13
USN 1OMAT31 Engineering Mathematics - lll Max. Marks:100 Note: Answer FIVEfull questions, selecting at least TWO questions from euch part. PART _ A expansion of the function f(x)= lxl in (-n.n). hence deduce that Zxcosx-sinx - ----------r----- X, x' 1q (06 Marks) (07 Marks) (06 Marks) (07 Marks) (06 Marks) closely to the (07 Marks) subject to the (06 Marks) the constraints, (07 Marks) Third Semester B.E. Degree Examination, Dec.2013 /Jan.20l4 Time: 3 hrs. a. b. c. a- b. 6) o o a (g o o EE G9 =r) -t o0' troo EB ol FO o> a2 o= oO 50tr -v >6 -ao !Q a- 6- o-i ,; .9 atE !o 6.v >'! oo- lo0 o= :o VL o t< -' ..i o o z P o | 'a. Find the Fourier series n2gl ,' -\. 8 fr(2n-l)r' b. Obtain the half-range cosine series for the function, f(x) = (* - 1)' in the interval 0 < x < 1 urd h"n.e jnq* that n2 = *{+ * * * +. } ' (07 Marks) u'3'5',) c. Compute the constant term and frst two harmonics of the Fourier series of (x) given by, Obtain the Fourier cosine translorm of f(x) = --1 . ' 1+x' [r - x: for lxl < Find the Fourier transform ol itx; = I - t 0 forlxl > 0 b. (07 Marks) Find the inverse Fourier sine transform of #r. (07 Marks) Obtain the various possible solutions of two dimensional Laplace's equation, u** * ur, = 0 by the method of sepaiation of variables. (07 Marks) a) ^) . _, o-u o-u Solve the one.dimensional wave equation, C': . --, 0'< x,< / under the following dx- dt' VA VL conditions (i) u(0, t) : u(1,0 : 0 (ii) u(x, 0) : T where uo is constant (iiD ff{*,o) = o. c. Obtain the D'Almbert's solution of the wave equation un = C2u** subject to the conditions .au u(x" 0) : flx) and f (x.0) = 0. 4 a. Find the best values of a, b, c, if the equation y=a+bx+cx2 is to fit most fo llo wing observations. Solve the following by graphical method to maximize z = 50x + 60y constraints,2x+ 3y<1500, 3x+2y<1500, 0( x <400 and 0<y<400. By using Simplex method, maximize P=4xr -2xr-x. subject to xr +x2 *X. (3,2xr+Zxr*X. ( 4,xr-x, <0, X, )0 and xz )0. x 0 TC J 2n ; J TE 4n " J 5x ; J 2n f(x) 1.0 1.4 1.9 r.7 1.5 1.2 1.0 x I 2 J 4 5 v 10 t2 13 t6 t9 c.

3rd semester Computer Science and Information Science Engg (2013 December) Question Papers

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Page 1: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

USN 1OMAT31

Engineering Mathematics - lllMax. Marks:100

Note: Answer FIVEfull questions, selectingat least TWO questions from euch part.

PART _ Aexpansion of the function f(x)= lxl in (-n.n). hence deduce that

Zxcosx-sinx -

----------r----- X,x'

1q

(06 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

(06 Marks)

closely to the

(07 Marks)

subject to the

(06 Marks)

the constraints,

(07 Marks)

Third Semester B.E. Degree Examination, Dec.2013 /Jan.20l4

Time: 3 hrs.

a.

b.

c.

a-

b.

6)oo

a

(g

oo

EE

G9

=r)-to0'troo

EBolFO

o>a2

o=

oO

50tr

-v>6

-ao!Q

a- 6-

o-i,; .9

atE

!o6.v>'!oo-lo0o=

:oVLo

t<-' ..i

oozPo

| 'a. Find the Fourier series

n2gl,' -\.8 fr(2n-l)r'

b. Obtain the half-range cosine series for the function, f(x) = (* - 1)' in the interval 0 < x < 1

urd h"n.e jnq* that n2 = *{+ * * * +. } '

(07 Marks)u'3'5',)c. Compute the constant term and frst two harmonics of the Fourier series of (x) given by,

Obtain the Fourier cosine translorm of f(x) = --1 .' 1+x'[r - x: for lxl <Find the Fourier transform ol itx; = I -

t 0 forlxl >0

b.

(07 Marks)

Find the inverse Fourier sine transform of #r.

(07 Marks)

Obtain the various possible solutions of two dimensional Laplace's equation, u** * ur, = 0

by the method of sepaiation of variables. (07 Marks)a)

^). _, o-u o-uSolve the one.dimensional wave equation, C': . --, 0'< x,< / under the following

dx- dt'VA VL

conditions (i) u(0, t) : u(1,0 : 0 (ii) u(x, 0) : T where uo is constant

(iiD ff{*,o) = o.

c. Obtain the D'Almbert's solution of the wave equation un = C2u** subject to the conditions

.auu(x" 0) : flx) and f (x.0) = 0.

4 a. Find the best values of a, b, c, if the equation y=a+bx+cx2 is to fit most

fo llo wing observations.

Solve the following by graphical method to maximize z = 50x + 60y

constraints,2x+ 3y<1500, 3x+2y<1500, 0( x <400 and 0<y<400.By using Simplex method, maximize P=4xr -2xr-x. subject toxr +x2 *X. (3,2xr+Zxr*X. ( 4,xr-x, <0, X, )0 and xz )0.

x 0 TC

J

2n;

J

TE 4n

"J

5x;J

2n

f(x) 1.0 1.4 1.9 r.7 1.5 1.2 1.0

x I 2 J 4 5

v 10 t2 13 t6 t9

c.

Page 2: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

5a.

b.

6 a. A

74.

8a.b.

c.

o.

1OMAT31PART _ B

Using Newton-Raphson method, find a real root of xsinx+cosx = 0 nearer to n, carryoutthree iterations upto 4-decimals places. (07 Marks)Find the largest eigen value and the corresponding eigen vector of the matrix,

lz -l oll.^.1| -^' ', -^'

I

10 -l 2lBy using the power method by taking the initial vector ur [t t 1]r carryout 5-iterationi.

Solve the following system of equations by Relaxation method: $7 Marks)

12x+ y-tz=31 ; 2x+8y -z=24; 3x+4y+102=58 (06Marks)

nducted in a slum localit ls the followins informati lassified below,conducted m a slum localltv reveaN tne ro[owl ton as c

Income oer dav in Rupees 'x' llnder 10 t0 -20 20-30 30-40 40-50Numbers of persons 'y' 20 45 115 2i0 115

Estimate the;probable number of persons in the income group VO:to 25. (07 Marks)

by taking 6 - equal strips and hencec.

Determine (x),as a polynomials in x for the data given below by Using the Newton's divideddifference formula. (07 Marks)

1 ,,,,'

Evaluate f--I-4, by usinf'simpson'sjl+x'deduce an approximate value of log'; 2';

^) ^)Solve the wave equation, + = 4*, sub.lect to u(0, t)

dt- 0x-u(x, 0) : x(4 - x) by taking h,:ir,-a :

!.,5 unto' ,steps.

Solve numerically the equalio, + = + subject to the'aAx-

[,t;"t'"

b.

c.

(06 Marks)

: 0, u(4, t) : 0, u1(x, 0) : 0 and

(07 Marks)

conditions, u(0, t) : 0 : u(1, t),

It > 0 and u(x,0)= qinnx, 0<x<1, carryout the computationfortwo levels taking h =a

, ,, (07 Marks)

with the boundary conditions as

'"t (06 Marks)

Fig. Q7 (c)

0000Find the z-transform ol (i) sinh n0 (iD coshn0

Iano K.:

- -

16 ',..,'"

Solve u* * u,, = 0 in the following square region

indi,ryd in the Fig. Q7 (c).

20

30

Find the inverse z-transform or, 222 +32

(z+2)(z- 4)

Solve the difference equation, yn*z * 6y,*, * 9yn =2"with yo = Yr = 0 by using z-transform.

{<*r.*X<

2 of2

(07 Marks)

(06 Marks)

x 2 4 5,, 6 8 l0f(x) 10 96 196 350 868 1746

Jt:o 1 oo 1oo 50

(ur) n-

(07 Marks)

Page 3: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

USN MATDIP3Ol

Max. Marks:10CI,

,,; .,,',,, (06 Marks)

'' (07 Marks)

rlllrirl

(06 Marks)

(07 Marks)

(07 Marks)

(06 Marks)(07 Marks)

(07 Marks)

Third Semester B,E. Degree Examination, Dec.2013 lJan.20l{

Advanced Mathematics - I

Note: Answer any FIVEfull questions.

b.

c.

(J(J

o

a

o()L

E9bor

de-Xn-*ltoo.=N

oXJoEi-O

=!

o2

a=

o()

orob0tr

.Ya66rE(6-?()or=

o. 6.

oj

a=6E,LOJEo.i>' (P

ooocbo(J=go

o

(-) <-No

z

o

Time: 3 hrs.

;',

6a.

b.

c.

I , a:' Express the complex number (t +iXl-+ 3i)

in the form x + iy.

- fl7t, ,.. , "(3-42i)'

Expand coss 0 in a series of cosines multiples of 0.

2 a. Find the nth derivative of sin(ax + b).b. Ify: (sin-r x)2, shawthat (1-r')yn*, -(2n+l)xy,*r -n2yn =0.

. I r -3t2 Ic. Findthenlhderivativeof I +, - i - l.Is(x -l) (i-tf 2x +3).]

3 a- Using Taylor's theorem, expresS'the polynomial"")xt +7x2 + x - 6 in powers of (x - 1).

b. Using Maclaurin's series, expand tan x:,lto the term containing x5.

c. If Z:"t + ,u' - 3axy then prove 161 !J- = :': ..,. AyAx dxAy

3*y:l,find+. (o6Marks)4 a. Ifu=xlogxywherext+yt+ . dx

b. If z: (x, y) and x = e" +e-u andy = e-" -eu, prove that 5 -- =x.J -y :.(07 Marks)

;, u,,. ^.'-

y, & - Nc. If u=x+3y2 * z',v=4x2yz, w= 222 -xy, findthe*r".oi,99{t') at(1,-1,0,).- a$.y.2)

::' " '' Marks)

5 a. Obtain the reduction lormula fo ( n I

,,, ,,,,,, 'eductron lormula lor

J sm x dx . ,,,"', , (06 Marks)

u, v'dxb. Evaluate l+

o 1? -x'

Evaluate IIfr, + eY)dydx.l3

lll

Evaluate JJ Je..'.'Oxdydz.000

l/Find the value "i lf

1)t\2J'

Prove that B(m,n) [email protected](m + n)

,"'.,{07 Marks)

,,::'

(oz M+rko)

(06 Marks)

(07 Marks)

(07 Marks)

Page 4: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

-l

7 a. Solve t = ""-" +x' 'e." .

b. Solve 7y -*' -y' which is homogeneous in x and y.

tffi,;1;u*1_ffi,,ft

solve *--, =e'*(x+1)'

MATDIP3Ol

(06 Marks)

(07 Marks)i.'\.::.. ::,.b..

,d}q3

,= ffi"ut,

(06 Marks)

(07 Marks)

(07 Marks)

t,:==

{<{<**{.

fl3'",t.t

- .&.$ 4,' .ii :il i 't"\I

i f"!l\ /:r# $

.:::i'rr:il:a6#*&/rryh.

\::::t:d"Yv

h

.+\' f ,Si: -.f'\-Jf :I W fl'Iq"

*\" .tr

*(P =.-iu, ,l=,.1 =';*J

u{ a

u !'

,,"{Fr#'\* ote u,r'q- Y..

:a"'a:: '::::

"" ::

''t:"':'

*'

..........

'":":""

'At

\vi'' +'

\-y3,::...,,: .;;;::

s

-&1

t 't'"'!:'; r.."r, .! t

.. q"1\.-J't,

..::::.

t:,::'

'ttttt"'"*'I' '.::..{fl .:

&'!" ::'

2 of2

Page 5: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

USN

Time: 3 hrs.

10cs32

Max. Marks:100

(07 Marks)(05 Marks)

(06 Marks)(04 Marks)

(06 Marks)

(04 Marks)

(08 Marks)

(12 Marks)

Third Semester B.E. Degree Examination, Dec.2013 /Jan.20l4

Electronic Gircuits

a.

c.

a.

b.

c.

a.

b.

doog

E(!

C)

o

ER50-

G,9-.o

Io0'Eoo

.=N

9#-O

-!

3z;!i

o()

o'tfb0i

-s'O cd

..o

or=

^X

oi.

oEAELO

5.v>,!bo"=boo=E-3F>=oVLo

t<-i 6i(-)

Z

oE

Explain the criteria for selecting a suitable operating point and factors affecting the stability.(08 Marks)

Determine the operating point for a fixed bias circuit shown in Fig.Ql1b;. Given B : 100 and

VeE : 0.7V. Draw the load line.

PART * A

Explain transistor as a switch.

What are the differences between BJTs and FETs?Explain the working of a CMOS inverter.

Note: Answer FIVE full questions, selectingat least TWO questions from each part,

ii) NEPiv) Quantum efficiency

Explain the construction, working and principle of operation of an n-channel JFET.lto Marks)

Explain the classification of optoelectronic devices.Define the following terms:i) Responsivity

c. iii) Response timeExplain the working of cathode ray tube with a neat diagram. What are the advantages anddisadvantages of CRT? (10 Marks)

a. What is the need for cascading amplifier? Explain two stage cascaded amplifier with a blockdiagram.

b. Derive the expressions for: i) Current gain ii) Input impedanceiii) Voltage gain iv) Output admittance

PART _ Ba. Briefly explain the classification of amplifier based on input and output parameter of interest

[Vi, Vo, Iiand 16]. (12 Marks)b. With a neat block diagram, explain amplifier with negative feed back. (04 Marks)c. Calculate the values of harmonic distortion components for an output signal having an

amplitude of 5V at fundamental frequency, second harmonic component of 0.5V, thkdharmonic component of 0.2V and fourth harmonic component of 0.05V and find total

Va =lsv

Fig.Q1(b)

harmonic distortion. (04 Marks)

Page 6: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

10cs32

6 a. What are necessary conditions for loop gain and phase shift for sustained oscillationsaccording to Barkhausen criterion? (04 Marks)

b. Explain the working of an Astable multivibrator using IC 555 timer with circuit diagram andrelevant waveforms.

c. Explain the working of RC low pass RC high pass circuit.

7 a. Explain the steps involved in custom design of mains transformer.b. What are SMPS? Compare linear power supplies with SMPS.c. Explain the working of three terminal voltage regulators.

frequency expec{ed is 50 Hz?

a. What should be the slew rate choosen for an OPAMP as an inverting amplifier configurationwith gain of l'O,when input is a sinusoidal signal with peak to peak value of 2V and highest

(08 Marks)(08 Mdrks)

:

(06 Marks)(07 Marks)(07 Marks)

(04 Marks)b. Explain the working:of an OPAMP window comparator with circuit diagram. (08 Marks)c. Explain the lead and lag type of phase shifter. (08 Marks)

{<*{<*tr* i

.. ....,)t\.

..'

i

::1 ,:

2 of2

Page 7: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

USN 10cs33

Third Semester B.E. Degree Examination, Dec. 20l3lJan.2014Logic Design

Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting

atleast TWO questions from esch part.

PART _ AI a. With the aid of the circuit diagram, explain the operation of 2 - input TTL NAND gate._

(08 Marks)b. What are universal gates? Implement the following function using universal gates only

((a + n)C )D (06 Marks)c. Write the truth table of the logic circuit having 3 input A:,,,B and C and output output

expressed as y=ABC+ABC . Also simplify the exsression using Boolean expression

and implement the logic circuit using NAND gates? (06 Marks)

2 a. Using Q - M method, ,lrnpti1y the expressions (A, B, C, D) : ,(0, 3, 5,6,7 ll, lD).Writethe gate diagram for the simplified expression using NAND - NAND gates. (10Marks)

b. A digital system is to be designed in which the month of the year is given as input is four bitform. The month January is represented as '0000' February'0001' and so on. The output ofthe system should be '1' corresponding to the input of the month containing 31 days orotherwise it is '0' consider the excess numbers in the input beyond '1011' as don't careconditions for system of four variables (A. B- C. D) find the lollowing :

i) Boolean expression in !m and tm formii) Write the truth tableiii) Using K - map. simplify the Boolean expression of canonical minterm foriv) Implement the simplified equation using NAND - NAND gates.

3 a. Write a 4: 1 MUX verilog program using conditional 'assign' and 'case' statement.(06

b. What are static hazards? How to design hazards free circuit? Explainwith an example.(06 Marks)(08 Marks)

4 a- Draw the logic diagram of clock D - flip/flop write its truth table and characteristicequation, state diagram and excitation table, what is the draw back JK flip/flop. (10 Marks)

b. Differentiate between combinational circuit and sequential circuits. (05 Marks)c. Show how a SR flip/flop can be converted into T - flip/flop. (05 Marks)

PART - B

5 a. Using negative edge triggered JK flipiflop, draw the logic diagram of a 4-bitserial-in-serial-out shift register. Draw the waveform to shift the binary number 10i0 intothis register. Also draw the waveform for 4 clock transistor when J: K: 0. (08 Marks)

b. Explain the working of mod - 4 ring counter. (06 Marks)c. Explain with a neat diagram, how shift register can be applied for serial addition. (06 Marks)

(Joo!a(!

(!

()

(.)I

oX

cotroa.=N

Yd)otr-<()

rs()(l)

a0c

.G

!d

3o'CaOE

s5.tro.oj

9E1oalE

LOx.9Y,

i50U-*otr>9Lo

.i o.i

()oz

o

c. Explain IV - bit magnitude comparator.

'er.\.X*l*s:- i

ft,!- \c \;6\ I

fr,Y l; 7

.1_*7

Page 8: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

10cs33

6 a. With the help of neat block diagram and timing diagram, explain the working of a mod -16ripple counter constructed using the edge triggered JK- flip/flop. (08 Marks)

b. Designasynchronous counterforthe sequence 0 -+4 + 1-+ 2-+6 -+ 0 +4, using SRflip-fIop. (12 Marks)

7 a. Design a sequence detector that receives bindery data stream as its input, X and signalswhen a combinations '011' arrives at the input by making its output. Y high which otherwiseremain line consider data is coming from left, i. e the first bit to be identified is l. Second1 and third 0 from the input sequence. Design mealy model?

b. Realize the sequential circuit for the state diagram.

"L; 0

, : Fie. Q7(b)

Explain 2-bit simultaneous A./D converter.

*;l

(14 Marks)(06 Marks)

(10 Marks)

(04 Marks)

8a.b.

c.

What is binary ladder? Explain the binary ladder with a digital input of 1000. (06 Marks)What is accuracy and resolution of the D/A converter? What is the resolution of a 12bitDlAconverter which uses binary ladder? If the full scale output is + 10 V, what is the resolutionin volts?

E{<***

'tTl ,*= I

2 of2

Page 9: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

USN

Time: 3 hrs.Note: Answer FIVE full questions, selecting

PART - AI a. Define power set of a set. Determine power sets of the following sets.

A= {a, {b}} B: {0, 1,{0}}.

b. Write the following propositions in symbolic form and find its negation.then x2 * 1 is even.

c. Let p(x), q(x) and r(x) be open statements, determine whethe2ffiivalid or not

, (rS;;V, [p(x) -+ q(x) ] ll-r.

ar\

V" I q1x) -+ r(x) I i ;fl d-, ,1 ', I '.,'LM 'rkt ,. 1

10cs34

Max. Marks:100

(04 Marks)

For all x, if x is odd(04 Marks)

Third Semester B.E. Degree Examination, Dec. 2Dl3/Jan.2Ol4Discrete Mathematical Structures

oo(.)

ECq

o()L

BE

693,cjl j

=eo'=+

o:f

-O-!

o>o2

a::oOc\

26

ie:Eo''

9d3oa lr=

!o5.">.hco-- cI)

gd)

F>(-)

:-()oZ6L

b. Using laws of set theory show that (A n B) U [Bn ((C n D) U (C n D))] : B n (AU C).

c. In a surve 1r of 260 college students, the following data were obtai ned; 64 [:1^[lT]Mathematics eourse, 94 had take CS course, 58 had take EC course. 28 had taken bothMathematics and F,C course. 26 had taken both Mathematics and CS course, 22 had takenboth CS and EC course, and 14 had taken all three types of courses. Determine :

i) How many of these students had taken none of the three courses?ii) How many had taken,only CS course? (06 Marks)

d. An integer is selected at random from 3 through 17 inclusive. If A is the event that a numberdivisible by 3 is chosen, and B is the even that the number exceeds 10. Determine Pr(A),Pr(B), Pr(A [) B) and Pr(A U B). (05 Marks)

2 a. Let p, q be primitive statements for whieh implication p -) q is false. Determine the truthvaluescfthe following: i)p n qii) -rpvq iii) q +piv) --rq+ -1p. (05Marks)

b. By constructing truth table. Show that the compound propositions p ^ (: q v r) andp v (q n r r) are not logically equivalent. (05 Marks)

c. Prove that (:p v q) ^

(p ^(pn

q)) ep ^

q. Hence deduce that (-r p ^

q) v (p v (p v q)) c>p v q. (05 Marks)

d. Show that R v S follows logically from the premises. C v D, (C v D) -+ --lH,-r H -+ (A n -r B) and (A n -r B) -+ R v S. (05 Marks)

3 a. Write down the converse, inverse and contrapositive of the following statement, for whichthe set of real numbers is the universe. Also indicate their truth values. V*[ (x>3) -+ 1xL911.

(06 Marks)

.'.v*[ p(x) -+ r(x)]. i.;\ " , (06 Marks)d. Give a direct proof of he statement : "The square of an odd intNfoen-e,4dbi*eger" .sn*eflQsXllTe$er

l:j;;V (04 Marks)

4 a. Using mathematical induction, prove that 4n. (n'- 7) for all positive integers n > 6.(06 Marks)

L FortheFibonaccisequenceFe,Fr,Fz- - - -. Prove that pn =*[[y)' [+]'] ,or Marks)

D.

c. Find an explicit formula for an : on -l * n, ar : 4 for n> 2. (06 Marks)

Page 10: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

10cs34

PART _ B

5 a. Define the Cartesian product of two sets. For any non - empty sets A, B and C prove thatA x (B UC) : (A x B) l-J (A x C). (05 Marks)

b. Define the fbllowing with one example fbr each i) Function ii) one - to one function iii) onto function. (06 Marks)

c. State the pigeonhole principle. An office employs 13 clerks. Show that at least.2 of themwill have birthdays during the same month of the year. (04 Marks)

d. Letf : R->R, g:R-+Rbedefinedbyf(x):x2, andg(x):x+5. Determine f . gandg. f.Show that the composition of two functions is not commutative. (05 Marks)

a. LetA: {1,2,3,4\, andletRtherelationdefinedbyR: {(x, y) l*, y e A, x<y}.Determine whether R is reflexive, symmetric antisymmetric, or transitive. (05 Marks)

b. What is partition of a set. If R : {(1, 1), (1,2), (2,7'), (2,2), (3, 4), (4,3), (3, 3), (4, 4)}defined on the set A : U, 2, 3,4). Determine the partition induced. (05 Marks)

c. Definepartial order. IfRisarelationonA:{1.2.3.4}definedbyXRYifxly.Provethar(A, R) is a POSET. Draw its Hasse diagram. : (06 Marks)

d. Let A : {2, 3, 4, 6, 8, 12,24} and let < denotes the partial order of divisibility that is x < ymeans xly. Let B : {4, 6,121. Determine :

i) All upper bounds of Bii) All lower bounds of Biii) Least upper bound of Biv) Greatest lower bound of B.

a. Define abelian group. Prove that a group C is aiifAn iff (ab)2 : a'b' for all a, b, e G.

b. If H and K are subgroups:;ru ,.orp G. Prove ,nu, , O K is also a sub group "f

G. [3] il:Hlc. Define homomarphism anod isomorphism in group. Let f be homomorphism from a group

G1 to group G2. Prove that :

it If er is the identity in Gr and e: is the identity in Gz. then (e1)': e2

ii) (a-r) =,[(a)]-' for all a e Gr.

a. An encoding function E:27, -+ Z)is given by the generator matrix :

[rollolG=l I

L0 r 0 I l.li) Determine all the code wordsii) Find the associated parity - check matrix Hiii) UseHtodecodereceivedwords:1 1 101, 1 101 1.

(04 Marks)

(08 Marks)

(07 Marks)b. A binary symmetric channel has probability P : 0.05 of incorrect transmission. If the word

C : 01 101 1 101 is transmitted, what is the probability that i) single error occurs ii) a doubleerror occurs iii) a triple error occurs iv) tluee errors occur no two of them consecutive?

c. Define a ring. In a ring (R, r, 0) tbr all a, b e R, prove that (08 Marks)

i) a.0:0'a:0

{<*{<rftr<

2 of2

ii) a(- b) : (- a) b: - (ab). (05 Marks)

Page 11: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

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Third Semester B.E. Degree Examination, Dec.2013 I Jan.2Ol,4Data Structures with G

Time: 3 hrs. Max. Marks:100

Note: Answer ony FIVEfull questions, selecting atleast TWO questionfrom eerch port.

PART - AI a. Write the syntax and usage of the following operators in C language :

i)" .selection ii) Indirection iii) Address. ;...,, (06 Marks)b. What,is,rneant by rvalue and [value expression? Give examples. '"; (04 Marks)c. Distinguish,,,,,between static and dynamic memory allocation. With' syntax, explain four

dynamic memory allocation functions. (10 Marks)::::",'

2 a. Write an user defiqqd function in C to find if two fractions'are equal. Use structure data type

b.

c.Write a C program to merge two files of integers to produce a third file. (06 Marks)Write a C program to concatenate First name and Last name of a person without using anylibrary function. (08 Marks)

Define stack. List atleast f"r. rriii"ations of r,u.f.. (05 Marks)Write an algorithm for evaluating apo$ fii expression and trace it on 123 + * 321 - + *.

. ",ii.,; i'-! (09Marks)Write C functions for implementi_-4gpiimitive stack operations. (07 Marks)

What is recursion? Evaluate fib(4), that is fin{ing 4'h term of Fibonacci sequence usingrecursion and iteration. Which is better? (08 Marks)

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b. Write the static implementation of priority queue in C language. With illustration, explainmajor limitation of suqh a queue. (12 Marks)

PART - BGive the str.uctural features of a linked list. Discuss how an"'affay, can be used to store alinked list, ,. (05 Marks)Givgn a singly linked list with plist as the external pointer, write an algorithm to insert anew.'node to the end of the list. Assume nodes hold integers. (05 Marks)FIow is a stack implemented using linked list? Write C program for the same. (10 Marks)

What is a circularly linked list? Write algorithm for merging two circularly linked lists.(07 &X,arks)

Write the algorithm for deleting the first occurrence of a given valve from a doubly. linkedlist. (08 Marks)Discuss how to implement a queue using circular linked list. (05 Marks)

Define complete binary tree and almost complete binary tree. Give examples. (05 Marks)With suitable example, explain implicit array representation of binary search tree. (05 Marks)What is a binary search tree? Write an algorithm to construct a binary search tree. (10 Marks)

a. What is tree traversing? Explain the standard methods available for tree rrur"rr,n*dff-l';b. write short notes on : i) circular queue ii) Efficiency of recursion. (ff Tfl*,

Page 12: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

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Third Semester B.E. Degree Examination, Dec.2013 lJan.2Dl4

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c. Explain three access specifiers.

Why friend function is required? Write a program to add two complex number using friendfunction. (08 Marks)Explain generic function with an example. (06 Marks)

(06 Marks)Write a program to overload * * operator.

Mention types of inheritanCa. Explain multiple and multilevel inheritance with example.

PART _ BExplain'fu order of innovocation of constructor and destructor with an example.Exp-lain with an example virtual base class.

"E plain passing parameter to base class. ,Krt ar

6 .a-. 'Difference between early binding and late binding.

, b. What is virtual functioni Explain with an example.: c. Explain the abstract class with an ex-ample.

7 a. What are the flags that associated with the file operation?b. Explain the following functions:

i) setfill( ) ii) width( ) iii) precision( ) iv) setiosflags( )c. Mention the name of file movement pointer. Explain each.

8 a. Explain C+* exception handling function with example.b. What is vector? Explain function of a vector.c. Write a program to create a list and sorting the elements of the list.

Object Oriented Programming with G++

Note: Answer FIVE full questions, selectingat least TWO iuestions from each parl .

PART _ Atnl\t -n

Exptfu various features of object oriented programming. (08 Marks)What is,'inline function? Explain with an example. Mention its advantages. (06 Marks)What is function overloading? Write a program to swap two inleger and two float numberusing function overloading. (06 Marks)

What is class? Write a program to create a class called employee which consists name. desg.ecode and salary as a data member and read, write as a function member, using this class toread and print 10 employee information. (08 Marks)What is constructor? Mention its types. Explain paiameterized constructor with an example.

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Page 13: 3rd  semester Computer Science and Information Science Engg (2013 December) Question Papers

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Third Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4UNIX and Shell Programming

Time: 3 hrs. Max. Marks:100Notez Answer FIVEfull questions, selecting

atleost TWO questions from eoch part.taaacuJt , 77 v al ucJaaarf ,J J t ltIII yuL ra put a.

PART - A

1 a. With a neat diagram, explain the relation ship between the Kernel and the shell of IINIX.(07 Marks)

b. What are internal and external commands in UNIX? Explain any three with examples ineach type. (07 Marks)

c. What is parent - child relationship? With the help of diagram explain the UNIX file system.(06 IVlarks)

2 a. List and explain any four commands which are used for handling ordinary files. (07 Marks)b. Explain each column of o,iltput Ls - I command. (07 Marks)c' what is editor? Explain the tluee modes of vi editor. (06 Marks)

3 a. Explain the following :

i) Shell wild cards ii) /dev/null and /dev /tty. (08 Marks)b. Define the term process. Explain mechanism of process creation in [NIX. (06 Marks)c. Explain any four L|NIX environrnental variables. (06 Marks)

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List and explain the different ways of setting directory permissions.Explain the following filters,with examples :

i) head ii) tail iii) cut iv) paste.Explain hardlink and symbolic link, with examples.

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a. Explain the grep, egrep and fgrep, with examples.b. Explain Sed command with all options.c. Describe the salient features of LINIX operating system.

Explain the special parameters used by the shell programming.Write an shell script that accepts two file names as arguments, checkthese files are common permission or different permission.Explain the following : i) expr ii) shift iii) set iv) read.

What is awk? List and explain any three built - in functions in awk.Write an awk program to print transpose of a given matrix.Explain with examples, the simple awk filtering.

Explain briefly the features offered by PERL.Explain chop( ) and split( ) with examples.Write a PERL program to conveft an unsigned binary to decimal.

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