question No 4 and Question No 8 are compulsory.

3. Attempt Any TWO remaining questions from Section I and

Any TWO questions from Section II.

4. Use of non programmable calculator is allowed.

Section-I Marks

107

50

1 a Give principle, construction and working of single beam

spectrophotometer. 6

b Explain preparation, properties and applications of phenol formaldehyde

plastic 5

c Give preparation, properties and applications of GRP. 5

2 a Explain ion exchange process for softening of water.. 8

b Find out temporary, permanent and total hardness in water sample with

following impurities in mg/lit.

i)Ca(HCO3)2= 10.5 ii) MgCl2 =20.5 iii)Mg(HCO3)2=11.5

iv) CaSO4 =18.5 v) KCl= 9.8 (Does not contribute to hardness).

8

3 a Give principle, construction and working of glass electrode. 6

b Compare addition and condensation polymerization 5

c Explain mechanical method of synthesis of nanomaterial. 5

4

Write a note on any four

18

a Classification of chromatography

b Lamberts law.

c Alkalinity

d Enlist different impurities present in natural water

e Conducting polymers

f Composite material

Section-II Marks

50

5 a Following observations were recorded in a bomb calorimeter

experiment. Calculate the gross and net calorific value of the fuel

contains 5.7 hydrogen.

1. Weight of empty crucible= 3.175 gm

2. Weight of crucible +fuel= 4.085 gm

3. Mass of water in calorimeter = 2500 gm

4. Water equivalent of calorimeter = 470 gm

5. Observed rise in temperature = 2.410C

6. Cooling correction = 0.0350C

7. Fuse wire correction= 11.5 Cal

8

b Define green chemistry? Give basic principles of green chemistry. 8

6

a Explain how you will determine calorific value of gaseous fuel by using

Boy‟s gas calorimeter.

6

108

b What is electrochemical corrosion? Discuss hydrogen evolution

mechanism with example.

5

2 Give composition, properties and applications of ferrous alloy 5

7

a Give composition, properties and applications of brass alloy. 6

b Explain hot dipping in details. 5

c What are the factors affecting on the rate of corrosion? 5

8 Write a note on any four 18

a Fuel cell.

b characteristics of good fuel

c Galvanization

d Metal spraying

e Oxidation corrosion

f Duralumin &alnico

Assignments


Assignment No. 1

Assignment

Title

Unit: Water CO3

20 M

Batch I 1. Find out temporary, permanent and total hardness in water sample

with following impurities

i)Ca(HCO3)2= 81 mg/lit ii) MgCO3 =84 mg/lit

iii) CaCl2=22.2 mg/lit iv) MaSO4 = 60pp mg/lit

v)KCl=30 mg/lit (Does not contribute to hardness).

8

2. Write short note on Dissolved chlorides. 4

3. Write a note dissolved oxygen. 4

4. Define acidity. Explain its dermination method. 4

Batch II 1. Find out temporary, permanent and total hardness in water sample

with following impurities

i)Ca(HCO3)2= 12 mg/lit ii) MgCO3 =10 mg/lit

iii) CaCl2=16.5 mg/lit iv) MaSO4 =8 mg/lit

v)KCl=22 mg/lit (Does not contribute to hardness).

8

2. Discuss water softening treatment by ion exchange method 4

3. Discuss in short ill effects of hard water. 4

4. Explain alkalinity of water sample 4

109

Batch III 1. The water sample analysis found to contain following impurities

in mg/lit. Calculate temporary, permanent and total hardness in

water sample.

i)Ca(HCO3 )2= 10.5mg/lit ii) MgCO3 =11.5mg/lit

Iii) CaCl2=18.5 mg/lit iv) MaSO4 =20.5mg/lit

8

2. What are the bad effects of using hard water in industrial

application?

4

3. Write a note on acidity. 4

4. Enlist different impurities present in natural water 4

Assignment No. 2

Assignment

Title

Unit2: Instrumental methods of chemical analysis CO4

20M

Batch I 1. Define pH. Explain the construction and working of glass

electrode

6

2. Give the advantages and disadvantages of instrumental methods. 5

3. Explain Lambert law. 5

4. Explain applications of pH metry 4

Batch II 1. Explain the working of single beam spectrophotometer and their

functions

6

2. Draw a neat and lebelled schematic represention of GLC 5

3. Give the advantages and disadvantages of instrumental methods 5

4. State Lambert-Beers law. Derive the equation for Lambert‟s law 4

Batch III 1. Give principle and technique of gas liquid chromatography 6

2. Give classification of chromatographic technique. 5

3. Give the advantages and disadvantages of instrumental methods 5

4. Explain applications of GLC 4

Assignment No. 3

Assignment

Title

Advanced Material CO3

20 M

Batch I 1. Explain preparation, properties and applications of phenol

formaldehyde resin.

5

2. Distinguish between thermosetting and thermo softening polymers 5

3. Give classification of composite material. 5

4. Write applications of nanomaterial. 5

Batch II 1. Explain preparation, properties and applications of urea

formaldehyde resin.

5

2. Distinguish between thermosetting and thermo softening polymers 5

3. Write a note on FRP 5

4. Explain synthesis of nonmaterial using vapour deposition method 5

110

Batch III 1. Explain preparation, properties and applications of epoxy resin. 5

2. Distinguish between addition and condensation polymers. 5

3. Write a note on FRP 5

4. Explain synthesis of nanomaterial using mechanical method. 5

Assignment No. 4

Assignment

Title

Unit 4: Fuels CO4

20 M

Batch I 1. Following observations were recorded in a bomb calorimeter


contains 5.7 hydrogen.



Mass of water in calorimeter = 2500 gm





8

2. Define fuel. Explain characteristics of good fuel. 6

3. Write a note on fuel cell. 6

Batch II 1. Following observations were recorded in a bomb calorimeter


contains 6 %hydrogen.



Mass of water in calorimeter =1500 gm





8

2. Explain how you will determine calorific value of gaseous fuel by

using Boy‟s gas calorimeter.

6

3. Enlist different characteristics of good fuel 6

111

Batch III 1. Following observations were recorded in a bomb calorimeter


contains 6 %hydrogen.



Mass of water in calorimeter =1500 gm




2.Fuse wire correction= 10.5 Cal

3. Explain how you will determine calorific value of gaseous fuel by

using Bomb calorimeter.

4.How fuel cells are classified?

8

6

6

Assignment No. 5

Assignment

Title

Unit 5: Corrosion CO5

20M

Batch I 1. Define corrosion. Give classification of corrosion. 6

2. Define corrosion. Explain the mechanism of hydrogen evolution

in electrochemical corrosion.

7

3. Define corrosion. Explain the mechanism of oxygen absorption in


7

Batch II 1. Discuss factors affecting on rate of corrosion. 7

2. What is Cathodic Protection? Explain cathodic protection as a

method to prevent corrosion.

7

3. Explain electroplating process 6

Batch III 1. Write a note on metal spraying. 7

2. Explain prevention method of metal from corrosion by proper

design

7

3. What are the different factors affecting on corrosion 6

Assignment No. 6

Assignment

Title

Unit 6: Metallic materials and green chemistry CO6

20 M

Batch I 1. Explain purposes of making alloy. 5

2. Write a note on stainless steel. 5

3. Write composition and uses of Nichrome. 5

4. Enlist different goals of Green chemistry. 5

Batch II 1. Write properties and uses of Mild carbon steel. 5

2. Write composition, properties and uses of brass. 5

3. Write a note on Tin alloy. 5

4. Write composition, properties and uses of ferrous alloy. 5

112

Batch III 1. Explain purposes of making alloy 5

1. Write compostion and uses of Alnico and Duralumin 5

2. Enlist different goals of Green chemistry 5

3. Write properties and uses of Medium carbon steel. 5

List of Experiments:

Sr.No. Name of the experiment CO

1. Determination of acidity of water CO1

2. Determination of alkalinity of water CO1

3. Determination of chloride content of water by Mohr‟s method CO1

4. Determination of total hardness of water by EDTA method. CO1

5. Preparation of phenol formaldehyde resin CO3

6. Preparation of urea formaldehyde resin CO3

7. Determination of copper in brass CO6

8. Demonstration of pH meter CO2

9. Demonstration of photo-colorimeter/ spectrophotometer CO2

List of additional experiments

Assignment No. 1

Experiment Title Unit 5: Corrosion CO5

Batch I 1. Determination of rate of corrosion of aluminum in acidic and basic

medium

Batch II 2. Determination of rate of corrosion of aluminum in acidic and basic

medium

Batch III 3. Determination of rate of corrosion of aluminum in acidic and basic

medium


Assignment No. 1

Assignment Title CO

Batch I 1. Spectrophometric dermination of iron in vitamin tablet CO2

2. Demonstration of paper chromatography using plant extract.

Batch II 1. Demonstration of paper chromatography using plant

extract. CO2

2. Water samples from five different sources, eg. Well, Hand

Pump, Water Supply, etc. from neighborhood to be collected by

each group of two students and following tests to be conducted:

Qualitative Analysis (with the help of field test kits available) or

the following:

Total Solid dissolved

Chlorine

Fluorine

Iron

CO1

113

Nitrite

Sulphide/Sulphate

Batch III 1. Water samples from five different sources, eg. Well, Hand

Pump, Water Supply, etc. from neighborhood to be

collected by each group of two students and following tests

to be conducted:

Qualitative Analysis (with the help of field test kits available) or

the following:

Total Solid dissolved

Chlorine

Fluorine

Iron

Nitrite

Sulphide/Sulphate

CO1

2. Demonstration of paper chromatography using plant

extract.

CO2


Fundamental of Electronics & Computer Programming

Course E&TC Course Code

Examination

Scheme Theory Term Work OE Total

Max. Marks 50 25 -- 75

Contact

Hours/ week 2 2 -- 4

Prepared by Mr. R.S.Vathare Date 02/05/2014

Prerequisites Basic knowledge of Electricity, fundamental concepts regarding physics,

Analytical perspective regarding applications where electronics is used.

Course Outcomes


CO1 Students will be able & identify & use basic components in electronics

engineering.

CO2 Describe the characteristics of p-n junction diode devices and its use for a given

application

CO3 Able to design the digital logic circuits using logic gates &flip flops.

CO4 Student will be able to understand the concept & working of different types of

transducers.

CO5 Able to identify & describe the working of electronics appliances used for daily

needs.

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POs COs a b c d E f g h i j k l

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Course Contents


Hours

Section I

1.

Semiconductor Devices and Applications:

Half Wave & Full Wave rectifiers. BJT characteristics, load line,

operating point, leakage currents, saturation and cutoff mode of

operations, Need for stabilization, fixed bias, emitter bias, self bias, bias

stability with respect to variation in ICO, VBE& β, Stabilization factors,

thermal stability, RC coupled CE amplifier, Regulated power supply.

7 Hrs

2.

Digital Electronics:

Logic Gates- Basic gate, Universal gates. Boolean algebra.

Logic Families, Sequential logic, half adder, full adder, multiplexer, de-

multiplexer, Combinational logic, Flip-flops(JK Flip-flop)

6 Hrs

3.

Applications:

Transducers: for Displacement, level, temperature, pressure, Speed

measurements, Range Specifications Limitations

Appliances: Block Diagram, Specifications, Operation and use of the

appliances: Digital Thermometer, Digital Watch, Weighing machine,

Microwave oven and Mobile handset

7 Hrs

Text/Reference Books:

Sr.No. Title of Book Author Publisher/Edition Topics

1 A Text of Applied

Electronics R. S. Sedha S. Chand U1,U3

2 Basic Electronics

Engineering

Vijay Baru,

RajendraKaduskar, S

T Gaikwad

Wiley/DREAMTECH U1

3 Principle of Electronics V.K.Mehta S. Chand U1,U2,U3

4 Digital Principles &

Applications

Albert Malvino,

Donald Leach TMGH Publications U2

5 Electronic

Instrumentation H.S.Kalsi TMGH Publications U3

115

Scheme of Marks


I

1 Semiconductor Devices and Applications 16

2 Digital Electronics 16

3 Applications 18

Course Unitization

Section

Unit Course

Outcomes No. of Questions in


I

1 Semiconductor Devices and

Applications CO1,CO2 02

2 Digital Electronics CO3,CO4 01 01

3 Applications CO5 02


Section I

Unit No 1 Unit Title Semiconductor Devices and Applications Planned

Hrs. 07

Unit Outcomes


UO1 Understand basics of electronics components and circuits. CO1

UO2 Identify characteristics of electronics devises, Need for stabilization CO2

Lesson schedule

Class

No.


1 Introduction, Half Wave & Full Wave rectifiers.

2 BJT characteristics, load line, operating point,

3 Leakage currents, saturation and cutoff mode of operations,

4 Need for stabilization, fixed bias, emitter bias, self bias,

5 Bias stability with respect to variation in ICO, VBE& β, Stabilization factors,

6 Thermal stability, RC coupled CE amplifier,

7 Regulated power supply.

Review Questions

Q1 Explain in detail Half Wave & Full Wave rectifiers CO1

Q2 Draw and Explain BJT characteristics, load line, operating point, leakage

currents. CO1

Q3 Explain modes of operation of BJT. CO1

Q4 Why Need for stabilization is required and bias stability with respect to CO2

116

variation in ICO, VBE& β, Stabilization factors,

Q5 With neat circuit diagram explain fixed bias, emitter bias &self bias circuit CO2

Q6 Draw and explain RC coupled CE amplifier CO2

Unit No 2 Unit Title Digital Electronics Planned

Hrs. 06

Unit Outcomes


UO1 Understand basics of combinational and sequential logic CO3

UO2 Identify logic families of IC‟s CO3

UO3 Analyze and use logic gates CO3

Lesson schedule

Class

No. Details to be covered

1 Logic Gates- Basic gate, Universal gates.

2 Introduction of Boolean algebra.

3 Logic Families, Sequential logic.

4 Half adder and full adder

5 Multiplexer and de-multiplexer,

6 Combinational logic, Introduction to flip-flops

7 JK Flip-flop

Review Questions

Q1 Explain all Logic Gates- Basic gate, Universal gates. CO3

Q2 Write a note on Boolean algebra. CO3

Q3 With the help of truth table explain half adder and full adder. CO3

Q4 Explain 8:1 multiplexer in detail. CO3

Q5 Draw and explain 1:4 de-multiplexer. CO3

Q6 Explain in detail JK flip-flop. CO3

Unit No 3 Unit Title Applications Planned

Hrs. 07

Unit Outcomes


UO1 Understand basic applications of transducers and appliances CO4

UO2 Analyze and use different types of transducers for measurements CO5

Lesson schedule

Class

No.


1 Introduction of TransducersRange Specifications Limitations

2 Transducers for Displacement measurement, level measurement

3 Transducers for temperature, pressure, Speed measurements

4 Introduction to Appliances: Block Diagram, Specifications, Operation and use of the

appliances.

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5 Digital Thermometer, Digital Watch.

6 Block Diagram, Specifications, Operation and use of Weighing machine.

7 Microwave oven and Mobile handset.

Review Questions

Q1 Explain Displacement measurement Transducers and its Range,

Specifications, Limitations CO4

Q2 Write a note on level measurement CO4

Q3 Write a note on temperature, pressure, Speed measurements CO4

Q4

With the help of block Diagram, Specifications, Operation of the appliances:

a) Digital Thermometer

b) Digital Watch

c) Weighing machine

d) Microwave oven

e) Mobile handset

CO5


Course Title : Fundamentals of Electronics

Duration: 90 minutes Max.

Marks50

Instructions:

1) All questions are compulsory for section-I

2) Figures to the right indicate full marks.

3) Assume suitable data if necessary

Section-I

Marks

1 Solve any two 16

A Explain full wave rectifier with centre tap transformer with necessary

waveforms 8

B Explain all gates with its truth table 8

C With help of neat block diagramexplain in detail mobile handset 8

2 Solve any two 16

A Explain BJT characteristics in detail 8

B Explain in detail JK flip flop 8

C Explain in detail microwave oven 8

3 Solve any three 18

118

A Explain 8:1 multiplexer with truth table 6

B With help of neat circuit diagram explain regulated power supply 6

C Explain half adder in detail. 6

d With help of neat block diagram explain digital thermometer 6

e Explain fixed bias circuit for biasing transistor. 6

Assignments


Assignment

Title

CO1,CO2,CO3

Batch I 1. With help of neat circuit diagram explain regulated power supply

2. Explain fixed bias circuit for biasing transistor.

3. Differentiate between Combinational & Sequential circuits?

4. What do you mean basic gates & derived gates? Explain with the help of

examples?

5. What are the methods used for measurement of pressure? Explain any one

in detail?

6. What do you mean by transducer? Explain any one displacement

transducer in detail?

Batch II 1. Explain BJT characteristics in detail.

2. Show that it is possible to derive all the gates from basic gates.

3. What do you mean by Boolean algebra? Explain all the laws of Boolean

algebra?

4. Explain the construction & working of digital thermometer?

5. What do you mean by transducer? Explain the construction & working of

LVDT in detail?

6. Explain the construction & working of digital watch?

Batch III 1. Briefly explain the different types of logic families?

2. Explain with the help of truth table working of

a) Full adder

b) Clocked RS latch

c) 1:4 demultiplxer

d) 4:1 multiplxer

3. Explain with the help of neat diagram & truth table working of positive

edge triggered JK flip flop

4. Explain the method of level measurement?

5. Explain the construction & working of Washing machine in brief?

6. Explain the method of speed measurement using tachometer?

List of experiments

Any five experiments out of eight

Exp. No. 1 Testing of Electronics components-resistors, capacitors, inductors, diode,

119

transistor, LED and switches using multimeter& CRO.

Exp. No.2 VI characteristics of PN junction diode and zener diode.

Exp. No. 3 Study of Half wave & Full wave rectifier and their comparison.

Exp. No. 4 Study of Frequency response of CE amplifier

Exp. No. 5 Study of truth tables of logic gates: OR, AND, NOT, NAND, NOR, EXOR

Exp. No. 6 Measurement of Distance using LVDT/Strain Gauge.

Exp. No. 7 Measurement of Temperature using any transducer.

Exp. No. 8 Study of Mobile Handset.

Computer Programming (Section II)

Course Computer Programming Course Code

Examination

Scheme


Max. Marks 100 25 --- 125

Contact

Hours/ week

4 2 -- 6

Prepared by Ms. Sujata A. Pardeshi & Ms. Pooja Akulwar Date 29 April 2014

Prerequisites This course requires the student to know about the basics of computer hardware and software, how to use computer.

Course Outcomes


CO1 To Acquire the essential knowledge of computer systems and peripherals

CO2 To understand the Data representation & Number System

CO3 To know operating system features and system software‟s

CO4 To gain knowledge of Unix /Linux Commands

CO5 To acquire usages of application software and their uses

CO6 To understand the use of computer networks and internet

CO7 Acquire the essential knowledge of programming techniques and their usage – algorithms, flowcharts, and control structures


POs COs


CO1 √ √

CO2 √ √

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CO4 √

CO5 √ √ √

CO6 √ √

CO7

120

Course Contents


Hours

Section II

4. Computer Basics:

Generation and classification of computers, Computer system

component – CPU, Input Unit, Output Unit, Storage Unit, Applications

of Computers

9 HRS

Computer Architecture :

Details of components of digital computer system – CPU,

Communication among the various units, Instruction format, cycle

Inside the Computer :

Study of System cabin, SMPS, Motherboard, Ports and Interfaces,

Expansion Cards, Memory Chips, storage devices

5 Data Representation in Computer:

Types of number system, Binary, Octal, Hexadecimal and their

conversion, Types of coding schemes – ASCII & Unicode

10 HRS

Computer Software :

Operating system – types Operating system , functions , Unix /Linux ,

Windows 7 – Structures and Features

System Software – Interpreter , Assembler, Compiler

Application Software – Word Processor, Spreadsheets, Presentations ,

DBMS

Unix and Linux commands – Ls, CAT, CD, MKDIR, RMDIR and

Other command, & use of any editor in Linux

6 Computer Programming and Languages:

Program Development Cycle, Algorithm, Flowcharts, Programming

Control Structures – sequence, selection, repetition

programming languages – Introduction to low level and high level PL

10 HRS

Introduction to Computer Networks – Definition and needs of

computer network, standards – OSI, TCP/IP, Types of Networks –

LAN, WAN, MAN, Type of network topologies , Internet (WWW),

emerging computing environment

Reference Books:


01 Introduction to Information

Technology,

ITL, Education

Solutions LTD,

Pearson Education

ALL

02 Fundamentals of Computers V. Rajaram PHI Publications Unit No. 1

03 UNIX concepts and

applications SunitaBha Das, TMGH

Unit No. 5.3

04 Computer Fundamentals

Architecture and Organization

B. Ram New Age International

Publishers

Unit No. 4.2

121

Scheme of Marks


II 4.1 Generation and classification of computers, Computer system

component – CPU, Input Unit, Output Unit, Storage Unit,

Applications of Computers

8

4.2 Details of components of digital computer system – CPU,

Communication among the various units, Instruction format, cycle

8

4.3 Study of System cabin, SMPS, Motherboard, Ports and Interfaces,

Expansion Cards, Memory Chips, storage devices

8

5.1 Types of number system, Binary, Octal, Hexadecimal and their

conversion, Types of coding schemes – ASCII & Unicode

8

5.2 Operating system – types Operating system , functions , Unix /Linux

, Windows 7 – Structures and Features

System Software – Interpreter , Assembler, Compiler

Application Software – Word Processor, Spreadsheets, Presentations

, DBMS

8

5.3 Unix and Linux commands – Ls, CAT, CD, MKDIR, RMDIR and

Other command, & use of any editor in Linux

8

6.1 Definition and needs of computer network, standards – OSI, TCP/IP,

Types of Networks – LAN, WAN, MAN, Type of network

topologies , Internet (WWW), emerging computing environment

9

6.2 Program Development Cycle, Algorithm, Flowcharts, Programming

Control Structures – sequence, selection, repetition

programming languages – Introduction to low level and high level PL

9

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in


II 4.1 Computer Basics CO1 2 questions with

mixing of sub-

questions from Unit No.4

-

4.2 Computer Architecture CO1

4.3 Inside a computer system CO1

5.1 Data Representation in Computer CO2 2 questions

with mixing of

sub-questions from Unit No.5

& Unit No. 6.1

5.2

Computer Software –Types and

Functions, System Software CO3

Application Software‟s CO5

5.3 Unix and Linux commands CO4

6.1 Introduction to Computer Networks C06

6.2

Computer Programming and

Languages

CO7

122


Section I

Unit No 01 Unit Title Computer Basics, Architecture & Inside the

Computers

Planned

Hrs.

7

Unit Outcomes


UO1 To Acquire the essential knowledge of computer systems and peripherals CO1

UO2 To understand the architecture of computer

UO3 To get about the inside components of computers

Lesson schedule

Class

No.


1 Computer basics - H/W and S/W unit, characteristics of computers

2,3 Generation of Computers - Study of each generation of computers with its

characteristics and limitations

4 4. Classification of Computers - study of Minicomputers, Micro Computers

5 Mainframe and super computers with comparison of their characteristics and

advantages

6 Expose to Applications of Computers

7 Central Processing Unit, Registers, Control Unit

8 System Bus and its use, Cache Memory and Its Types

9 The Communication way from Processor to memory and Processor to I/O devices

Communication, Instruction format and Instruction Cycle

10 Inside the computer - System cabin, SMPS, Motherboard

11 Ports and Interfaces, Expansion Cards, Memory Chips, storage devices

Review Questions

Q1 Write a short note on characteristics & Applications of computer CO1

Q2 Explain generations of the computers CO1

Q3 Write down Classification of computers CO1

Q4 State the difference between the first and third generation of computers CO1

Q5 Explain the Central Processing unit of the Computer CO1

Q6 Explain System Bus and its use, Cache Memory and Its Types CO1

Q7 Explain Communication from Processor to memory and Processor to I/O

devices Communication, Instruction format and Instruction Cycle

CO1

Q8 write a short note on DMA / direct memory access unit CO1

Q9 Explain Instruction Cycle & describe the various steps involved CO1

Q10 What are expansion cards? How many types of expansion cards used in a

computer system

CO1

Unit

No

02 Unit Title Data Representation in Computer, Computer

Software Planned

Hrs.

8

Unit Outcomes


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UO1 To understand the Data representation & Number System CO2

UO2 To know operating system features and system software‟s CO3

UO3 To gain knowledge of Unix /Linux Commands CO4

U04 To acquire usages of application software and their uses CO5

Lesson schedule

Class

No.


12 The basics of number system, types of number system, Conversion from Decimal to

binary, octal and hexadecimal

13 The conversion from Binary number system to decimal, octal and hexadecimal

number system

14 The conversion of fraction decimal to other number systems and vice versa and coding

schemes

15 The conversion of Octal number system to Decimal, Hexadecimal, Binary number

system & conversion for fractional numbers

16 The conversion of Hexadecimal number system to Decimal, Binary, Octal number

systems and understanding of the Coding schemes

17 Computer Software‟s and their types, study of Operating System software‟s ,types,

functions and features

18 System software‟s - Assembler, Interpreter, compiler,

19 Understanding the usages of applications software - word processor, spreadsheet,

presentation and DBMS

20 The structure & features of Unix/Linux and Windows 7.0 operating system

21 Unix and Linux Commands

Review Questions

Q1 Convert following binary numbers into decimal numbers: 1010, 1101, 11011011 CO2

Q2 Write down the steps to convert the binary number to equivalent hexadecimal with example

CO2

Q3 Write down the steps to convert the Octal number to equivalent hexadecimal with example

CO2

Q4 Find out octal equivalent of (6A)16 , (123)10, (1010)2 CO2

Q5 State difference between system software and application software’s with example

CO3

Q6 Explain the spreadsheet application and their usage and DBMS applications CO5

Q7 Write a short note on application software’s CO5

Q8 Explain system software’s and explains assembler, interpreter and compiler CO3

Q9 Write a short note system software’s CO3

Q10 Explain the word processor its application CO5

Q11 Explain the presentation application software and its usage CO5

Q12 Explain following Linux/Unix commands -MKDIR, CAT, CD, LS CO4

Q13 Write a short note on Unix Operating system and its features CO4

Q14 List out and explain the types of operating system CO3

Q15 List out and explain the features of operating system CO3

124

Unit No 03 Unit Title Computer Programming & Languages,

Introduction to Computer Networks

Planned

Hrs.

7

Unit Outcomes


UO1 Demonstrate use of computer networks and internet CO6

UO2 Acquire the essential knowledge of programming techniques and their usage

– algorithms, flowcharts, and control structures

CO7

Lesson schedule

Class

No.


22 To understand the Computer Network - definition, function, and need, the types of

networks with its features

23 Types of networks topology

24 OSI model and TCP/IP Model

25 The computer language and comparative study of types of languages, program

development life cycle

26 Learning of algorithms and flowcharts and their usages

27 Writing algorithm and drawing flowcharts for simple programs

28 Control structures - conditional control structure - if, if...else and nested if else, and

writing algorithms and flowcharts for conditional programs

29 Learning of loop control structures - writing algorithm and flowcharts loop based

programs

Review Questions

Q1 Explain the types of network operating system CO6

Q2 Write a short note on Explain LAN, WAN and MAN CO6

Q3 Define the computer networks and explain needs CO6

Q4 Define the computer networks and explain its types CO6

Q5 Explain TCP/IP Model CO6

Q6 Explain OSI model CO6

Q7 Define the computer networks and explain the topologies of computer

network

CO6

Q8 Define the algorithms and list out the characteristics of algorithms CO7

Q9 Explain program development cycle CO7

Q10 State the difference between low level and high level programming

language

CO7

Q11 Write down the algorithm and flowcharts for following programming

statement – Accept the roll no and marks for subjects and display the total

and percentage. If percentage is less than 40 display fail, if percentage >40

and <60 display pass , otherwise display first class remark

CO7

Q12 Define flow chart & List out guidelines for preparing flowcharts CO7

Q13 Explain the basic program control structures with example CO7

125


Course Title : Fundamentals of Electronics & Computer Programming

Duration 3 hours Max.

Marks

Instructions: 50 1) Figures to the right indicate full marks

2) All Questions are compulsory.

3) Use of Non Programmable calculator is allowed.

Section-II

Marks

1 a Classify various computer system. Explain any three classification of

computers 8

b Explain Instruction Cycle in detail 8

c Explain Central Processing unit 8

2 a Convert

1. Hex to Binary ------------- CFG

2. Hex To Octal ------------- A217

3. Binary to Decimal ------- 111.0111

4. Binary to Hex ------------ 1111.11

8

b Explain following UNIX command with example – LS, CD, CAT &

MKDIR 8

c List and Explain the types of operating system

3 a Explain OSI Model 9

b Explain program development cycle 9

c List & Explain different types of computer networks 9

Assignments


Assignment No. 1

Assignment Title Study of basics of computer systems and peripherals CO1

Batch I Study of the computers with Central Processing Unit

Batch II Study of the computer architecture

Batch III Study of the computer internal components – SMPS, System Case etc

Assignment No. 2

Assignment Title To acquire the usages of the application software CO2,

CO3

126

Batch I Working with MS Word and problem solving with case study of generating

the students profile

Batch II Working with MS Excel and problem solving with case study of

generating the students mark sheet generation & employee salary

calculations

Batch III Working with MS PowerPoint and working with case study of generating

presentation on given subject

Assignment No.3

Assignment Title To gain the knowledge of Unix Operating system CO4

Batch I Explain the any Unix 2 commands

Batch II Differentiate between the MS DOS, Windows OS and Linux OS with

example

Batch III List out one operating system details as per the studied types of the

operating system.

Assignment No.3

Assignment Title Problem solving with Data Representation & Number

System

CO5

Batch I Explain the procedure to convert Decimal to binary, octal and hexadecimal

with minimum four examples [Consider the fractional number also]

Batch II Explain the procedure to convert binary to decimal, octal and hexadecimal

with minimum four examples. [ Consider the fractional number also]

Batch III Explain the procedure to convert octal to hexadecimal & vice versa with

minimum four examples. [ Consider the fractional number also]


Assignment No. 1

Assignment Title Understanding of the current trends of min, mainframe

and supercomputers in the angle of group discussion.

CO1

Batch I List out the recent names & usages top 3 mainframe, mini, micro and

supercomputers

Batch II List out the recent names & usages top mini computers & explain this

batch to the other students.

Batch III List out the recent names & usages top 3 supercomputers


Assignment No. 1

Assignment Title Understanding of Computer Network and emerging trends

of Internet & WWW. For this assignment students should

submit the combined report on the following assignments

given to them and oral will be conducted by the respective

subject teacher.

CO6

Batch I Explain how the internet works with the help of browser working.

Batch II Explain the Internet Service Providers

Batch III List out the to do list to get access with the Internet with respect to the

types of connection

127


Applied Mechanics

Course Applied Mechanics Course Code 40904

Examination

Scheme


Max. Marks 100 25 125

Contact

Hours/ week

3 -- 3

Prepared by Mr.D.R.Patil Date 08/05/2014

Prerequisites This course requires the students to know about the basic concepts of calculus,

vector mechanics and Newton‟s laws of motions.

Course Outcomes


CO1 Give practice in applying their knowledge of mathematics, science, and engineering

and to expand this knowledge into the vast area of “rigid body Mechanics”.

CO2 Design by requiring the solution of open ended problems.

CO3 Prepare the students for higher level courses such as courses in Mechanics of Solids,

Mechanical Design and Structural Analysis.

CO4 Understand the various force systems and its effect on static bodies and moving

bodies.

CO5 Find the resultant and locate it from any point for any given structures.

CO6 Calculate the support reactions for any given beam.

CO7 Determine the member forces in various members of a truss by method of joint or

section.

CO8 Understand geometric properties of plain lamina.

CO9 Understand dynamics of rigid bodies.

CO10 Design the speed of the vehicle at any angle of banking of road and super elevation.

CO11 Study the effect of impact loads on various bodies.

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POs

COs


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CO4 √ √ √

CO5 √ √ √

CO6 √ √ √ √ √

CO7 √ √ √

CO8 √

CO9 √

CO10 √ √

CO11 √

Course Contents

Unit

No. Title

No. of

Hours

Section I

1. Fundamentals of Statics:

Basic Concepts and Fundamental Laws, Force, Moment and Couple, System of

Forces, Resultant, Resolution and Composition of Forces, Varignon‟s Theorem,

Law of Moments.

07

2. Equilibrium:

Lamis‟ Theorem, Free Body Diagram, Equilibrium of Forces, Equilibrium

conditions, Surface friction for bodies on horizontal and inclined planes.

Beams:

Types of Loads, Types of supports, Analysis of Simple beams, Virtual work

method for support reactions.

07

3. Analysis of Truss:

Types of Trusses, Assumptions, Methods of Analysis:- Method of Joints.

Method of Section, Analysis of Simple truss with maximum seven members.

06

Section II

4. Centroid and Moment of Inertia:

Centroid and Center of Gravity, Moment of Inertia of Standard shapes from

first principle, Parallel and perpendicular axis theorem, Moment of Inertia of

plain and composite figures, Radius of Gyration.

07

5. Kinetics of Linear and Circular motion:

Introduction to Kinematics of Linear and Circular motion (no numerical on

kinematics), Kinetics of linear motion, Newton‟s Laws, D‟Alembert‟s

Principle, Work- Energy Principle, Impulse Momentum Principal, Kinetics of

Circular Motion.

09

129

6. Impact and Collision:

Impact, Types of Impact, Law of conservation of Momentum, Coefficient of

Restitution, Numerical on Direct central Impact.

04

Reference Books:


1. Vector Mechanics for

Engineers Vol.-I and II

F. P. Beer and E. R.

Johnston

Tata Mc-Graw Hill

Publication. All

2. Engineering Mechanics. Irving H. Shames Prentice Hall of India All

3. Engineering Mechanics S. Timoshenko Tata McGraw-Hill All

4. Strength of Materials S. Ramamrutham Dhanapat Rai

Publishing Company All

5. Engineering Mechanics S. S. Bhavikattis New Age

International Pvt. Ltd All

6. Engineering Mechanics R. K. Bansal and

Sanjay Bansal

Scheme of Marks


I 1, 2, 3 Fundamentals of Statics, Equilibrium and beams,

Analysis of trusses. 50

II 4, 5, 6 Centroid and moment of inertia, Kinetics of linear and

circular motion, Impact and collision. 50

Course Unitization

Sect

-ion

Unit Course

Outcomes No. of Questions in


I

1. Fundamentals of Statics CO1 2 questions

from units 1 &

2. Internal

option for Q2.b.

on unit2.

2. Equilibrium and beams CO2

3. Analysis of trusses CO3

II

4. Centroid and moment of

inertia CO4

5. Kinetics of linear and

circular motion CO5

2 questions from

units 5 & 6.

Internal option for

Q1.b. in unit 5 6. Impact and collision CO6

130


Section I

Unit

No 1 Unit Title Fundamentals of Statics

Planned

Hrs. 07

Unit Outcomes


UO1 Understand basic concepts and fundamental laws of motions.

UO2 Explain definition of force, various force systems, moment and couple.

UO3 Describe the types of force systems, moments and couples.

UO4 Differentiate between resultant and equilibrant force

UO5 Differentiate between resolution and composition of forces.

UO6 Prove and apply Varignon‟s theorem or law of moment.

UO7 Explain triangle law, parallelogram law and polygon law of forces.

UO8 Determine the resultant force of any force system and to locate it from any given point.

Lesson schedule

Class


1 Fundamentals of vector mechanics and laws of motions.

2 Definition of force, various force systems, moment and couple and types of all.

3 Differences between resolution and composition, resultant and equilibrant.

4 Various laws - triangle law, parallelogram law, polygon law of forces and law of

moment.

5 Numerical problems.



Review Questions

Q1 State and prove law of parallelogram law of forces.

Q2 Explain resolution and composition of forces.

Q3 State and explain “law of transmissibility of forces”

Q4 Define a force. State the characteristics of a force.

Q5 Define a couple and prove that moment of couple is constant anywhere in the plane of

couple.

Q6 Define and explain moment of force.

131

Q7 Define a force system. Name the different force systems.

Q8 What do you mean by moment and couple? Explain its types.

Unit

No 2 Unit Title Equilibrium and beams

Planned

Hrs. 07

Unit Outcomes


UO1 Understand Lami‟s theorem.

UO2 Describe the F.B.D.

UO3 Explain equilibrium conditions.

UO4 Evaluate frictional force of body on horizontal or inclined plane.

UO5 Know about the types of supports, loadings, beams.

UO6 Determine the support reactions by analytical method or by virtual work method.

Lesson schedule

Class


1 Equilibrium conditions- Analytical and graphical. Types and principle of equilibrium.

2 Free body diagrams and Lami‟s theorem.

3 Numerical problems on equilibrium. Types of supports, loadings, beams.

4 Numerical problems on equilibrium.

5 Types of supports, loadings, beams. Virtual work principle.



Review Questions

Q1 State the analytical conditions of equilibrium for coplanar concurrent forces and

coplanar non-concurrent forces.

Q2 Define and explain: i) Angle of repose, ii) Angle of friction, iii) Coefficient of friction.

Q3 With suitable examples explain F.B.D

Q4 State Lami‟s theorem. What are the limitations of it?

Q5 Write short notes on virtual work and virtual displacement.

Q6 Explain different types of beams.

Q7 State and explain principle of virtual work.

Q8 What are different types of beam supports?

Unit

No 3 Unit Title Analysis of trusses.

Planned

Hrs. 06

Unit Outcomes

132


UO1 Differentiate statically determinate and indeterminate trusses.

UO2 Differentiate perfect and imperfect trusses.

UO3 Explain assumptions made in the analysis of truss.

UO4 Differentiate two force, three force and zero force members.

UO5 Discuss the methods of analysis of truss.

UO6 Determine the forces in all the members of truss.

Lesson schedule

Class


1 Statically determinate and indeterminate trusses, perfect and imperfect trusses and

assumptions.

2 Various force members and method of analysis of truss.

3 Numerical problems on method of joints.

4 Numerical problems on method of sections.



Review Questions

Q1

What is difference between: A) Statically determinate and indeterminate truss,

B) Perfect and imperfect truss,

C) Deficient and redundant truss.

Q2 What are the assumptions made in the analysis of truss

Q3 What are two force, three force and zero force members?

Q4 State the methods of analysis of truss. Explain any one in detail.

Unit

No 4 Unit Title Centroid and moment of inertia

Planned

Hrs. 07

Unit Outcomes


UO1 Differentiate between Centroid and center of gravity.

UO2 Know various formulas to find out the location of C.G. and M.I. of various sections.

UO3 State parallel axes and perpendicular axes theorems.

UO4 Understand definition of radius of gyration and how to find it.

UO5 Determine M.I. for various sections.

Lesson schedule

Class Details to be covered

133

No.

1 Difference between Centroid and center of gravity.

2 Numerical problems on finding out location of Centroid.

3 M.I., Radius of gyration, parallel axes and perpendicular axes theorems.

4 M.I. of various sections such as triangle, rectangle, circle etc.




Review Questions

Q1 Explain the terms: A) Centroid and C.G., B) Polar M.I., C) Radius of gyration.

Q2 State and prove parallel axis theorem.

Q3 State and prove perpendicular axis theorem.

Q4 Derive an expression for M.I. of a circular section about its diameter, from first

principles.

Q5 Derive an expression for M.I. of a rectangular section about its base.

Q6 Using first principle, find the expression for M.I. of a triangle about its base.

Unit

No 5 Unit Title Kinetics of linear and circular motion

Planned

Hrs. 09

Unit Outcomes


UO1 Differentiate between linear motion and circular motion.

UO2 Understand effect of gravitational force on the body.

UO3 Study and draw the motion diagrams.

UO4 Get the basic equations of linear, circular motion and the combination of both.

UO5 Differentiate between centrifugal and centripetal force.

UO6 Design the maximum or minimum velocity on the curved roads.

UO7 1. Apply the Newton‟s second law of motion.

UO8 State D‟Alembert‟s principle & apply the same to the numericals.

UO9 Define work, power and energy.

UO10 State impulse-momentum principle and apply the same to the numericals.

UO11 Solve the numericals on the pile and hammer also.

Lesson schedule

Class


134

1 Linear motion and circular motion, basic equations.

2 Motion under gravity and motion diagrams.

3 Centrifugal and centripetal force, superelevtion, angle of banking.

4 Numericals on superelevtion.

5 Newton‟s second law of motion- theory and numericals.

6 D‟Alembert‟s principle, work energy principle.

7 Numericals on D‟Alembert‟s principle and work energy principle.

8 Numericals on D‟Alembert‟s principle and work energy principle.

9 Impulse-momentum principle- theory and numericals.

Review Questions

Q1 State and explain D‟Alembert‟s principle.

Q2 Distinguish between linear motion and circular motion.

Q3 Write a note on Centrifugal and centripetal force.

Q4 Derive the basic equations of linear motion.

Q5 Derive the expression for displacement in nth

second with uniform linear acceleration.

Unit

No 6 Unit Title Impact and collision

Planned

Hrs. 04

Unit Outcomes


UO1 Understand impact definition and types.

UO2 State law of conservation of momentum.

UO3 Know definition of coefficient of restitution.

UO4 Explain effect of direct central impact.

Lesson schedule

Class


1 Impact- definition and types, law of conservation of momentum.

2 Coefficient of restitution. Numericals.



Review Questions

Q1 Define and explain a) collision of elastic bodies and loss of K.E.

b) Law of conservation of momentum.

Q2 What do you mean by direct impact and indirect impact?

Q3 Define coefficient of restitution. Derive expression for it.

135


Course Title : Applied Mechanics

Duration: 3 Hrs. Max. Marks: 100

Instructions:

All questions are compulsory.

Use of non programmable calculator is allowed.

Section-I

Marks

1 a State and prove law of parallelogram law of forces. 4

b Find equilibrant force of the given force system w.r.t. point P.

12

2 a Write short notes on virtual work and virtual displacement. 6

b Two smooth cylinders A & B rest on a smooth inclined plane and

supported by smooth vertical plane as shown in fig. Determine

reactions at points of contact. Cylinder A weighs 500N and is 0.2 in

diameter, Cylinder B weighs 1200N and is 0.4 in diameter.

12

OR

b A beam ABCDE, simply supported at A &D, carries a U.D.L. of 20

KN/m from A to B; a point load of 20 KN at E and a clockwise

moment of 40KNm at C. Using principle of virtual work, determine

the support reactions. Take AB=2m, BC=CD=1.5m and DE=1m.

12

3 a What are the assumptions made in the analysis of truss? 4

b Determine the various member forces of the truss shown in fig. 12

136

4 a State and prove perpendicular axis theorem. 4

b Find the polar M.I. of the shaded lamina as shown in fig.

12

5 a Write a note on Centrifugal and centripetal force. 6

b Two masses of 80 kg and 20 kg are connected by a thread and move

along a rough horizontal plane under action of a 400 n as shown in fig.

The coefficient of friction at sliding surface is 0.3. Determine the

common acceleration of both objects and the tension in the string,

using D‟Alembert‟s principle.

12

OR 4

b A body of mass 30 kg is projected up on an inclined plane of slope 300

with an initial velocity of 10 m/sec. Take µ =0.2. Calculate a) distance

travelled before coming to the rest, b) the time required to reach the

highest point & c) the time required and final velocity to return to the

starting point.

12

6 a What do you mean by direct impact and indirect impact? 4

b The coefficient of restitution between two spheres of masses 1 kg and

5 kg is 0.75. The 1 kg sphere moving with a velocity of 3 m/sec strikes

the another sphere moving in the same direction with velocity

60cm/sec. Find the velocities of the two spheres after impact and the

loss of K.E. during impact.

6

c A 10 gm bullet is shot horizontally into a wooden block of mass 1 kg. 6

137

The bullet gets embedded in the block is displaced on a rough

horizontal table (µ=0.2) through 1m. What is the firing velocity of the

bullet?

Assignments


Assignment No. 1

Assignment

Title

Fundamentals of Statics

All Batches 1. A non-concurrent force system acts on a lamina as shown in the fig 1;

determine the magnitude of force P such that the resultant of the force system passes through point E. Hence determine the resultant.

Fig. 1

Fig. 2

2. For the force system shown in fig.2, find the resultant and its point of

application w.r.t. point A along the bar.

3. Find equilibrant force of the given force system w.r.t. point P. Refer fig. 3.

Fig. 3

138

Fig. 4

4. Forces of magnitude P, 2P, 3P, 4P and 5P act from the successive corners of

a rectangular pentagon towards the center of the pentagon. Find the magnitude and direction of the resultant force.

5. A member of a crane is attached by 3 cables. (Refer Fig.4). If TAC= 8 kN,

TAD=10.4 kN. Determine tension in the cable AE if resultant of three cables is directed along AB. Also find the corresponding resultant.

6. A bracket is subjected to three forces and a couple as shown in fig. 5.

Determine magnitude, direction and the line of action of the resultant

w.r.t. A.

Fig. 5

Fig. 6

7. Determine angle θ for which resultant of three forces is vertical. Also find

corresponding magnitude of R. Refer fig. 6.

8. A square plate 6cm X 6cm with its center at the origin is subjected to four

forces as under:

139

No. Magnitude From To

1 100 N (1,2) (3,3)

2 150 N (0,1) (-3,3)

3 200 N (-2,0) (-1,-3)

4 250 N (1,-2) (3,0)

The plate also carries a clockwise moment o 50 N-cm at its center.

Determine the magnitude, direction and the line of action of the resultant

w.r.t. in the X-axis.

9. Three concurrent forces –

i) 40 N along X- axis

ii) 40 N making angle α with negative Y –axis measured anti-

clockwise.

iii) 80 N making angle α with negative X –axis measured anti-

clockwise.

Find the angle α and the magnitude of the resultant force given that the

resultant is vertical (along Y axis).

Assignment No. 2

Assignment

Title

Equilibrium and beams

All Batches 1. Explain different types of loads.

2. Two blocks, tied together by a 200 inclined string are to be moved by a

force P as shown in the fig 1.. Find the magnitude of force P if the

coefficient of friction under block A is0.25 and block B is 0.4.

Fig. 1

Fig. 2

3. Two smooth cylinders A & B rest on a smooth inclined plane and

140

supported by smooth vertical plane as shown in fig. 2. Determine

reactions at points of contact. Cylinder A weighs 500N and is 0.2 in diameter, Cylinder B weighs 1200N and is 0.4 in diameter.

4. Two spheres of diameter 180mm and 60mm rests on three planes as

shown in fig.3. The weight of bigger sphere is 60N and that of smaller sphere is 30N. Determine reactions at points of contact.

Fig. 3

Fig. 4 5. Two blocks 1 and 2 of weighs 1290 N and 570 N are resting on the

horizontal surface as shown in fig. 4. The block 2 is attached to a vertical

wall by inclined string AB. Find the magnitude of the horizontal force P

that will be necessary to cause slipping to impend. Take µ between the

surface and the block as 0.4 and µ between blocks as 0.25.

6. Two cylinders of weighs 200 N & 100 N are hinged at their centers to a

rigid bar of negligible weight. What force should be applied to keep them

at the position as shown in fig?

7. A beam ABCDEF is supported at A & E. The beam carries a point load of

58KN acting vertically downloads at B; another point load of 85 KN at

point C making an angle of 71.5650 with horizontal; a udl of 18 KN/m

from D to F and a clockwise couple of 56 KNm at F. If support A is

141

hinged and support E is roller support, determine reactions at the supports.

Length(AB)=0.5m, L(BC)=L(CD)=L(DE)=1m, L(EF)=1.5m.

8. Find the support reactions for the beam shown in fig.

9. A beam ABCDE, simply supported at A &D, carries a U.D.L. of 20 KN/m

from A to B; a point load of 20 KN at E and a clockwise moment of

40KNm at C. Using principle of virtual work, determine the support

reactions. Take AB=2m, BC=CD=1.5m and DE=1m.

10. A simply supported beam of span 4 m supports a central point load of 100

KN and a central concentrated moment of 50 KNm (Clock-wise). Find

support reactions.

11. A simply supported beam AB is subjected to distributed load increasing

1500N/m to 4500 N/m from end A to B. AB=6m. Determine support

reactions.

Assignment No. 3

Assignment

Title

Analysis of trusses

All Batches 1. Determine the various member forces of the truss shown in fig. 1. by

method of sections.

Fig. 1

142

2. Determine the various member forces of the truss shown in fig.2. by

method of joints.

3. Determine the various member forces of the truss shown in fig.3. by

method of sections.

Fig. 3

Fig. 4

4. Find the forces in the members AB, AC, BD and VD as shown in fig. 4.

5. For the truss shown in fig.5. below, calculate the forces in each member.

Fig. 5

143

Fig. 6

6. Determine the various member forces of the truss shown in fig.6 by

method of joints.

7. A cantilever truss is subjected to loads as shown in fig. Find all the

member forces and tabulate the result.

Assignment No. 4

Assignment

Title

Centroid and moment of inertia

All Batches

1. Find Ixx, Iyy and polar M.I. of the shaded area shown in fig. 1 below.

Fig.1

144

Fig. 2

2. Find the polar M.I. of the shaded lamina as shown in fig. 2.

3. ABC is an isosceles triangle. A square of side “a” is removed from the

triangular laminar as shown in fig. The M.I. of the triangle about its base

reduces to 20%. Determine the side of the square.

4. Calculate M.I. for the shaded part of the lamina as shown in the fig.3

about the centroidal horizontal axis.

Fig.3

30

90

100

a

145

Fig.4

5. Compute the M.I. of the shaded area as shown in the fig. 4 about X-X

axis. Also calculate radius of gyration about XX axis.

6. For the section shown in fig.5, determine M.I. about two mutually

perpendicular axes.

Fig. 5 Fig. 6

Fig. 7

7. From a plate 4 cm X 8 cm, a semi-circle of 4 cm diameter is cut as shown

in fig. 6. „O‟ is the center of it. Determine the Centroid of remaining

portion of the plate and M.I. of the plate about its base.

8. For the composite section shown in fig. 7 determine the M.I. about its

base.

146

Assignment No. 5

Assignment

Title

Kinetics of linear and circular motion

All Batches 1. Two masses of 80 kg and 20 kg are connected by a thread and move along a

rough horizontal plane under action of a 400 n as shown in fig. The

coefficient of friction at sliding surface is 0.3. Determine the common

acceleration of both objects and the tension in the string, using D‟Alembert‟s

principle.

2. A circular automobile track has a radius of 183 m. The track is so designed

that when a car travels at a speed of 193 kmph, the force between the

automobile and track is normal to the surface of the track. Find the angle of

banking.

3. In what distance will body „A‟ shown in fig. attains a velocity of 3 m/s

starting from rest.

Take µ = 0.2. Assume pulley is smooth. What is the tension in the chord?

4. A pile of 500 kg mass is driven into ground by dropping a hammer freely,

having as mass of 318 kg through a height of 2.7 m. If the pile is driven into

the ground by 0.15m, calculate the average resistance of the soil.

5. Find at what maximum speed a vehicle can move round a flat curve of 60 m

radius without slide slip. Also find the limiting value of height of C.G. of

vehicle if overturning consideration should not limit the speed of vehicle on

this curve. Given weight of vehicle is 22 kN. Base width = 1.6 m. Coefficient

of friction between tires and road surface= 0.5.

6. A body of mass 30 kg is projected up on an inclined plane of slope 300 with

an initial velocity of 10 m/sec. Take µ =0.2. Calculate a) distance travelled

before coming to the rest, b) the time required to reach the highest point & c)

the time required and final velocity to return to the starting point.

7. A 10 gm bullet is shot horizontally into a wooden block of mass 1 kg. The

bullet gets embedded in the block is displaced on a rough horizontal table

(µ=0.2) through 1m. What is the firing velocity of the bullet?

8. A body weighing 300 N is pushed up on a 300 plane by a 400 N force acting

parallel to the plane. If the initial velocity of the body is 1.5 sec and µ = 0.2,

what velocity will the body have after moving 6 m?

147

Assignment No. 6

Assignment

Title

Impact and collision

All Batches 1. The coefficient of restitution between two spheres of masses 1 kg and 5 kg is

0.75. The 1 kg sphere moving with a velocity of 3 m/sec strikes the another

sphere moving in the same direction with velocity 60cm/sec. Find the velocities of the two spheres after impact and the loss of K.E. during impact.

2. A ball of 4 kg mass moving with velocity of 2m/s impinges directly on

another ball of 5 kg mass moving with a velocity of 1 m/s in opposite

direction. If e= 0.5, find the velocity of balls after impact. Also find the loss of

energy due to impact.

3. A ball of 100 gm mass strikes directly on another ball of same mass which is

at rest. The first ball comes to the rest due to the impact. Find the loss of K.E.

if e=0.707.

4. A vehicle of mass 600 kg and moving with a velocity of 12 m/s strikes

another vehicle of mass 400 kg moving at 9 m/s in the same direction. Both

get coupled together due to impact. Find the common velocity with which the two vehicles will move. Also find the loss of K.E. due to impact.

5. 80 N and 150 N bodies are approaching each other with a velocity of 20 m/s

and 6 m/s. What will be the velocity of each body after impact? How much is loss of K.E.? Take e=0.6. Assume 80N block is moving from LHS to RHS.

6. Three perfectly elastic bodies A,B and C of mass 20 kg, 40 kg and 80 kg

moving in the same direction with velocities of 4 m/s, 1m/s and 0.75 m/s

respectively. If the body A strikes with B, which in turns impact with the body

C, find the velocities of bodies after impact.

7. A vehicle of mass 600 kg and moving with a velocity of 12 m/s strikes

another vehicle of mass 400 kg moving at 8 m/s in the same direction. Both

get coupled together due to impact. Find the common velocity with which the

two vehicles will move. Also find the loss of K.E. due to impact.

148


Basic Mechanical Engineering

Course Basic Mechanical Engineering Course Code

Examination

Scheme


Max. Marks 100 25 125

Contact

Hours/ week

3 2 5

Prepared by P J Sawant/ S.S.Patil Date 01/05/2014

Prerequisites This course requires the student to know about the basics of physics, chemistry

& mathematics

Course Outcomes


CO1 Impart knowledge of basic concepts of thermodynamics applied to industrial

application

CO2 Understand basics of I. C. Engine and different cycles.

CO3 Understand basics of Refrigeration and Air conditioning systems

CO4 Understand principle of energy conversion system and power plants

CO5 Understand and identify power transmission devices with their functions

CO6 Learn and understand manufacturing process


POs COs


CO1 √ √ √ √

CO2 √

CO3 √

CO4 √

CO5 √ √

CO6 √

149

Course Contents


Hours

Section I

1. Thermodynamics.

Thermodynamic State, Process, Cycle, Thermodynamic System, Heat,

work, Internal Energy, First Law of Thermodynamics, Application of

First Law to steady Flow and Non-Flow processes, Limitations of First

Law (Numerical Treatment) Statements of Second Law of

Thermodynamics.

07

2. Introduction to I C Engine

Carnot Engine, Construction and Working of C.I and S.I., Two stroke,

Four Stroke Cycles, Air standard cycles- Carnot Cycle, Joule Cycle,

Otto Cycle, Air Standard efficiency (Descriptive Treatment only)

07

3 Introduction to Refrigeration and Air Conditioning:

Carnot refrigerator, Refrigerant types and properties, Vapour

compression and vapour absorption system, solar refrigeration, Window

Air Conditioning, Psychometric properties of moist air, Applications of

refrigeration and air conditioning (Descriptive Treatment only)

07

Section II

4 Energy Sources and power plants:

Renewable and non-renewable, Solar-flat plate collector, concentric

collector–Parabolic and cylindrical, Photovoltaic cell, Wind,

Geothermal, Tidal, Hydropower plant, Steam Power plant, Bio-gas, Bio-

Diesel (Descriptive Treatment only).

07

5 Mechanical Power Transmission and Energy conversion devices:

Type of Belt and belt drives, chain drive, Types of gears and gear

Trains, Types

of Coupling, Types of Bearings (Numerical Treatment on belt drive),

Types Construction, working and applications of Pumps, compressor

and Hydraulic Turbines

07

6 Introduction to manufacturing processes:

Casting Process, Steps involved in casting processes, and their

applications, Metal removing processes and their applications, Metal

Joining Processes – welding, soldering and brazing and their

applications.

07

Reference Books:


1 Solar Energy Dr.S.P. Sukathame Tata Mc-Graw Hill

Publication

4

2 Non-Conventional Sources of G.D. Rai Khanna Publication 4

150

Energy

3 Engineering Thermodynamics R.Joel

The English

Language Book

Society

1

4 Engineering Thermodynamics Achultan Prentice Hall of

India.

1

5 Thermal Engineering R.K. Rajput , Laxmi

Publication, Delhi

1

6 Elements of Heat Engine Patel and

Karamchandani

Acharya Book

depot.

1

7 Power Plant Engineering Arora and

Domkunwar

Dhanpat Rai and

Sons

1

8 Manufacturing Technology

Volume I and II P. N. Rao,

Tata Mc-Graw Hill

Publication

6

9 Elements of Workshop

Technology, Vol.I and II, Hajara Choudhari

Media Promoters

6

10 Basic Mechanical Engineering Basant Agrawal &

C. M. Agrwal

Wiley India Pvt.

Ltd.

1-6

11 Energy Technology S. Rao and Dr.B.B.

Parulekar Khanna Publication

4

Scheme of Marks


I 1, 2 and 3 Thermodynamics, Introduction to I C Engine,

Refrigeration and Air Conditioning System

50

II 4,5,and 6 Energy Sources and power plants, Mechanical

Power Transmission and Energy conversion devices,

Introduction to manufacturing processes

50

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in

No Title CAT-I CAT-II

I 1 Thermodynamics CO1 Q1, Q2 All Questions are compulsory.

2 Introduction to I C Engine CO2

3 Introduction to Refrigeration and Air Conditioning

CO3

II 4 Energy Sources and power plants CO4 Q1, Q2 All Questions are compulsory.

5 Mechanical Power Transmission and Energy conversion devices

CO5

6 Manufacturing Processes CO6

151


Section I

Unit

No

1 Unit Title Thermodynamics Planned

Hrs.

07

Unit Outcomes


UO1 Impart knowledge of basic concepts of thermodynamics applied to industrial

application

CO1

Lesson schedule

Class

No.


1 Thermodynamic State, Process, Cycle

2 Thermodynamic System

3 Heat, work, Internal Energy

4 First Law of Thermodynamics, Application of First Law to steady Flow and Non-Flow

processes

5 Limitations of First Law

6 Describe the second laws statement

7 Examples on steady Flow and Non-Flow processes

Review Questions

Q1 Steam enters a nozzle with a specific enthalpy of 2940 KJ/Kg with

initial velocity 25 m/s and leaves with a specific enthalpy at 2540 KJ/Kg

Determine the velocity of steam leaving the nozzle if the process is

isentropic and potential energy changes are ignored (L7) (May 2006)

CO1

Q2 Define following terms associated with thermodynamics-

Thermodynamic systems, Thermodynamic equilibrium, Perpetual

Motion machine of second kind, Point Function and Path Function (L2,

L4) (May 2009)

CO1

Q3 Explain Heat & work (Nov. 2007) CO1

Q4 A fluid at a pressure of 3 bar, and with specific volume of 0.18 m3/kg,

contained in a cylinder behind a piston expands reversibly to a pressure

of 0.6 bar according to a law, p =C/v2 where C is a constant. Calculate

the work done by the fluid on the piston. (May 2008)

CO1

Unit

No

2 Unit Title Introduction to I C Engine Planned Hrs. 07

152

Unit Outcomes


UO2 Understand basics of I C Engine and different cycles. CO2

Lesson schedule

Class

No.


1 Carnot Engine, Construction and Working of C.I and S.I. Engine

2 Two stroke Engine

3 Four stroke Engine

4 Air standard cycles- Carnot Cycle

5 Joule Cycle

6 Otto Cycle

7 Air Standard efficiency

Review Questions

Q1 Distinguish between Two Stroke Engine and Four Stroke Engine

(May 2010, May 2011, Nov 2012)

CO 2

Q2 Compare between S. I. Engine & C. I. Engine. (May 2013, Nov 2011) CO 2

Q3 Explain in detail with neat sketch Joule Cycle. Derive expression for

efficiency for the same. (May 2013, Nov 2011)

CO 2

Q4 Explain the working & construction of C. I. Engine. (May 2008, Nov 2010) CO 2

Q5 Explain the working & construction of S. I. Engine. (May 2009, Nov 2012) CO 2

Unit

No

3 Unit Title Introduction to Refrigeration and Air

Conditioning

Planned Hrs. 07

Unit Outcomes


UO3 Understand basics of Refrigeration and Air conditioning systems CO3

Lesson schedule

Class

No.


1 Carnot refrigerator, Refrigerant types and properties

2 Vapour compression system

153

3 Vapour absorption system

4 solar refrigeration

5 Window Air Conditioning

6 Psychometric properties of moist air

7 Applications of refrigeration and air conditioning (Descriptive Treatment only)

Review Questions

Q1 With the help of neat sketch, explain construction and working of window air

conditioner.(May 2013)

CO3

Q2 Define sensible heat, latent heat, total heat, dry steam. (May 2013) CO3

Q3 Define dryness fraction of steam, latent heat, superheated steam, dry

saturated steam. (Nov 2012)

CO3

Q4 Explain construction and working of vapour compression refrigeration

system with neat sketch. (May 2011, Nov 2011)

CO3

Q5 Define Refrigeration, air conditioning, ton of refrigeration, C.O.P. (May

2011, May 2009)

CO3

Q6 Explain vapour absorption refrigeration cycle with neat sketch. (Nov 2012) CO3

SECTION II

Unit

No

4 Unit Title Planned Hrs. 07

Unit Outcomes


UO4 Understand principle of energy conversion system and power plants CO4

Lesson schedule

Class

No.


1 Renewable and non-renewable energy sources

2 Solar-flat plate collector, concentric collector–Parabolic and cylindrical

3 Photovoltaic cell, Wind power plant

4 Geothermal power plant, Tidal energy

5 Tidal power plant, Hydropower plant

6 Steam Power plant

7 Bio-gas, Bio-Diesel (Descriptive Treatment only).

Review Questions

Q1 With the help of neat sketch explain Geothermal power plant. CO 4

154

(May 2013, Nov 2012)

Q2 Write short note on Bio Diesel ,solar dryer and solar distillation, wave energy.

(May 2013)

CO 4

Q3 What are drawbacks of solar energy ?. (Nov 2012) CO 4

Q4 Explain construction and working of fuel cell' (Nov 2012) CO 4

Q5 Explain with neat sketch construction and working of hydro electric power

plant. (May 2011)

CO 4

Q6 Write short note on solar collectors, tidal energy. (May 2011) CO 4

Unit

No

5 Unit Title Mechanical Power Transmission and

Energy conversion devices

Planned Hrs. 07

Unit Outcomes


UO5 Understand and identify power transmission devices with their functions CO5

Lesson schedule

Class

No.


1 Type of Belt and belt drives, chain drive.

2 Types of gears and gear Trains

3 Types of Coupling

4 Types of Bearings

5 Types Construction, working and applications of Pumps

6 Types Construction, working and applications of , compressor

7 Types Construction, working and applications of Hydraulic Turbines

Review Questions

Q1 An open belt drive connects two pulleys of 500 mm diameter and 2m apart.

Initial Tension in belt is 400 N. If coefficient of friction in belt is 0.25, find

power transmitted at 700 rpm. Also calculate length of belt. (May 2010)

CO5

Q2 Explain construction and working of Kaplan Turbine. (Nov 2012, May 2009,

May 2011)

CO5

Q3 Explain construction and working of Francis Turbine( Nov. 2011 ) CO5

Q4 Derive an expression for Length of Cross Belt Drive. ( Nov. 2008 ) CO5

Q5 Explain with neat sketch construction and working of Centrifugal pump. CO5

155

( Nov. 2010 )

Unit

No

6 Unit Title Manufacturing Process Planned Hrs. 07

Unit Outcomes


UO6 Learn and understand manufacturing process CO6

Lesson schedule

Class

No.


1 Introduction to manufacturing processes

2 Casting Process, Steps involved in casting processes

3 Casting and their applications

4 Metal removing processes

5 Metal removing applications

6 Metal Joining Processes – welding, their applications

7 Metal Joining Processes – soldering and brazing and their applications

Review Questions

Q1 What are the steps involved in casting process. CO6

Q2 What are the different metal removing process CO6

Q3 Explain the different types of metal joining process with example CO6

Q4 How welding is classified explain the applications of same CO6


Course Title : Basic Mechanical Engineering Max.

Marks

Duration 3 Hours 100

Instructions: 1Attempt any three questions from each section

Section-I

Marks

1 a Explain different thermodynamic systems with example. 08

b A mass of air has an initial pressure of 1.3 MN/m2, volume 0.14 m

3 and

temperature 1350 C. It is expanded until its final pressure is 275

KN/m2and its volume becomes 0.56 m

3. Take R=0.287 KJ/Kg K

Determine 1) The mass of air 2) The final temperature of air.

10

2 a Explain the working of S.I. Four stroke engine with neat sketch. 8

156

b Describe Carnot Engine 8

3

a Explain Vapour Absorption refrigeration Cycle. 8

b Explain following terms

1) Humidity 2)Dry air

3) Degree of Saturation 4) relative Humidity

8

4 a Differentiate between Two stroke and four Stroke I C Engine 4

b Explain Different Properties required for refrigerant 4

c Explain PMM-I and PMM-II 4

d Explain similarities between heat and work 4

Section-II

5 a Explain with neat sketch the hydroelectric power plant. Write advantages

of the plant over other power plants

10

b Explain wind energy power plant with neat sketch 6

6 a Explain the Centrifugal Pump with neat sketch 8

b Derive the derivation for length of cross belt 8

7 a Define manufacturing process with examples. Explain facing and turning

operation with neat sketch

8

b Explain sand casting process in detail. 8

8 a Explain welding process 6

b Explain with neat sketch different solar collectors 6

C Explain with neat sketch Oldham coupling 6

Assignments


Experiment No. 1

Assignment Title Two stroke and Four Stroke Engine CO2

Batch I Demonstration of Two stroke and four stroke engine

Batch II Demonstration of Two stroke and four stroke engine

Batch III Demonstration of Two stroke and four stroke engine

Batch IV Demonstration of Two stroke and four stroke engine

Experiment No. 2

Assignment Title Vapour Compression Refrigeration System CO3

Batch I Demonstration of vapour compression refrigeration system and window air

Conditioner.

Batch II Demonstration of vapour compression refrigeration system and window air

Conditioner.

157

Batch III Demonstration of vapour compression refrigeration system and window air

Conditioner.

Batch IV Demonstration of vapour compression refrigeration system and window air

Conditioner.

Experiment No. 3

Assignment Title solar water heating system. CO4

Batch I Demonstration of solar water heating system.

Batch II Demonstration of solar water heating system.

Batch III Demonstration of solar water heating system.

Batch IV Demonstration of solar water heating system.

Experiment No. 4

Assignment Title Diesel power plant CO4

Batch I Demonstration of Diesel power plant

Batch II Demonstration of Diesel power plant

Batch III Demonstration of Diesel power plant

Batch IV Demonstration of Diesel power plant

Experiment No. 5

Assignment Title Gears and gear trains. CO5

Batch I Demonstration of types of Gears and gear trains.

Batch II Demonstration of types of Gears and gear trains.

Batch III Demonstration of types of Gears and gear trains.

Batch IV Demonstration of types of Gears and gear trains.

Experiment No. 6

Assignment Title Pumps and compressor. CO5

Batch I Demonstration of pumps and compressor.

Batch II Demonstration of pumps and compressor.

158

Batch III Demonstration of pumps and compressor.

Batch IV Demonstration of pumps and compressor.

Experiment No. 7

Assignment Title Hydraulic turbine CO5

Batch I Demonstration of hydraulic turbine

Batch II Demonstration of hydraulic turbine

Batch III Demonstration of hydraulic turbine

Batch IV Demonstration of hydraulic turbine

Experiment No. 8

Assignment Title Metal joining processes. CO6

Batch I Demonstration of metal joining processes.

Batch II Demonstration of metal joining processes.

Batch III Demonstration of metal joining processes.

Batch IV Demonstration of metal joining processes.


Assignment No. 1

Assignment Title Metal removal process CO6

Batch I Demonstration of Metal removal process

Batch II Demonstration of Metal removal process

Batch III Demonstration of Metal removal process

Batch IV Demonstration of Metal removal process

159

FE Engineering Semester II

Engineering Mathematics II

Course Engineering Mathematics II Course Code 41410

Examination

Scheme


Max. Marks 100 25 -- 125

Contact

Hours/ week

3 1 -- 4

Prepared by Ms. Patil P. V. Date 30/04/2014

Prerequisites Basic knowledge of results from Algebra.

Knowledge of Derivatives.

Knowledge of Definite and Indefinite integration.

Basic knowledge Geometry and Trigonometry.

Course Outcomes


CO1 classify, Identify and solve different types of ordinary differential equations of

first order and first degree.

CO2 apply the knowledge of ordinary differential equation of first order and first

degree to solve engineering problems.

CO3 apply different numerical methods for solving differential equation of first order

and first degree

CO4 evaluate integrations by using special functions and understand the purpose of

special functions

CO5 able to trace and rectify the equations in Cartesian and polar form

CO6 solve double integral and formulate for area, moment of inertia, centre of

gravity, mass of lamina and solve.


POs

COs


CO1 √

CO2 √ √ √ √

CO3 √ √

CO4 √

CO5 √

CO6 √ √

160

Course Contents


Hours

Section I

1. Ordinary Differential Equations of First Order and First Degree:

1. Linear differential equations

2. Reducible to Linear differential equations

3. Exact differential equations

4. Reducible to Exact differential equations

07

2. Applications of Ordinary Differential Equations of 1st Order &1

st

Degree

1. Applications to Orthogonal trajectories (Cartesian & Polar equations)

2. Applications to Simple Electrical Circuits

3. Newton‟s law of cooling

4. Rate of decay and growth

06

3. Numerical Solution of Ordinary Differential Equations of First

Order and First Degree:

1. Taylor 's series method

2. Euler's method

3. Modified Euler's method

4. Runge-Kutta fourth order formula

5. Simultaneous 1st order differential equations by Runge–Kutta method

08

Section II

4. Special Functions:

1. Gamma function and its properties

2. Beta function and its properties

3. Differentiation under integral sign

4. Error function and its properties

06

5. Curve Tracing:

1. Tracing of curvesin Cartesian form a) Semi cubical parabola,

b)Cissiod of Diocles,c)Strophoid, d)Astroid, e) Witch of Agnesi,

f) Common Catenary, g)Folium of Descartes,

2. Tracing of curvesin polar form a)Cardioid, b) Pascal‟s Limacon,

c) Lemniscate of Bernoulli,d) Parabola, e) Hyperbola,

f)Rose curves

3. Rectification of plane curves (Cartesian and Polar form)

06

6. Multiple Integration and its applications

1. Double Integrals and evaluation

2. Change of order of integration

3. Double Integrals in Polar Coordinates

4. Change into Polar

5. Area enclosed by plane curves

6. Mass of a plane lamina

7. Center of Gravity of Plane Lamina

8. Moment of inertia of plane lamina

09

161

Reference Books:


1 Higher Engineering Mathematics Dr. B. S. Grewal Khanna

Publishers,

Delhi.

All



P. N. Wartikar & J.

N. Wartikar

Pune Vidyarthi

Griha Prakashan,

Pune.

All

3 Higher Engineering Mathematics H.K. Das and Er.

Rajnish Varma

Chand Technical

publication

All


Mathematics

N. P. Bali, Iyengar Laxmi

Publications (P)

Ltd., New Delhi

All


Mathematics

Erwin Kreyszig Wiley India Pvt.

Ltd.

All


Mathematics

H. K. Dass, S.

Chand

New Delhi All


Mathematics Volume I

Peter V. O‟Neil and

Santosh K. Sengar,

Cengage Learning

All

8 Mathematical Methods of

Science and Engineering

Kanti B. Datta,

Cengage

Learning.

All

9 Numerical Methods Dr. B. S. Grewal Khanna

Publishers,

Delhi.

4

10 Numerical Methods S.S. Shastri 4

11 Differential Equation and Partial

Differential Equation

M.D.

Raisinghaniya.

1 & 2

12 Computer Based numerical &

Statistical techniques

Masish Goyal Laxmi

Publication

3

13 Higher Engineering Mathematics B.V. Raman Tata McGraw

Hill

All



P. N. Wartikar & J.

N. Wartikar

Pune Vidyarthi

Griha Prakashan,

Pune.

All

162

Scheme of Marks


I 1 Ordinary Differential Equations of First Order and First

Degree

15

2 Applications of Ordinary Differential Equations of First

Order and First Degree 15

3 Numerical Solution of Ordinary Differential Equations

of First Order and First Degree 20

II 4 Special Functions 15

5 Curve Tracing 15

6 Multiple Integration and its applications 20

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in


I 1 Ordinary Differential

Equations of First Order

and First Degree

CO1 Q.1

(15 Marks)

2 Applications of Ordinary

Differential Equations of

First Order and First

Degree

CO2 Q.2

(15 Marks)

3 Numerical Solution of

Ordinary Differential

Equations of First Order

and First Degree

CO3 Q.1

(15 Marks)

II 4 Special Functions

CO4 Q.2

(15 Marks)

5 Curve Tracing CO5

6 Multiple Integration and its

applications

CO6

163


Section I

Unit

No

1 Unit Title Ordinary Differential Equations of First

Order and First Degree

Planned

Hrs.

08

Unit Outcomes


UO1 Identify an ordinary differential equation and its order CO1

UO2 Idea about general solution, particular solution and singular solution

UO3 Verify whether a given function is a solution of a given ordinary differential

equation

UO4 Classify ordinary differential equations into linear and nonlinear equations

UO5 Solve first order linear differential equations

UO6 To obtain the solution of non-linear differential equation

UO7 Find solutions of exact and non-exact equations

Lesson schedule

Class

No.


1 Differential equation, Degree, Order and types of solutions

2 Exact Differential equation

3 Reducible to exact ( Rule 1,2)

4 Reducible to exact ( Rule 3,4)

5 Examples

6 Linear Differential Equation

7 Non-linear Differential Equation

8 Examples

Review Questions

Q1 Explain Degree, order of differential equation UO1

Q2 Solve 2(sin .cos ) cos .sin tan 0xx y e dx x y y dy UO7

Q3 Solve 2 1 2 1 0x y dx y x dy UO7

Q4 Solve 2 2 2 2 2 2 0x y a xdx x y b ydy UO7

Q5 Solve 22 22 0a xy y dx x y dy UO5,UO

7

Q6 Solve 2 sin 0yx e dy y x x dx UO7

Q7 Solve 11 cos log sin 0y y dx x x x y dyx

UO5

Q8 Solve

2 log

dy y

dx y y y x

UO5,UO

7

Q9 Solve

2 2( ) 2 1

ydx xdy dx

x y x

UO3

164

Q10 Solve 2 3 2 2( 2 ) 2 3 0yxe xy y dx a x y xy dy UO7

Q11 Solve 22 0xy y dx xdy UO5

Q12 Solve ( ) 0yx xxe dx dy e dx ye dy UO7

Q13 Solve 2 21 ( 1)

dyx x y x x

dx

UO5

Unit

No

2 Unit Title Applications of ordinary differential

equations of first order and first degree

Planne

d Hrs.

07

Unit Outcomes


UO1 Understand the different applications of ordinary differential equations in

different streams

CO2

UO2 Meaning of Orthogonal trajectories

UO3 Formation of orthogonal trajectory using ordinary differential equation for

the given curve

UO4 Solve differential equation occurred in simple electric circuit

UO5 Solve examples on Newton‟s law of cooling by using ordinary differential

equations

UO6 Use Newton‟s Law of Cooling to solve problems

UO7 Solve examples on Rate of decay and growth by using ordinary differential

equations

Lesson schedule

Class

No.


1 Different engineering applications of ordinary differential equations

2 Formation of orthogonal trajectories of Cartesian curves

3 Formation of orthogonal trajectories of Polar curves

4 Examples on Simple R-L-E electric circuit

5 Examples on Simple R-C-E electric circuit

6 Study of Newton‟s law of cooling

7 Study of rate of decay and growth

Review Questions

Q1 Find orthogonal trajectories of given curves

a) 2 2

2 21

x y

a b , being of the parameter

b) (1 cos )r a

c)

21 cos

a

r

d) 2 2 2 0x y gx c , where g is parameter

e) 2 2 24x y a

UO3

Q2 A resistance of 100 ohms, an inductance of 0.5 Henry are connected in UO4

165

series with a battery of 20 volts. Find the current in a circuit as a function

of t

Q3 The equation of electromotive force in terms of current I for an electrical

circuit having resistance R and a condenser of capacity C, in series, is

iE Ri dt

C. Find the current I at any time t, when 0 sinE E wt

UO4

Q4 A constant emf E volt is applied to a circuit containing constant resistance

R Ω in series & constant inductance L H. If the initial current is zero show

that a current built up to half its theoretical maximum in log 2L

Rsec

Q5 The number N of bacteria in a culture grew at a rate proportional yo N.

The value of N was initially 100 and increased to 332 in one hour. What

was the value of n after 11

2 hours?

UO7

Q6 Water at temperature 1000C cools 10 minutes to 80

0C in a room

temperature 250C.

Find (i) the temperature of water after 20 minutes, (ii) the time when the

temperature is 400C.

UO5

Unit

No

3 Unit Title Numerical solutions of ordinary differential


Planned

Hrs.

08

Unit Outcomes


UO1 understand the need for numerical methods CO3

UO2 different numerical methods to solve ordinary differential equations

UO3 solve ordinary differential equations by Taylor‟s series method

UO4 solve ordinary differential equations by Euler‟s method

UO5 solve ordinary differential equations by Modified Euler‟s method

UO6 solve ordinary differential equations by Runge kutta fourth order method

UO7 solve simultaneous first order differential equation by Runge Kutta method

Lesson schedule

Class

No.


1 study of numerical methods to solve first order ordinary differential equations

2 Formula of Taylor‟s series method and examples

166

3 Formula of Euler‟s method and examples

4 Formula of Euler‟s modified method and examples

5 Examples

6 Formula of Runge kutta fourth order method and examples

7 Solutions of simultaneous first order differential equations by Runge kutta method

8 Examples

Review Questions

Q1 Solve using Taylor‟s series method, the differential equation

dyx y

dx

numerically. Start from x=1, y=0 and carry to x=1.2 with h=0.1. Compare the

final results with the value of the exact solution

UO3

Q2 Using Euler‟s method find the approximate value of y when x=1.5 in five

steps given dy y x

dx xy and y (1)=2

UO4

Q3 Use Euler‟s modified method to find the value of y satisfying the equation

log( )dy

x ydx

, y(1)=2 for x=1.2 and x=1.4 correct to three decimal by taking

h=0.2

UO5

Q4 Solve numerically (using Runge Kutta fourth order method) the differential

equation 2 2dyx y

dx with the given condition x=1, y=1.5 in the interval (1,

1.2) with h=0.1

UO6

Q5 Solve Numerically by RK method ;

dy dzyz x xz y

dx dx given that

(0) 1; ( ) 1y z o for (0.2), ( .2)y z o

UO7

Section II

Unit

No

4 Unit Title Special Functions Planned

Hrs.

07

Unit Outcomes


UO1 Recall the definition and properties of the gamma and beta functions. CO4

UO2 Express some integrals through the gamma and beta functions.

UO3 Explains the usefulness of these special functions.

UO4 Understand purpose and functions of the Beta and Gamma functions

UO5 Express n and ( , )m n through some factorials

UO6 Solve definite integrals by using differention under integral sign and error

functions

Lesson schedule

167

Class

No.


1 Gamma function and its properties

2 Beta function and its properties

3 Examples on beta function

4 Differentiation under integral sign with constant limits

5 Differentiation under integral sign with parameter limits

6 Error function and its properties

7 Examples on error function

Review Questions

Q1 Prove that Γ(n+1) = nΓn UO1

Q2

Evaluate the following integrals

a) 4

04x

xdx b)

1

0 1log

x

xdx c)

0

n axx e dx d) 24

0

xa dx

UO2

,

UO5

Q3 Evaluate the following integrals

1

3 5

0

(1 )x x dx b)

/2

20 11 sin

2

d

c)

1

1

(1 ) (1 )m nx x dx d)

1/47

3

( 3)(7 )x x dx

Q6 Show that

8 6

24

0

(1 )0

(1 )

x xdx

x

Q7 Show that

/2 2 1 2 1

2 2

0

sin cos 1( , )

( sin cos ) 2

m n

m n m nd B m n

a b a b

Q8 Prove that

/2 /2

0 0sin

dsin d

Q9

Prove that

1

3 30

2

3 31

dx

x

Q10

Evaluate 0

1x

axee dx

x

UO6

Q11

Prove that

1

0

1log

log 1

a bx x adx

x b; a > 0, b > 0

Q 12 Define error function and verify all properties

Unit

No

5 Unit Title Curve Tracing Planned

Hrs.

08

168

Unit Outcomes


UO1 Trace y=f(x) in Cartesian plane CO5

UO2 Trace r=f( ) in polar plane

UO3 Convert Cartesian to polar by standard transformation.

UO4 Trace rose curve

UO5 Find arc length of plane Cartesian and polar curve

Lesson schedule

Class

No.


1 Procedure to trace Cartesian curve

2 Tracing of Semi cubical parabola, Cissiod of Diocles, Strophoid, Astroid, Witch of

Agnesi

3 Tracing of Common Catenary, Folium of Descartes

4 Tracing of Cardioid, Pascal‟s Limacon, Lemniscate of Bernoulli

5 Tracing of Parabola, Hyperbola, Rose curves

6 Rectification of plane Cartesian form

7 Rectification of plane polar curve

8 Examples

Review Questions

Q1 Trace 2 2

3ay x a x UO1

Q2 Trace 2 3

y a x x

Q3 Trace 2 2 2y a x x a x

Q4 Trace r = a(1+cosѲ) UO2

Q5 Trace 3 2cosr

Q6 Trace sin2r a UO4

Q7 Find the total length of the curve 3sin

3r a

UO5

Q8 Find the length of loop of the curve

2

2 13

xy x

Q9 Find the perimeter of cardioide 1 cosr a and show that the line

2

3

divides upper half of cardioide into two parts.

Unit

No

6 Unit Title Multiple Integration and its applications Planned

Hrs.

10

Unit Outcomes


UO1 Define the double integral over a general region with its two types. CO6,

CO5 UO2 Evaluate a double integral over a rectangular region.

169

UO3 Find limits of double integration.

UO4 Reverse the order of integration.

UO5 Find the area using double integral.

UO6 Find the mass for a thin plate covering a region R.

UO7 Find the moments of inertia for a thin plate in the xy-plane.

UO8 Evaluate integral using Polar Coordinates.

Lesson schedule

Class

No.


1 Definition of double integration

2 Evaluation of Double Integration

3 Change of order of integration

4 Double integration in polar form

5 Change into polar form

6 Area by double integration

7 Mass of Plane Lamina

8 Center of gravity of Plane Lamina

9 M.I. of Plane Lamina

10 Examples

Review Questions

Q1

Evaluate

2 2

2 2 2

0 0

a ya

a x y dxdy

UO2

Q2

Evaluate

1 sin22

0 0

cos

a

r drdr

UO8

Q3 Change the order of integration and evaluate

2 2

0

aya

y

xdxdy

x y

UO3

UO4

Q4

Change to polar co-ordinates and evaluate

24 164

22 2

0

1

16

y

y

dxdyx y

UO3

UO8

Q5 Find the area enclosed by between the parabolas 2 4 1y x and

2 2 2y x

UO5

Q6 Find the mass of the lamina bounded by the curve 2 3y x and the line y x .

If the density at a point varies as the distance of the point from X-axis.

UO6

Q7 Find the M.I. of the semi-circle about the line joining one end of the bounding

diameter to the midpoint of the arc.

UO7

170


Course Title : Engineering Mathematics II Max.

Marks

Duration 3 Hours 100

Instructions:

All questions are compulsory

Figures to the right indicates full marks

Use of non-programmable calculator is allowed

Section-I

Marks


a Solve 2

(sin .cos ) cos .sin tan 0x

x y e dx x y y dy 5

b Solve

2 2( ) 2 1

ydx xdy dx

x y x

5

c Solve

x y yxdye e e

dx

5

d Solve 2cos tan

dyx y x

dx

5


a Find orthogonal trajectory for the curve 2 2 cos2r a 5

b A voltage atEe is applied at t=0 to a circuit containing inductance L

and resistance R. Show that the current at any time t is Rt

at LE

e eR aL

5

c According to Newton‟s law of cooling, the rate at which a substance

cools in moving air is proportional to the difference between the

temperature of the substance that of the air. If the temperature of the air

is 300C and the substance from 100

0C to 70

0C in 15 minutes, find when

the temperature will be 400C.

5

d Uranium disintegrates at rate proportional to the amount present at any

instant. If M1 and M2 grams of uranium are present at a time T1 and T2

respectively, show that the half life of uranium is 2 1

1

2

log 2

log

T T

MM

5


a Using Taylor‟s series method, Obtain correct upto four decimal places,

a solution of the differential equation 2 2dyx y

dx with y=o when x=0

at x=0.4

5

171

b Given that 2dy

x ydx

and y=1 at x=0. Find an approximate value of y

at x=0.5 using Euler‟s method.

5

c Use Euler‟s modified method to solve 2 , (0) 1

dyx y y

dx. Find (0.4)y

taking h=0.2

5

d Use Runge kutta fourth order method to solve

( ) 1, (0) 1 1dy

x y y for xdx

5

e Solve Numerically by RK method ;

dy dzyz x xz y

dx dxgiven that

(0) 1; ( ) 1y z o for (0.2), ( .2)y z o

5

Section-II

Marks


a Evaluate

2 2h xe dx 5

b Evaluate 4 tan 2

/2tan sec

0e d

5

c Evaluate

5 2sin cos0

x x x dx 5

d Prove that

2 2

2 2

cos 1log ; , 0

20

x bax bxe e dx a bx a

;

a > 0, b > 0

5


a Trace

3 33y axyx

5

b Trace

11 cos

r

5

c Trace cos4r a 5

d For the curve

2

2 13

xy x prove that 2 2 24

3s y x , where s being

measured from origin to (x, y).

5


a Evaluate

22

2 2

1 2

2

y

y

x y dxdy 5

b Change the order of integration and evaluate

2

2

0

a a x

xa

xy dxdy 5

172

c Change to polar coordinates and evaluate

22 21R

dxdy

x yover one loop

of the lemniscates 2

2 2 2 2x y x y

5

d Find the mass of the lamina of the region included between the curves

y = log x, y = 0 , x = 2, having uniform density.

5

e Find area of the ellipse by using double integration 5

Assignments


Assignment No. 1

Assignment

Title

Differential equation of 1st order & 1

st degree CO1

Batch I Solve the following differential equations

1. 2(sin .cos ) cos .sin tan 0xx y e dx x y y dy

2. 2 1 2 1 0x y dx y x dy

3. 2 2 2 2 2 2 0x y a xdx x y b ydy

4. 22 22 0a xy y dx x y dy

5. 2 sin 0yx e dy y x x dx

6. 11 cos log sin 0y y dx x x x y dyx

7. 2 log

dy y

dx y y y x

8. 2 2( ) 2 1

ydx xdy dx

x y x

9. 2 3 2 2( 2 ) 2 3 0

yxe xy y dx a x y xy dy

10. 22 0xy y dx xdy

11. ( ) 0yx xxe dx dy e dx ye dy

173

12. 2 21 ( 1)

dyx x y x x

dx

13. x y yxdy

e e edx

14. 2 2 2 3 33 1 (2 1)

dyx x y x y ax

dx

15. 2cos tan

dyx y x

dx

Batch II Solve the following differential equations

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

2 3 xdyy e

dx

2 2(1 ) (1 ) 0y xy dx x xy x y dy

2 3(3 ) log 0y

x y dx x x dyx

22 22 0a xy y dx x y dy

1dx

x ydy

tan(1 ) sec

1

xdy yx e y

dx x

2

1

4 33 xdy

x y x e ydx

2 2( ) 2 1

ydx xdy dx

x y x

4 2 2 3 2 43 2(5 3 2 ) 2 3 5 0x x y xy dx x y x y y dy

2secy ydx xdy e dy

2

2

log (log )dy y y y y

dx x x

174

12.

13.

14.

15.

16.

Batch III Solve the following differential equations

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

2 21 ( 1)dy

x x y x xdx

x y yxdye e e

dx

2 2 2 3 33 1 (2 1)dy

x x y x y axdx

2 2 2(1 2 cos 2 ) (sin ) 0xy x xy dx x x dy

2 2

3

1 3

1 2

dy y x y

dx xy x

2 3 xdyy e

dx

2 2(1 ) (1 ) 0y xy dx x xy x y dy

22 22 0a xy y dx x y dy

tan(1 ) sec

1

xdy yx e y

dx x

2 2( ) 2 1

ydx xdy dx

x y x

4 2 2 3 2 43 2(5 3 2 ) 2 3 5 0x x y xy dx x y x y y dy

2

2

log (log )dy y y y y

dx x x

2 21 ( 1)dy

x x y x xdx

x y yxdye e e

dx

2 2 2 3 33 1 (2 1)dy

x x y x y axdx

175

11.

12.

Assignment No. 2

Assignment

Title

Applications of differential equation of 1st order & 1

st degree CO2

Batch I 1. Find the Orthogonal Trajectories of the following curves

a) 2 2 24x y a

b) sinn nr a n

c) 2 2 4 2 0y x xy cx

d) 2 2 2 0x y gx c ; where „g‟ is parameter

e) 2 3ay x

f) (1 cos )r a

2. A voltage atEe is applied t =0 to a circuit containing inductance L &

resistance R. Find current at any time t if initially t=0, I =0.

3. When a switch is closed, the current built up in an electric circuit is given

by di

E Ri Ldt

. If L=640, R=250, E=500 & i=0 when t=0. Show that

the current will approach 2 amp when t=∞.


resistance R. Show that any time t the current

Rtat LE

i e eR aL

5. A constant emf E volts is applied to a circuit containing constant resistance

R Ω in series & constant inductance L H. If the initial current is zero show

that a current built up to half its theoretical maximum in log2L

Rsec

Batch II 1. Find the Orthogonal Trajectories of the following curves

g) 2 2 24x y a

2 2 2(1 2 cos 2 ) (sin ) 0xy x xy dx x x dy

2 2

3

1 3

1 2

dy y x y

dx xy x

176

h) sinn nr a n

i) 2 2 4 2 0y x xy cx

j) 2 2 2 0x y gx c ; where „g‟ is parameter

k) 2

1 cos

ar

l) (1 cos )r a

m) 1p px cy




by di

E Ri Ldt



4. A circuit consists of a resistance R ohms and a condenser of C farads

connected to a constant e.m.f. E. If q/c is the voltage of the condenser at

time t after closing the circuit, show that the voltage at any time t is

E 1 t CRe

5. A 200 ohms resistor is connected in series with a capacitor of 0.001 farad

& e.m.f of 400e-3t

. If q =0 at t=0, find the maximum charge on the

capacitor.

Batch III 1. Find the Orthogonal Trajectories of the following curves

n) 2 2 24x y a

o) sinn nr a n

p) 2 2 4 2 0y x xy cx

q) 2 2 2 0x y gx c ; where „g‟ is parameter

r) 2

1 cos

ar

s) (1 cos )r a

177

t) 1p px cy




by di

E Ri Ldt



4. A circuit consists of a resistance R ohms and a condenser of C farads

connected to a constant e.m.f. E. If q/c is the voltage of the condenser at

time t after closing the circuit, show that the voltage at any time t is

E 1 t CRe

5. A 200 ohms resistor is connected in series with a capacitor of 0.001 farad

& e.m.f of 400e-3t

. If q =0 at t=0, find the maximum charge on the

capacitor.

Assignment No. 3

Assignment

Title

Numerical Solutions of differentiation of 1st order & 1

st degree

CO3

Batch I 1) Given that 2

dyxy

dxwith 1 1y . Find the value of y at x=2 in steps

of 0.2 by using Euler‟s method.

2) Use Euler‟s method to solve 21

dyy

dx with 0 0y obtain 0.1y ,

0.2y , 0.3y , 0.4y and 0.5y

3) Use Euler‟s modified method to find 0.2y , given that 2 0dy

ydx

with

0 1y by taking h=0.1

4) Solve 2dy

xydx

with 0 1.2x and 0 1.6403y by Euler‟s Modified

Method for 1.4x

5) Given the differential equation 2

1dy

dx x y with (4) 4y . Obtain (4.1)y

and (4.2)y by Taylor‟s series method.

178

6) Use Taylor‟s series method to solve 2 1

dyx y

dx with (0) 1y for

0.03x

Batch II 1) Given that 2

dyxy

dxwith 1 1y . Find the value of y at x=2 in steps

of 0.2 by using Euler‟s method.

2) Use Euler‟s method to solve 21

dyy

dx with 0 0y obtain 0.1y ,

0.2y , 0.3y , 0.4y and 0.5y

3) Use Euler‟s modified method to find 0.2y , given that 2 0dy

ydx

with

0 1y by taking h=0.1


1dy



5) Use Taylor‟s series method to solve 2 1

dyx y

dx with (0) 1y for

0.03x

6) Given that 2dy

x ydx

with 0 1y . Find the value of y at x=0.1 by

using Euler‟s modified method by taking h= 0.05

Batch III 1) Given that

2dyx y

dxwith 0 1y . Find the value of y at x=0.1 by

using Euler‟s modified method by taking h= 0.05

2) Use Euler‟s method to solve 2dy

x ydx

with 0 1y obtain 0.1y

with h = 0.02

3) Use Euler‟s method to find 0.1y , given that dy

x y xydx

with

0 1y by taking h =0.025

4) Solve 2dy

xydx

with 0 1.2x and 0 1.6403y by Euler‟s Modified

Method for 1.4x

179


1dy



6) Use Taylor‟s series method to find y upto four decimal places for

(1 ) 0xy dx dy with (1) 2y at 1.02x and also write series for y.

Assignment No. 4

Assignment

Title

Numerical Solutions of differentiation of 1st order & 1

st degree

CO3

Batch I

1) Using Runge Kutta Method, Solve

2 2

2 2

dy y x

dx y x with (0) 1y at 0.2x

and 0.4x

2) Solve 2dy

x ydx

with (0) 1y at 0.2x by Runge Kutta Method by

taking h = 0.1.

3) Solve the simultaneous first order differential equations by Runge Kutta

fourth order Method 1,dy dz

xz xydx dx

for 0.3x Given

0, 1, 0y z when x



x z x ydx dx

with

0 0 00, 2, 1 0.1x y z taking h


fourth order Method ,dx dy

y t x tdt dt

with initial conditions

1, 1, 0, 0.1x y whent taking h

Batch II 1) Using Runge Kutta Method, Solve

2dyxy x

dx with (0) 1y at

0.2x in two steps

2) Find y when 1.2x , given that 2

2 11

dy xy

dx x with 0 1x , 0 2y

and 0.2h by using R-K Method.



xy t ty xdt dt


1, 1, 0, 0.1x y when t taking h


180


xz ydx dx

with

1, 1, 0 0.2y z x taking h


fourth order Method ,dy dz

x z x ydx dx

with

0, 1, 0 0.1y z when x taking h

Batch III

1) Using Runge Kutta Method, Solve

2 2

2 2

dy y x

dx y x with (0) 1y at 0.2x

and 0.4x

2) Solve 2dy

x ydx

with (0) 1y at 0.2x by Runge Kutta Method by

taking h = 0.1.



y t x tdt dt


1, 1, 0, 0.1x y whent taking h



x z x ydx dx

with

0 0 00, 2, 1 0.1x y z taking h



xz xydx dx

for 0.3x Given

0, 1, 0y z when x

Assignment No. 5

Assignment

Title

Special functions

CO3

Batch I 1) Prove that Γ(n+1) = nΓn

2) Evaluate the following integrals

i)

4

04x

xdx ii)

1

0 1log

xdx

x

iii)

0

n axx e dx iv) 24

0

xa dx


i)

1

3 5

0

(1 )x x dx ii)

1/47

3

( 3)(7 )x x dx

181

4) Prove that

/2 /2

0 0sin

dsin d

5) Prove that

1

3 30

2

3 31

dx

x

6) Prove that

1

0

1log

log 1

a bx x adx

x b; a > 0, b > 0

7) Verify the rule of differentiation under integral sign for the integral 2

1

0

tan

ax

dxa

8) Define error function and state and prove any two properties of error

function

Batch II 1) Evaluate the following integrals

a)

0

n axx e dx d) 24

0

xa dx e) 2 2h xe dx


1)

/2

20 11 sin

2

d 2)

1/47

3

( 3)(7 )x x dx

3) Show that

8 6

24

0

(1 )0

(1 )

x xdx

x

4) Show that

/2 2 1 2 1

2 2

0

sin cos 1( , )

( sin cos ) 2

m n

m n m nd B m n

a b a b

5) Evaluate

0

1x

axee dx

x

6) Prove that 1

0

1log

log 1

a bx x adx

x b; a > 0, b > 0

7) Verify the rule of differentiation under integral sign for the

182

integral

2

1

0

tan

ax

dxa

8) Define error function and state and prove any two properties of error

function

Batch III 1) Prove that (n+1) = nΓn


1)

1

0 1log

xdx

x

2)

0

n axx e dx

3) 24

0

xa dx 4) 2 2h xe dx


1.

1

3 5

0

(1 )x x dx 2.

1 25

2

0

1

1

xx dx

x

4) Prove that

/2 /2

0 0sin

dsin d

5) Prove that 2 1

1.3.5.7...(2 1)2

n

n n

Assignment No. 6

Assignment

Title

Curve Tracing and Rectification CO6

Batch I Q1) Trace the following curve

1) 2 23ay x a x

2) 2 3y a x x

3) 2 2 2y a x x a x

4) 3 3 3x y axy

5) 3 2cosr

6) 2 3cosr

7) sin2r a

8) 1 cosr a

183

Q2) Find the total length of the curve 2 2 sin 2r a

Q3) For the curve

2

2 13

xy x prove that

2 2 24

3s y x , where s being

measured from origin to (x, y)

Q4) Find the length of loop of the curve 2/3 2/3 2/3x y a

Q5) Find the perimeter of cardioide 1 cosr a and show that the line

2

3 divides upper half of cardioide into two parts.

Batch II Trace the following curve

1) 2 23ay x a x

2) 2 3y a x x

3) cosh( / )y c x c

4) 3 3 3x y axy

5) 2 1cosr

6) 1 2cosr

7) sin2r a

8) 1 cosr a

Q2) Find the total length of the curve 2 2 cos2r a

Q3) Find the length of loop of the curve

2

2 13

xy x

Q4) Find the perimeter of cardioids 1 cosr a

Batch III Trace the following curve

1) cosh( / )y c x c

2) 2/3 2/3 2/3x y a

3) 2 2 2y a x x a x

4) 32y x a

184

5) cos ,r a b a b

6) 2 3cosr

7) cos2r a

8) 1 sinr a

Q2) Find the total length of the curve 1 cosr a

Q3) Find the length of loop of the curve 223ay x x a

Q4) Find the arc length of the curve coshx

y cc

which is measured from (

0, c) to

any point P(x, y)

Q5) Find the total length of the curve sin2r a

Assignment No. 7

Assignment

Title

Multiple Integrals CO7

Batch I 1) Evaluate following integrals

a)

(1 cos )

2

0 0

2 sin

a

r drd b)

2 2

2 2 2

0 0

a ya

a x y dydx

Q.2 Change the order and evaluate

a)

21 1

2 20 0 (1 ) 1

x

y

dydx

e x y b)

22

0 ( )

ya

ya

ydydx

a x ax y

Q.3 Evaluate xydxdy over the region bounded by 2 2y x and x y .

Q.4 Evaluate 3x dxdy over the circle

2 2 2x y ax .

Q. 5 Change to polar co-ordinates and evaluate

a)

3

2 20 0

a xx dxdy

x y b)

22 2

2 20 0

x xxdxdy

x y

Batch II 1) Evaluate following integrals

185

a)

/4 cos 2

22

0 0 1

rdrd

r b)

1

0 0

x

x ye dydx


a) 2

1 4

0 4

x

y

e dxdy b)

21 2

2 20

x

x

xdydx

x y

Q.3 Evaluate 2 2( )x y dxdy over the area of triangle whose vertices are

(0,1), (1,1) and (1,2)

Q.4 Evaluate 3r drd over the area included between the circles

2sin 4sinr and r .


a)

3

2 20 0

a xx dxdy

x y b)

2 2

22 2 2

0

a a x

ax x

dxdy

a x y

Batch III 1) Evaluate following integrals

a)

/2 cos

2 2

0 0

a

r a r drd b)

1 11/21/3 1/2

1 0

1x

x y x y dydx


a)

2 2

2

0 0

log( )

( )

a a yaxy x a dx

dyx a

b) 2

2

0

a a x

xa

xydxdy

Q.3 Evaluate 2 2 2a x y dxdy over the semi circle

2 2x y ax in

the positive quadrant

Q.4 Evaluate 2 2

rdrd

r a over the one loop of lemniscates

2 2 cos2r a .


a)

2 2

22 2 2

0

a a x

ax x

dxdy

a x y

b)

22 2

2 20 0

x xxdxdy

x y

186

Assignment No. 7

Assignment

Title

Applications of Multiple Integrations

Batch I 1. Find the area enclosed by between the parabolas 2 4 1y x and

2 2 2y x

2.Find the total area of sin 2r a

3.The density at any point of a cardioid (1 cos )r a varies as the square of its

distance from its axis of symmetry. Find its mass

4.Find the mass of the lamina bounded by the curve 2 3y x and the line y x . If

the density at a point varies as the distance of the point from X-axis.

5.Find the center of gravity of the area bounded by 2 2y x and x y

6.Find the C. G. of the arc of the cardioid (1 cos )r a lying above the initial

line.

7.Prove that the M. I. of the area included between the parabolas 2 4y ax and

2 4x ay about the x axis is 2144

35Ma where M is the mass of the area included

between the curves.

Batch II 1.Find the total area of (1 cos )r a

2.Find the total area bounded by 2 3(2 )y a x x and its asymptote

3.Find the mass of the lamina in the form of an ellipse 2 2

2 21

x y

a b if the density

at any point varies as the product of the distance from the axes of the ellipse

4.The density of a circular lamina is k times its distance from a given diameter.

Find its mass

5.Find the C. G. of the lamina bounded by 22 3y x and the line

3 2 1x y

6. Find the C. G. of the loop sin 2r a

7. An area is bounded by the curve coshx

y cc ,

The axes and the ordinate x=c. Find the radius of gyration about the y - axis

Batch III 1.Find the total area of (1 cos )r a

2.Find the total area bounded by 24y x x and theline y x

3.The density at any point of a cardioid (1 cos )r a varies as the square of its

distance from its axis of symmetry. Find its mass

4.Find the M.I. of the semi-circle about the line joining one end of the bounding


5.Find the C. G. of the area of the curve 2/3 2/3 2/3x y a lying in the first

quadrant

6.Find the centroid of the loop of the lemniscates 2 2 cos 2r a

7.Find the M.I. of the semi-circle about the line joining one end of the bounding

187


List of Tutorials

1. Examples on Differential equations

2. Examples on linear and reducible to linear Differential equations

3. Examples on applications of Differential equations

4. Examples on Eulers method, Modified Euler,s Method, and Taylor‟s series

method to solve differential equations of first order and first degree

5. Examples on Runge kutta method to solve differential equations of first order and

first degree and Runge kutta 4th

order method to solve simultaneous differential


6. Examples on Beta and Gamma function

7. Examples on differentiation under integral sign and Error function

8. Examples on tracing of curves in Cartesian and polar form

9. Examples on rectification in Cartesian and polar form

10. Examples on Multiple Integration


Assignment

1. Solve above given assignments by using scilab and verify your answer

2. Trace given curves by using software’s like function plotter

188

FE Engineering Semester II

Professional Communication -II

Course Professional Communication -II Course Code

Examination

Scheme


Max. Marks 25 25

Contact

Hours/ week

1 2 -- 3

Prepared by Mr. B. B. Pujari/ Dr. U. P. Jadhav Date 02/05/2014

Prerequisites English Language Skills-LSRW, usage of language in different situations;

execution of all the skills of language according to the need of situation

Course Outcomes


CO1 Write reports of various kinds

CO2 Know who he/she is and build positive attitude

CO3 Acquire decision making, leadership and problem solving skills

CO4 Know what is IQ and EQ

CO5 Develop in him/ her confidence and involve more in team work, public

speaking, debate, group discussion activities

CO6 Practice corporate manners and etiquettes

CO7 Know interview techniques and planning and managing careers


POs

COs


CO1 √

CO2 √

CO3 √ √

CO4 √

CO5 √ √

CO6 √ √

CO7 √

189

Course Contents


Hours

1. Developing writing skills 02

2. Behavioral skills 03

3. Presentation skills 03

4. Career Skills 02

Reference Books:


1 Handbook for Technical

Writing

David A.

McMurrey, Joanne

Buckley

Cengage 1

2 Communication Skills

Handbook: How to succeed in

written and oral

communication

Jane Summers,

Brette Smith

Wiley India

Pvt.Ltd

1 and 3

3 Soft Skills for Managers T. Kalyana

Chakravarthi, T.

Latha Chakravarthi,

Biztantra 2 and 4

4 Soft Skills for every one Jeff Butterfield Cengage 2, 3 and

4

5 Behavioral Science Abha Singh, Wiley India

Pvt.Ltd

2

6 An Introduction to Professional

English and Soft Skills

Bikram K. Das,

Kalyan Samantray

Cambridge

University

Press New Delhi.

2,4

7 Speaking Accurately K.C. Nambiar Cambridge

University Press

New Delhi

3

8 Speaking Effectively Jeremy Comfort,

Pamela Rogerson

Cambridge

University Press

New Delhi.

3

9 Cambridge English for Job

Hunting

Colm Downes Cambridge

University Press

New Delhi.

4

10 Body Language Allen Pease 3,4

190


Section I

Unit No 1 Unit Title Developing writing skills Planned

Hrs.

03

Unit Outcomes: To know the nature and importance of advanced technical writing,

techniques and types of report writing – survey, inspection and

investigation, data collections methods and utilization,


UO1 Understand advanced technical writing ,data collection and methods and its

utilization

CO1

UO2 Know the techniques of report writing and types of reports – survey,

inspection and investigation

CO1

Lesson schedule

Class

No.


1 Importance of advanced technical writing

2 Techniques of report writing, Data collection methods and utilization

3 Report Writing – survey , inspection and investigation

Unit No

2 Unit Title Behavioral skills Planned

Hrs.

04

Unit Outcomes: to study


UO1 Understand self-SWOT analysis, type of personality, personality traits CO2

UO2 Learn and practice techniques of developing positive attitude CO2

UO3 To apply decision making skills in problematic situations CO2

UO4 Recognize and understand leadership skills and responsibilities CO2

UO5 Understand and enhance emotional intelligence CO1

UO6 understand the problem and provide a solution with a case study CO2,3,

UO7 know stress and stress management and time management skills CO 4

UO8 understand team work ,organization of the team and goal oriented strategy of

the team

CO 4

Lesson schedule

Class

No.


1 Understanding Self and Attitude Building/ Developing Positive attitude

2 Decision making skills and Leadership skills

3 problem solving skills with a case study

191

4 Emotional intelligent, stress and time management

Unit No

3 Unit Title Presentation skills Planned

Hrs.

03

Unit Outcomes: understand presentation, its importance and techniques and learn

professional presentation and public speaking


UO1 Know the importance and techniques of presentation CO5

UO2 know the skills to present professionally CO5

UO3 Understand public speaking and its use CO5

Lesson schedule

Class

No.


1 the importance and techniques of presentation

2 professional presentation

3 public speaking

Unit No

4 Unit Title Career skills Planned

Hrs.

04

Unit Outcomes: To understand career planning and career management and its various

stages – job application (resume writing skills) ,interview (technique and

skills ), group discussion , debate and corporate manners and etiquettes

At the end of this unit the students should be able to

UO1 know the corporate manners and etiquettes CO6

UO2 understand planning and career management CO6

UO3 know job application and resume writing skills CO7

UO4 understand interview process and perform in interview with skills and

techniques

UO5 know and perform group discussions and debates CO7

Lesson schedule


1 corporate manners and etiquettes

2 planning and managing career

3 interview technique and skills

4 group discussion and debate

192

Course Plan

Course Workshop Practice-II Course Code

Examination

Scheme


Max. Marks 25 -- 125

Contact

Hours/ week

1 2 -- 2

Prepared by S. V. Dhanal Date

Prerequisites Safety, basic materials and tools

Course Outcomes


CO1 Know about Safety : Common hazards while working with engineering

equipment and related safety measures

CO2 Know about materials used in Industries, steels and alloys, cast iron, non-ferrous

metals, timber, plastics and polymers, glass etc. and; their applications.

CO3 To use properly measuring Instruments such as Steel rule, Vernier Caliper,

Micrometer, Dial indicator, Their least counts, common errors and care while

using them, Use of marking gauge, „V‟ block and surface plate.

CO4 To explain Carpentry and Fitting

CO5 To explain welding processes - Arc, Gas and Resistance.

CO6 To know sheet metal specification, working & operations like cutting, bending,

folding, punching, riveting ; Joining by brazing and soldering

CO7 To explain smithy operations like upsetting, drawing, bending, Forming ; Tools-

hammer, hot and cold chisels, swages, drifts, flatters, tongs, Anvils

CO8 to observe machine tools and processes- Metal removing, metal shaping, plastic

molding.

193


POs

COs

a b c d E F G H i j k l

CO1

CO2 √

CO3 √

CO4 √

CO5 √

CO6 √

C07 √

CO8 √

Course Contents


Hours

Section I

1. Safety : Common hazards while working with engineering equipment

and related safety measures.

1

2. Materials : Brief introduction of materials used in Industries, steels and

alloys, cast iron, non-ferrous metals, timber, plastics and polymers,

glass etc. and; their applications.

2

3. Measuring Instruments : Brief introduction to instruments like – Steel

rule, Vernier Caliper, Micrometer, Dial indicator, Their least counts,

common errors and care while using them, Use of marking gauge, „V‟

block and surface plate.

2

4. Carpentry and Fitting : Brief study of various hand tools like chisel,

saw, planer and fitting tools like files, saw, drills, taps and dies.

1

5 Welding : Classification and brief introduction to welding processes -

Arc, Gas and Resistance.

2

6 Sheet Metal Working : Specifications of metal sheets, Surface coatings ;

Operations like cutting, bending, folding, punching, riveting ; Joining by

brazing and soldering.

2

7 Smithy : Introduction to smithy operations like upsetting, drawing,

bending, Forming ; Tools- hammer, hot and cold chisels, swages, drifts,

flatters, tongs, Anvils.

2

8 Smithy : Introduction to smithy operations like upsetting, drawing,

bending, Forming ; Tools- hammer, hot and cold chisels, swages, drifts,


1

194

Reference Books:

Sr. No. Title of Book Author Publisher/Edition Units

1 Course in Workshop

Technology, Vol – I,

B. S. Raghuvanshi,

A

Dhanapat Rai

and Sons

1 to 8

2 , Elements of Workshop

Technology, Vol – I,

.

Hajara Choudhari Media Promoters 1 to 8

3 Workshop Technology, Vol Gupta and Kaushik, – I, New Heights 1 to 8


Section I

Unit No 1 Unit Title Safety Planne

d Hrs.

01

Unit Outcomes


UO1 Know about industrial safety CO

Lesson schedule

Class

No.


1 Common hazards while working with engineering equipment and

related safety measures

Unit No 2 Unit Title Materials Planne

d Hrs.

02

Unit Outcomes


UO1 explain materials used in Industries, steels and alloys, cast iron, non-

ferrous metals, timber, plastics and polymers, glass

etc. and; their applications.

CO2

UO2 CO2

Lesson schedule

Class

No.


1 steels and alloys, cast iron, non-ferrous metals, timber

2 plastics and polymers, glass etc. and; their applications.

Unit No 3 Unit Title Measuring Instruments Planne

d Hrs.

02

Unit Outcomes

195


UO1 explain instruments like – Steel rule, Vernier Caliper, Micrometer, Dial

indicator,

CO3

UO2 least counts, common errors and care while using them, Use of marking

gauge, „V‟ block and surface plate.

CO3

Lesson schedule

Class

No.


1 Steel rule, Vernier Caliper, Micrometer, Dial indicator,

2 „V‟ block and surface plate.

Unit No 4 Unit Title Carpentry and Fitting Planne

d Hrs.

01

Unit Outcomes


UO1 study of various hand tools like chisel, saw, CO4

UO2 planer and fitting tools like files, saw, drills, taps and dies. CO4

Lesson schedule

Class

No.


1 study of various hand tools like chisel, saw, planer and fitting tools like files, saw,

drills, taps and dies.

Unit No 5 Unit Title Welding Planne

d Hrs.

02

Unit Outcomes


UO1 Classify welding processes - Arc, CO5

UO2 Gas and Resistance CO5

Lesson schedule

Class

No.


1 Arc welding

2 Gas and Resistance welding

Unit No 6 Unit Title Sheet Metal Working Planne

d Hrs.

02

Unit Outcomes


196

UO1 specify metal sheets, explain surface coatings ;

CO6

UO1 explain operations like cutting, bending, folding, punching, riveting ;

Joining by brazing and soldering.

CO6

Lesson schedule

Class

No.


1 metal sheets, surface coatings

2 cutting, bending, folding, punching, riveting ; Joining by brazing and soldering.

Unit No 7 Unit Title Smithy Planne

d Hrs.

02

Unit Outcomes


UO1 know smithy operations like upsetting, drawing, bending,

CO7

UO2 Forming ; Tools- hammer, hot and cold chisels, swages, drifts,


CO7

Lesson schedule

Class

No.


1 like upsetting, drawing, bending

2 hammer, hot and cold chisels, swages, drifts, flatters, tongs, Anvils.

Unit No 8 Unit Title machine tools and processes Planne

d Hrs.

01

Unit Outcomes


UO1 to observe machine tools and processes- Metal removing,

metal shaping, plastic molding.

CO8

Lesson schedule

Class

No.


1 Metal removing, metal shaping, plastic molding.

Documents

FIRST YEAR ENGINEERING - sginstitute.in · 3 First Year Engineering Course Common to All Branches Semester II: Physics Group Sr. No. Subject Teaching / Week (Hours/Week) Examination