QP. Code : xxxx.x PHYSICS, CHEMISTRY & MATHEMATICS - Fiitjee … paper class 12.pdf · 2017. 9. 23. · National Admissions Office : FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai,

Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 1

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FIITJEE - JEE (Mains)

QP. Code : xxxx.x

PHYSICS, CHEMISTRY & MATHEMATICS

Time Allotted: 3 Hours

Maximum Marks: 360

Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Important Instructions:

1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is

strictly prohibited.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer

Sheet and fill in the particulars carefully.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30

questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one

fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will

be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any question will be treated

as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above.

8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1 and Side-2 of the Answer

Sheet. Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any

electronic device, etc. except the Admit Card inside the examination hall / room.

10. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall.

However, the candidates are allowed to take away this Test Booklet with them.

11. Do not fold or make any stray marks on the Answer Sheet.

Name of the Candidate (in Capital Letters) :_____________________________________

Enrolment Number :_________________________________________________________

Batch :________________________ Date of Examination : ________________________


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Section 1 (Part A) PHYSICS

1. Two cells of emf’s approximately 5V and 10V are to be accurately compared using a potentiometer of length 400cm. (a) The battery that runs the potentiometer should have voltage of 8V (b) The battery of potentiometer can have a voltage of 15V and R adjusted so that the potential drop across the wire slightly exceeds 10V. (c) The first portion of 50 cm of wire itself should have a potential drop of 10V (d) Potentiometer is usually used for comparing resistances and not voltages.

2. A metal rod of Length 10 cm and a rectangular cross-section of 1 cm × 1

2cm is connected to

a battery across opposite faces. The resistance will be

(a) maximum when the battery is connected across 1 cm × 1

2 cm faces.

(b) maximum when the battery is connected across 10 cm × 1 cm faces.

(c) maximum when the battery is connected across 10 cm × 1

2 cm faces.

(d) same irrespective of the three faces.

3. Which of the following characteristics of electrons determines the current in a conductor? (a) Drift velocity alone (b) Thermal velocity alone (c) Both drift velocity and thermal velocity (d) Neither drift nor thermal velocity.

4. A capacitor of 4F is connected as shown in the circuit.

The internal resistance of the battery is 0.5. The amount of charge on the capacitor plates will be

(a) 0 (b) 4C (c) 16C (d) 8C

5. The electrostatic potential on the surface of a charged conducting sphere is 100V. Two

statements are made in this regards S1: At any point inside the sphere, electric intensity is zero. S2: At any point inside the sphere, the electrostatic potential is 100V. Which of the following is a correct statement? (a) S1 is true but S2 is false (b) Both S1 & S2 are false (c) S1 is true, S2 is also true and S1 is the cause of S2 (d) S1 is true, S2 is also true but the statements are independent.

6. Equipotentials at a great distance from a collection of charges whose total sum is not zero

are approximately (a) spheres (b) planes (c) paraboloids (d) ellipsoids.

7. A parallel plate capacitor is made of two dielectric blocks

in series One of the blocks has thickness d1 and dielectric constant k1 and the other has thickness d2 and dielectric constant k2 as shown in figure. This arrangement can be thought as a dielectric slab of thickness d(=d1+d2) and effective dielectric constant k. The k is

(a) 1 1 2 2

1 2

k d k d

d d

(b) 1 1 2 2

1 2

k d k d

k k

(c)

1 2 1 2

1 1 2 2

k k d d

k d k d

(d) 1 2

1 2

2k k

k k


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8.

Five charges q1, q2, q3, q4 and q5 are fixed at their positions as shown in the figure. S is a Gaussian

surface. The Gauss’s law is given by 0s

qE.ds

. Which

of the following statements is correct? (a) E on the LHS of the above equation will have a contribution from q1, q5 and q3 while q on the RHS will have a contribution from q2 and q4 only. (b) E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q2 and q4 only. (c) E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q1, q3 and q5 only. (d) Both E on the LHS and q on the RHS will have contributions from q2 and q4 only.

9. A point charge +q, is placed at a distance d from an isolated conducting plane. The field at a

point P on the plane is (a) directed perpendicular to the plane and away from the plane (b)directed perpendicular to the plane but towards the plane. (c) directed radially away from the point charge. (d) directed radially towards the point charge.

10. Figure shows electric field lines in which an electric dipole

moment p is placed as shown. Which of the following statement is correct? (a) The dipole will not experience any force. (b) The dipole will experience a force towards right. (c) The dipole will experience a force towards left. (d) The dipole will experience a force upwards.

11. A particle of mass m and charge q enters a region of

magnetic field (as shown) with speed v. There is a region in which the magnetic field is absent, as shown. The particle after entering the region collides elastically with a rigid wall. Time after which the velocity of particle becomes anti parallel to its initial velocity is

(a) m

42qB

(b) m

2qB

(c) m

24qB

(d) m

2 34qB

12. A current carrying circular loop of radius R is placed in the x-y plane with centre at the

origin. Half of the loop with x>0 is now bent so that it now lies in the y-z plane. (a) The magnitude of magnetic moment now diminishes. (b) The magnetic moment does not charge. (c) The magnitude of B at (0.0.z),x>>R increases. (d) The magnitude of B at (0.0.z),x>>R unchanged.

13. A circular current loop of magnetic moment M is in an arbitrary orientation in an

external magnetic field B. The work done to rotate the loop by 30° about an axis perpendicular to its plane is

(a) MB (b) MB

32

(c) MB

2 (d) zero.


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14. A toroid of ‘n’ turns, mean radius R and cross-sectional radius ‘a’ carries current I. It is

placed on a horizontal table taken as x-y plane. Its magnetic moment M (a) is non-zero and points in the z-direction by symmetry.

(b) points along the axis of the tortoid m M

(c) is zero, otherwise there would be a field falling as 3

1

r at large distances outside the

toroid. (d) is pointing radially outwards.

15. A block of mass m and charge q is connected to a point O with help of an inextensible

string. The system is on a horizontal table. An electric field is switched on in direction perpendicular to string. What will be tension in string when it becomes parallel to electric field?

(a)qE

2 (b)3qE (c)

qE

(d).

3qE

5

16. A loop carrying current I lies in the x-y plane as shown in

the figure. The unit vector k is coming out of the plane of the paper. The magnetic moment of the current loop is

(A) 2 â I k (B) 2 ˆ1 a I k2

(C) 2 ˆ1 a I k2

(D) 2 ˆ(2 1)a I k

y

x

a

a

I

17.

The figure shows two infinite semi-cylindrical shells: shell-1 and shell-2. Shell-1 carries current i1 in inward direction normal to the plane of paper, while shell-2 carries same current i1, in opposite direction. A long straight conductor lying along the common axis of the shells is carrying current i2 in direction same as that of current in shell-1.

force per unit length on the wire is

(a) zero (b) 0 1 2i i

2 r

(c) 0 1 22 i i

r

(d) 0 1 2

2

2 i i

r

18. A meter bridge is set up as shown, to determine an

unknown resistance ‘X’ using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is (a)10.2 ohm (b) 10.6 ohm (c) 10.8 ohm (d) 11.1 ohm

B

10

A

X

19. A parallel plate capacitor C with plates of unit area and

separation d is filled with a liquid of dielectric constant K =

2. The level of liquid is d

3 initially. Suppose the liquid level

decreases at a constant speed V, the time constant as a

C

d R d

3


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function of time t is

(a) 06 R

5d 3Vt

(b) 0

2 2 2

(15d 9Vt) R

2d 3dVt 9V t

(c) 06 R

5d 3Vt

(d) 0

2 2 2

(15d 9Vt) R

2d 3dVt 9V t

20. A wire of length L and 3 identical cells of negligible internal resistance are connected in

series. Due to the current, the temperature of the wire is raised by T in a time t. A number N of similar cells is now connected in series with a wire of the same material and cross

section but of length 2L. The temperature of the wire is raised by the same amount T in the same time t. The value of N is

(A) 4 (B) 6 (C) 8 (D) 9

21.

The resultant capacitance of given circuit is

(a) 3C (b) 2C (c) C (d) 3

C

22. A and B two concentric spheres. If A is given a charge Q

while B is earthed as shown in figure: (a) the charge density of A and B are same (b) the field inside and outside A is zero (c) the field between A and B is not zero (d) the field inside and outside B is zero.

23. n small drops of the same size are charged to V volt each. If they coalesce to form a single large drop, then its potential will be (a) (V/n) (b) Vn (c) Vn1/3 (d) Vn2/3

24. An electric field is given by NE yi x jC

. The work done by the E in moving 1 C charge

from Ar 2i 2j m

to Br 4i j m

is

(a) +4 J (b) –4 J (c) +8 J (d) zero 25. In a certain region of space, the potential field depends on x and y coordinates as V=(x2–y2) .

The corresponding electric field lines in x–y plane are correctly represented by:

26. In a permanent magnet at room temperature (a) magnetic moment of each molecule is zero. (b) the individual molecules have non-zero magnetic moments which are all perfectly

aligned. (c) domains are partially aligned.

(d) domains are all perfectly aligned. 27. A paramagnetic sample shows a net magnetization of 8 Am–1 when placed in an external

magnetic field of 0.6T at a temperature of 4K. When the same sample is placed in an external magnetic field of 0.2T at a temperature of 16K, the magnetization will be


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(a) 32

3Am–1 (b)

2

3Am–1 (c) 6Am–1 (d) 2.4Am–1.

28. Find charge on capacitor in steady state in given circuit

(a) 9.6 C (b) 7.2C (c) 4.8C (d) 2.4C.

29. Plates of a parallel plate capacitor C have charges CV

and 3 CV on its plates. If switch is closed at t=0. Then initial rate at which heat energy is produced in resistance R is

(a) 2V

R (b)

24V

R

(c)29V

R (d)

216V

R

30. Two wires are of same length and same area of cross-section. If first wire has resistivity

1 and temperature coefficient of resistance 1 but second wire has resistivity 2 and

temperature coefficient of resistance 2. Their series equivalent resistance is independent of small temperature changes. Then

(a) 1+2=0 (b) 11=22 (c) 11+22=0 (d) 12+21=0

Section 2 (Part A) CHEMISTRY 1. Propanone and propanal are:

(a) geometrical isomers (b) chain isomers

(c) functional isomers (d) position isomers

2. Which type of isomerism is shown by diethyl ether and methyl propyl ether?

(a) chain (b) functional (c) metamerism (d) position

3. Which of the following is chiral carbon ?

(a) CH4 (b) CH3I (c) CH2Cl2 (d) CHIBrCl

4. Which of the following is optically active ?

(a) Butane (b) 4-methyl heptanes

(c) 3-methyl heptane (d) 2-methyl heptane

5. The correct statement about the compounds (A), (B) and (C) is

H C OH

COOCH3

H C OH

COOH

(A)

H C OH

COOH

H C OH

COOCH 3

(B)

H C OH

COOH

OH C H

COOCH 3

(C) (a) A and B are identical (b) A and B are diastereomers

(c) A and C are enantiomers (d) A and B are enantiomers.


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6. Which of the following pairs of structures represent enantiomers ?

(a) OH C H

COOH

CH3

and H C OH

CH3

COOH

(b) CH3 C OH

H

COOH

and HO C CH3

COOH

H

(c) H C CH3

COOH

OH

and CH3 C H

OH

COOH

(d) HOOC C OH

CH3

H

and HOOC C H

OH

CH3

7. The most stable conformer of 2, 3-dimethylbutane is

(a)

CH3

CH3H

CH3

CH3H

(b)

CH3

HCH3CH3

CH3H

(c)

H

CH3CH3

CH3

CH3H

(d)

CH3 CH3

HCH3

CH3

H

8. Which of the following carbocation is most stable?

CH2+

(a)

CH2

+

NO2

(b)

CH2

+

OH

(c)

CH2

+

OH

(d)

9. Which of the following shows maximum enol content

O(a)

(b) O

(c) O

(d) O

10. The compound, whose stereochemical formula is written below, exhibits x-geometrical

isomers and y-optical isomers.

CH3

Br

H

OH

H

CH3

(a) 4 and 4 (b) 2 and 2 (c) 2 and 4 (d) 4 and 2

11. An organic compound, C3H6O does not give a precipitate with 2, 4-dinitrophenylhydrazine

reagent and does not react with metallic sodium. It could be

(a) CH3 – CH2 – CHO (b) CH2 = CH – CH2OH

(c) CH3 – CO – CH3 (d) CH2 = CH – O – CH3

22. CH3 CH2 Cl

CH3

OH Ag+ (aq.)

?

The major product formed is

CH3 C CH2 CH3

O

(a)

CH3 C CH2 OH

OH

CH3

(b)

CH3 C

CH3

H O

(c)

CH3 C CH2

CH3

HO

CH3(d)

12.


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13. Which products of the following reactions give iodoform test ?

(a) Ph – C CH 2

2

/?

H O H

Hg

(b) 4

||/

3 2

OPd BaSOCH C Cl H

(i) CH3MgBr(c)

CN

(ii) H3O+ ?

(d) All of them

14. In the given reaction:

C CH2CH3 CH2 CH2 CH2 Cl

OCH3MgBr

(P)

(P) will be :

(a)O

CH3

CH3

(b)

O

CH3

CH3

(c) CH3 C

MgBr

CH3

CH2 CH2 CH2 CH2Cl

(d) CH3 C

OH

CH3

CH2 CH2 CH2 CH2 Cl

15. Which of the following is not a resonating form of benzaldehyde ?

C OH

(a)

C O+

H

(b)

C OH

(c)+

C OH

(d)

+

16. How will you convert butan-2-one to propanoic acid ? (a) Tollen’s reagent (b) Fehling solution (c) NaOH/I2/H+ (d) NaOH/NaI/H+

27.CH3

OC2H5

O

O

(A)

(B)

NaBH4

LiAlH4

A & B are respectively

(a)

CH3

OC2H5

O

OH

and CH3

OH

OH

+ C2H5OH

(b)

CH3

OH

OH

CH3

OC2H5

O

OH

and

(c)

CH3

OC2H5

OH

OH

andCH3

OC2H5

O

OH

(d) None

17.


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18. Ph – C C – CH3 2+ +Hg /HA, A is:

(a) Ph

CH3

O

(b)

Ph

CH3

O

(c)Ph

CH3

OH

(d)Ph

CH3

OH

19. When m-chloro benzaldehyde is treated with 50% KOH solution; the product(s) obtained is

(are)

(a)

OH

COO

+

OH

CH2OH

(b)

Cl

COO

+

Cl

CH2OH

(c)

Cl

CH CH

OH OH

OH

(d)

OH

CH CH

OH OH

OH

30.

MgBr

(i) CO2

(ii) H3+O

P

In the above reaction, product P is CHO

(a)

COOH

(b)

(c)

OH

(d) C6H5CC6H5

O

21. Which of the following does not give canizarro reaction :

CHO(a)

CH2CHO(b)

CHOCH3(c)

CHOO2N(d)

22. The product(s) obtained via oxymercuration (HgSO4 + H2SO4) of 1-butyne would be

(a) CH3CH2COCH3 (b) CH3CH2CH2CHO

(c) CH3CH2CHO + HCHO (d) CH3CH2COOH + HCOOH

23. In the Cannizaro’s reacting given below:

2Ph – CHO OH Ph - CH2OH + PhCO2

The slowest step is:

(a) the attack of OH at the carbonyl group

(b) the transfer of hydride to the carbonyl group

(c) the abstraction of proton from the carboxylic acid

(d) the deprotonation of Ph-CH2OH

24. Which of the following will react with water to form stable hydrate

(a) HCOOH (b) Cl3C.CHO (c) CCl4 (d) CH3CHO

20.


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25. Compound A (molecular formula C3H8O) is treated with acidified potassium dichromate to form a product B (molecular formula C3H6O). B forms a shining silver mirror on warming with ammonical silver nitrate. B when treated with an aqueous solution of H2NCONHNH2 and sodium acetate gives a product C. Identify the structure of C:

(a) CH3CH2CH = N.NHCONH2 (b)

3

3 2|

CH

CH C N.NHCONH

(c)

3

3 2|

CH

CH C N.CONHNH (d) CH3CH2CH = N.CONHNH2

26. Which of the following is inert towards SN-1 reaction ? (a) Ethyl chloride (b) Isopropyl chloride

(c)

Cl (d)

Cl

BCOO

N2

+30.

The product (B) is

(a)

(b)

(c)

(d)

C N

+Ether

AH3O

+

B.

MgBr

31.

C

O

(a)

C

N- MgBr

(b)

C

N - H

(c)

C

N- OH

(d)

29. At isoelectric point pH of the compound below is

(a) 3.22 (b) 6.96 (c) 8.05 (d) 5.93

27.

28.


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NH2

CH3OH

NaNO2 + HCl

?33.

The product formed is

(a)

O

CH3OH

(b)

OCH3

(c)

COOH

CH2NH2

(d)

CH3 OH

O

Section 3 (Part A) MATHEMATICS

1. Which of the following have same graph.

. 1 a b

Ix y

II. bx+ ay = xy .

bxIII y

x a

&a I II only &b II III only

&c I III only d nonehavethesame graph

2. The function : 1,1 0,f R , defined as 2 3 2 1

cos1 1

x x x x xf x

x x

, is

a even function b onto function c periodic function d invertible

3. The range of cos

;11

xf x where Fractional part function, is

[0,1 11] [10 11,1)a [0,1 11) [10 11,1)b [0,1 11] (10 11,1)c [0,1 11) (10 11,1)d

4. Which of the following is an identical function

2

2; a f x x g x x 2

sin sin 2; g

21 tan

x xb f x x

x

1 1 ;c f x sin x cos x 1 1g x tan x cot x 2 4 ;d f x cos x sin x 4 2g x cos x sin x

5. If 0; 0, ;g x f x x then which of the following is true

0

x

a g t f t dt is decreasing 0

1 1

x

b g t f t dt is decreasing

1

0

x

c g t f t dt is decreasing 1

0

1 1

x

d g t f t dt is increasing

30.


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6. tanx , ,

tan 2 tan, ,

1 tanx tan 2 x

when xis rational

f x x xwhen xis irrational

Then in , , the number of points where f x is discontinuous is

0a 2b 4c 6d

7. If 2d

f ax xdx

, then ' f bx

2x

ab

2 2

3

b xb

a

2 2

2

b xc

a

2 2b xd

a

8.

2

3

0

sin3 ln . 1 1 2

lim. sin . 1 cos

x

xx x x x

x

x x x x

0a 2b 4c 6d

9. Let 2

sin sinlim sinxt x

x tf

x t

. Then the range of f x is

( ,1]a 1,0b 0,1c [ 1, ) d

10. The value of

2 29 11 1 4 13 3limx

x x x x

x

5a 3b 3c 5d

11. Let R be a relation on the set A = {1,2,3,4,…..,2013}. If { (1,2), (2,3), (4,5), (6,6) } R and n be

the number of ordered pairs in R, then the least possible value of n, for R to be symmetric

and transitive but not reflexive is

(a) 16 (b) 14 (c) 12 (d) 10

12. Let 1

0

xe dx a – ln a, where [.] → Greatest Integer Function then ' 'a equal to a N

1a 2b 3c 4d

13. Let 5 4 3 2

15 4 3 2 1

x x x x xf x then value of 1 1

df x at x is

dx

1a 2b 3c d not exist

14. Let 1

1 11 & 1

x x

f x g xx x

; 0,x . Then which of the following is increasing

function for positive x

a g x f x b g f x c g f g x d f f g x


_______________________________________________________________________________________________________________________________________________


15. Let y =f(x) be a continuous function with f(0)=0, say. Given below is the graph of its derivative

function y= 'f x . Let , , &a b c d denotes the number of points of maximum, minimum,

inflexion & critical points of y=f(x) respectively in (0,11). Then

3a a 4b b 5c c 7d d

16. Let f : [1,5] →[2,4] be a bijective function such that 1df (x) 0 x [1,5]

dx

, then

5 4

1

1 2

f(x)dx f (x)dx

(a) 12 (b) 16 (c) 18 (d) 24

17. Let 2

, 0& 0 0; ,x

f x x f a b Rx

such that a b then the value of b

a

f x dx is

(a) a–b (b) a b (c) b a (d) b–a

18. If

441 1 6

2 2

1 0

1

1 1

x x x

dx A and dx Bx x

then value of 3 12A B , where Greatest Integer

function.

0a 1b 1c d noneof these

19. Let f x be a quadratic polynomial where 1 0f . Then

1

0

16 0 4

2

1

f x dx f f

f

1a 2b 3c 4d

20. Consider the function 2 27 12 . 4 3 . 2 . 5 f x x x x x x x . Then Rolle’s Theorem for

f(x) is NOT applicable in the interval

(a) [1,3] (b) [2,4] (c) [3,5] d noneof these

21. The range of the interval f: 1,3 →R under the mapping 34 12f x x x is

(a) [–72,8] (b) [–8,72] (c) [–8,8] (d) [8,72]

22. Let f(x+T)=f(x), where T>0, The minimum possible value of T for

f(x) = sin2x – cot2x + sec2x.cosec2x – tan2x + cos2x.

(a)1 (b) /2 (c) (d) None of these.


_______________________________________________________________________________________________________________________________________________


23. If 2

7 8 71 2

a

x xx x x dx c

a

then value of ' 'a is

2a 4b 6c 8d

24. The value of

11

210

tan1

1 2 2tan

2

xdx

x

x x =

(a) 0 (b) 1/2 (c) 1 2d

25. If 2

3

1

2 4

x

x

f x t t dt

then ' 1f has the value

4a 8b 12c 16d

26. Let f be the function such that 216

1; 0.1

f x x xx

Then 8f equals

(a) 1 (b) 7 (c) 73 (d) 91

27. A continuous real function ( )f x satisfiy 4 2f x f x x R . If 1

0

2 f x dx , then 4

1

f x dx

a 10 b 12 c 14 d 16

28. The function :f R R defined as 12 tan2

xf x e

is

a odd b even c onto &d manyone into

29. The integral values of n, the value of 2 2lim 1 1

n

n n n n , where [.] → Greatest

Integer Function

1

2a 1b 2c 3d

30. Let 3100 99f x x x then set of values of x satisfying the inequality

3

100 99 100 1f x f x f x is

99,0 99, a , 1 0,1b 1,0 1,c 100,0 100,d


_______________________________________________________________________________________________________________________________________________


FIITJEE - JEE (Mains)

ANSWER KEY Physics:

1. b 2. a 3. a 4. d 5. c

6. a 7. c 8. b 9. b 10. c

11. a 12. a 13. d 14. c 15. b

16. b 17. d 18. b 19. c 20. c

21. a 22. c 23. d 24. d 25. d

26. c 27. b 28. a 29. c 30. c

Chemistry:

1 2 3 4 5 6 7 8 9 10

C C D C D B B D B C

11 12 13 14 15 16 17 18 19 20

D A D B B C C A B B

21 22 23 24 25 26 27 28 29 30

B A B B A C A A A B

MATHEMATICS

1 2 3 4 5 6 7 8 9 10

D A A D C D B A C D

11 12 13 14 15 16 17 18 19 20

B B A D D C C C A C

21 22 23 24 25 26 27 28 29 30

B B D B C D C A A C


_______________________________________________________________________________________________________________________________________________




Maximum Marks: 210

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination Hall before the end of the test.

BA

TC

HE

S –

12

14

FIITJEE

CPT1 - 1

CODE: Set- A

PAPER - 1


_______________________________________________________________________________________________________________________________________________


INSTRUCTIONS

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet

before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Parts.

3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.

4. Each part is further divided into two sections: Section-A & Section-C

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.

B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and

write in ink your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

(i) Section-A (01 – 10) contains 10 multiple choice questions which have only one correct answer. Each question

carries +3 marks for correct answer and – 1 mark for wrong answer.

Section-A (11 – 15) contains 5 multiple choice questions which have one or more than one correct

answer. Each question carries +4 marks for correct answer. There is no negative marking.

(ii) Section-C (01 – 05) contains 5 Numerical based questions with single digit integer as answer, ranging from 0 to

9 and each question carries +4 marks for correct answer. There is no negative marking..


_______________________________________________________________________________________________________________________________________________


Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________


_______________________________________________________________________________________________________________________________________________


Useful Data Chemistry:

Gas Constant R = 8.314 J K1 mol1

= 0.0821 Lit atm K1 mol1

= 1.987 2 Cal K1 mol1

Avogadro's Number Na = 6.023 1023

Planck’s Constant h = 6.626 10–34 Js

= 6.25 x 10-27 erg.s

1 Faraday = 96500 Coulomb

1 calorie = 4.2 Joule

1 amu = 1.66 x 10-27 kg

1 eV = 1.6 x 10-19 J

Atomic No : H=1, D=1, Li=3, Na=11, K=19, Rb=37, Cs=55, F=9, Ca=20, He=2, O=8,

Au=79.

Atomic Masses: He=4, Mg=24, C=12, O=16, N=14, P=31, Br=80, Cu=63.5, Fe=56, Mn=55,

Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6

Useful Data Physics:

Acceleration due to gravity g = 10 2m/ s


_______________________________________________________________________________________________________________________________________________


PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS

SSEECCTTIIOONNAA

Single Correct Choice Type

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)

out of which ONLY ONE is correct.

1. An ideal ammeter and an ideal voltmeter are connected as

shown. The ammeter and voltmeter reading for

R1 = 5, R2 = 15, R3 = 1.25 and E = 20V are given as

(a) 6.25 A, 3.75 V (b) 3.00 A, 5 V

(c) 3.75 A, 3.75 V (d) 3.75 A; 6.25 V

E

A V R1

R2 R3

2. Two spheres of radii r and R carry charges q and Q respectively. When they are connected by a wire, there will

be no loss of energy of the system if

(a) qr = QR (b) qR = Qr (c) qr2 = QR

2 (d) qR

2 = Qr

2

3. An electric field given by 2ˆ Ê 4i 3(y 2)j

pierces Gaussian cube of side 1m placed at origin such that its three

sides represents x, y and z axes. The net charge enclosed within the cube is

(a) 04 (b)

03 (c) 05 (d) zero

4. A dipole of dipole moment p is kept at the centre of a ring of radius R and charge q. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is

(a) zero (b) 3

0

pq

4 R

(c) 3

0

pq

2 R (d)

3

0

pq

4 R only if the charge is uniformly distributed on the ring.

5. A conductor in the form of a right angle ABC with AB = 3 cm and BC = 4 cm carries a current of 10 A. There is a

uniform magnetic field of 5 T perpendicular to the plane of the conductor. The force on the conductor will be

(a) 1.5 N (b) 2.0 N (c) 2.5 N (d) 3.5 N

Space for Rough Work


_______________________________________________________________________________________________________________________________________________


6. A parallel plate capacitor of capacitance C = 2 F (without dielectrics) is filled by dielectric slabs as shown in

figure. Then the new capacitance of the capacitor is :

(a) 7.8 F (b) 3.9 F

(c) 2.4 F (d) 8 F

7. A long straight wire, carrying current I, is bent at its midpoint to form an angle of 45°. Magnetic field at point P,

distance R from point of bending is equal to :

(a) 0( 2 1) I

4 R

(b) 0( 2 1) I

4 R

(c) 0( 2 1) I

4 2 R

(d) 0( 2 1) I

2 2 R

8. Figure shows an amperian path ABCDA. Part ABC is in vertical

plane PSTU while part CDA is in horizontal plane PQRS.

Direction of circulation along the path is shown by an arrow near

point B and at D. B.d for this path according to Ampere’s law

will be :

(a) 1 2 3 0(i i i ) (b)

1 2 0( i i )

(c) 3 0i (d)

1 2 0(i i )

9. Five conducting plates are placed parallel to each other, Separation between them is d and area of each plate

is A. Plate number 1, 2 and 3 are connected with each other and at the same time through a cell of emf E. The

charge on plate number 1 is :

(a) 0E A

d

(b) 0E A

2d

(c) 02E A

d

(d) zero

T

U

1i

3i

Q

R 1i

S

D C

P 3i

2i

2i

A B

45° R

P

I

I

E

1 2 3

4

5

3K 6

1K 2

w w

d

d

2K 4


_______________________________________________________________________________________________________________________________________________


10. Half part of ring is uniformly positively charged and other half is

uniformly negatively charged. Ring is in equilibrium in uniform

electric field as shown and free to rotate about an axis passing

through its centre and perpendicular to plane. The equilibrium is

(a) stable (b) unstable

(c) neutral (d) can be stable or unstable

E0

+ +

+

+ +

+ + + – –

– – – – – – –



_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONN -- BB

(Multi Correct Choice Type)

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out

of which ONE OR MORE may be correct.

11. In the circuit shown in figure:

(a) i =2.5 A when S1is closed and S2 is open

(b) 20

i A3

when S1 is open and S2 is closed

(c) 5

i3

A when S1 and S2 both are open

(d) i =20A when both S1 and S2 are closed

S2 S1

1 2 3 10V

20V i

12. An observer A and a charge Q are fixed in a stationary

frame 1F . An observer B is fixed in a frame

2F , which is

moving with respect to 1F :

(a) both A and B will observe electric field

(b) both A and B will observe magnetic field

(c) neither A nor B will observe magnetic field

(d) B will observe magnetic field but A will not

•Q A B

F1 F2

13. Two plates of a parallel plate capacitors carry charges q and –q and

are separated by a distance x from each other. The capacitor is

connected to a constant voltage source0V . The distance between the

plates is changed to x dx. Then in steady state.

(a) change in electrostatic energy stored in the capacitor is Udx

x

,

where U is initial potential energy.

(b) change in electrostatic energy stored in the capacitor is Ux

dx

V0

x

–q +q

(c) attraction force between the plates is 1

qE2

(d) attraction force between the plates is qE. (where E is electric field between the plates)

14. When some potential difference is maintained between A

and B, current I enters the network at A and leaves at B.

(a) The equivalent resistance between A and B is 8 .

(b) C and D are at the same potential.

(c) no current flows between C and D.

(d) current 3I

5 flows from D to C.

20 5 C

20 5 D

A B


_______________________________________________________________________________________________________________________________________________


15. A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are

possible?

(a) E = 0, B = 0 (b) E = 0, B 0 (c) E 0, B = 0 (d) E 0, B 0



_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNCC

Integer Answer Type

1 The following curve represents the variation of

potential of points along x-axis due to two-point

charges q1 and q2 separated by a distance 2a. Find

the ratio of magnitude of two charges (point O is

origin and coordinates of point P is a

, 03

(-a,0) O

2q

V

1q

(a,0) P

x

y

2. The region between X = 0 and X = Lm is filled with uniform steady magnetic field ˆ2Tk . A particle of mass 2

kg, positive charge 1C and velocity 2(m/s) i travels along x-axis and enters the region of the magnetic field

(neglect gravity). Find the value of L if the particle emerges from the region of magnetic field with its final

velocity at an angle 300 to its initial velocity.

3. In the diagram there are four conducting plates A, B, C and D placed parallel to each other at equal separation

L. If plate C starts moving towards plate B with velocity v. Find the current (in mA) flowing in the wire connecting

A and D. (assume all other plates to be fixed)

(Given: q2 = 2C, q3 = 3C, v = 30 m/s, L = 0.05 m )

+q1

–q1

+q2

–q2

–q3 +q3

v A B C D

4. The figure shows a RC circuit with a parallel plate capacitor.

Before switching on the circuit, plate A of the capacitor has a

charge –Q0 while plate B has no net charge. Now, at

t = 0, the circuit is switched on. How much time (in second) will

elapse before the net charge on plate A becomes zero. (Given C =

1F, Q0 = 1mC, = 1000 V and 62 10

Rln3

)

R

A B

–Q0

S

5. A thin insulated wire forms a plane spiral of N = 100 tight turns

carrying a current I = 8 mA. The radii of inside and outside turns

as shown in figure are equal to a = 50 mm and b = 100 mm.

Find the magnetic induction (in micro tesla) upto the nearest

integer at the centre of the spiral;



_______________________________________________________________________________________________________________________________________________


PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY

SSEECCTTIIOONNAA




1. The correct IUPAC NAME of the following compound is

(a) 4-Methyl-5-chloronitrobenzene (b) 2-chloro-1-methyl-4-Nitrobenzene

(c) 3-chloro-4-methyl-1-nitrobenzene (d) 1-chloro-2-methyl-5-nitrobenzene

2. Allyl isocyanide has

(a) 9 & 4 bonds (b) 8 and 5 bonds

(c) 9 ,3 bonds & 2-nonbonded electrons (d) 8 ,3 , bonds and 4 non bonded electrons.

3. In the following groups

OAC,

(I)

OMe

(II)

2OSO Me

III

2 3OSO CF

IV

The order of leaving groups ability is

(a) I > II > III > IV (b) IV > III > I > II

(c) III > II > I > IV (d) II > III > IV > I

4.

Column-I (Comp.) Column – II (Ka)

(a) Benzoic acid (p) 53.3 10

(b) p-nitrobenzoic acid (q) 510.2 10

(c) p-chlorobenzoic acid (r) 530.6 10

(d) p-methoxy benzoic acid (s) 56.4 10

(e) p-methyl benzoic acid (t) 54.2 10


NO2

Cl

CH3


_______________________________________________________________________________________________________________________________________________


Which is correct match for acids in column I with their ka’s in column II

a b c d e

A T P Q R S

B S R P Q T

C R S P T Q

D S R Q P T

5. Among the following compounds I, II & III

Which of the following statement is incorrect

(a) I & III are enantiomers

(b) I & II are diastereomers

(c) II & III are diastereomers

(d) All are incorrect

6. In the given reaction

2

KCN/EtOH

H O Product

(a) & (b)

(c) (d)


CH3

CH3

OH H

OHH

III

CH3

CH3

OH H

HOH

II

CH3

CH3

H OH

HOH

I

OCHO2

OC

O

OK+

OCH2OH

OC

OH

CN

H2

OC

O

CO

O

OC

O

CHO

OH

OH

O


_______________________________________________________________________________________________________________________________________________


7. OH

Product (major)

Product in the above reaction

(a) (b) (c) (d) None

8. When phenol is reacted with 3CHCl and NaOH followed by acidification, salicylaldehyde is obtained, which of

the following species are involved in the above mentioned reaction as intermediate.

(a) (b) (c) (d)

9. The reaction of with HBr gives

(a) (b)

(c) (d)

10. When benzene sulphonic acid and p-nitrophenol is treated with 3NaHCO , the gases released respectively are

(a) 2 2SO ,NO (b) 2SO ,NO (c) 2 2SO ,CO (d) 2 2CO ,CO


O

CH3

O

O-

O

CHCl2

O-

O

H

CHCl

OH

CHCl2

OHO

H

OH

CH3 CH CH OH

CH3 CH2 CH

Br

OH CH3 CHBrCH2 OH

CH3 CH2 CH

Br

Br CH3 CHBrCH2 Br


_______________________________________________________________________________________________________________________________________________






11.

Identify the reagents that can perform this conversion successfully

(a) 2H ,Raney Ni (b)

2Mg,THF,H O

(c) 4 2NaBH ,H O (d)

||

O

H C H , OH

12. The correct statement(s) about solvent effect is/are

(a) Decreasing solvent polarity causes a large increase in the rate of the 2NS attack by ammonia on an alkyl

halide 3 3R X NH RNH X

(b) Increasing solvent polarity causes a large decrease in the rate of the 2NS attack by hydroxide ion on

trimethyl sulphonium ion.

3 3 3 3 2Trimethyl sulphoniumion DMS

HO (CH ) S CH OH (CH ) S

(c) Increasing solvent polarity causes a small decrease in the rate of the 2NS attack by trimethyl amine on

trimethyl sulphonium ion

3 3 3 3 3 3 3 3 2(CH ) N (CH ) S CH N(CH ) (CH ) S

(d) All are incorrect.


OCH2OH

OC

O

H


_______________________________________________________________________________________________________________________________________________


13. KOH

3CHCl X Y

X & Y are

(a) X = (b) X =

(c) Y = (d) Y =

14. In the given reaction

2 6 2 2B H ,THF H O ,NaOH TsCl t BuO K (Y)

The product ‘Y’ is

(a) Position isomer of X (b) Identical to X

(c) Chain isomer of X (d) An oxidation product of (X)

15. Which of the following reactions give alkylation product.

N

H

N

H

CHO N

H

CHCl2

N

Cl

N

Cl

(X)

CH3


_______________________________________________________________________________________________________________________________________________


(a) + H

(b) + H

(c) 3AlCl

3CH COCl (d) 3AlCl

3Me CCOCl


OH


_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNCC

Integer Answer Type

1. The sum of total stereoisomers and fractions on the fractional distillation of 2,3-Dichloropentane is

2. OH

3CH CHO nHCHO

in the preparation of final product if aldol formed is (x) then what is (x + n)?

3. Total no. of chiral centres present in the following compounds is

OH

OHOH

OH

OH

O

H

OH

OH

H

H

OH

CH2OH

H

O

H

OH

OH

H

CH2OH

H CH2OH


_______________________________________________________________________________________________________________________________________________


4. Observe the following reaction and find out that how many number of reactant stereoisomers can be reduced to

optically inactive meso products

4NaBH

5. How many 3CHI will be released from the given compound.

2I /NaOH


CHO

CHOH

CHOH

CHOH

CHOH

CH2OH

CH2OH

(CHOH)4

CH2OH

O O


_______________________________________________________________________________________________________________________________________________


PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS

SSEECCTTIIOONNAA




1. Let |x|{e sgnx}f(x) e and

|x|[e sgnx]g(x) e ,x R where { x } and [ ] denotes the fractional part and integral part

functions respectively. Also h(x) ln(f(x)) ln(g(x)) then for all real x, h (x) is

(A) an odd function (B) an even function

(C) neither an odd nor an even function (D) both odd as well as even function

2. Which of the following function is surjective but not injective

(A) f : R R 4 3 2f(x) x 2x x 1 (B) f : R R 3f(x) x x 1

(C) f : R R 2f(x) 1 x (D) f : R R 3 2f(x) x 2x x 1

3. If 3f(x) 2x 7x 5 then 1f (4) is

(A) equal to 1 (B) equal to 2 (C) equal to 1/3 (D) non existent

4. The function x b,x 0

g(x)cosx,x 0

can be made differentiable at x = 0.

(A) if b is equal to zero (B) if b is not equal to zero

(C) if b takes any real value (D) for no value of b

5. If y is a function of x then 2

2

d y dyy 0

dxdx . If x is a function of y then the equation becomes

(A) 2

2

d x dxx 0

dydy (B)

32

2

d x dxy 0

dydy

(C)

22

2

d x dxy 0

dydy

(D)

22

2

d x dxx 0

dydy


_______________________________________________________________________________________________________________________________________________


6. Which one of the following statement is true?

(A) If x cLimf(x) g(x)

and x cLimf(x)

exist, then x cLimg(x)

exists.

(B) If x cLimf(x) g(x)

exists, then x cLimf(x)

and x cLimg(x)

exist.

(C) If x cLim(f(x) g(x))

and x cLimf(x)

exist, then x cLimg(x)

exist.

(D) If x cLim(f(x) g(x))

exists, then x cLimf(x)

and x cLimg(x)

exist.



_______________________________________________________________________________________________________________________________________________


7. 2 2 2 2

3 3 3 3n

1 n 2 (n 1) 3 (n 2) ..... n .1Lim

1 2 3 ..... n

is equal to :

(A) 1

3 (B)

2

3 (C)

1

2 (D)

1

6

8. If 2

2

x bx 25f(x)

x 7x 10

for x 5 and f is continuous at x = 5, then f (5) has the value equal to

(A) 0 (B) 5 (C) 10 (D) 25

x 3 x

x 1 x

2 2 6

2 2

if x 2

9. Let f(x) then

2x 4

x 3x 2

if x 2

(A) f(2) 8 f is continuous at x = 2 (B) f(2) 16 f is continuous at x = 2

(C) f(2 ) f(2 ) f is discontinuous (D) f has a removable discontinuity at x = 2

10. If x

2

x e cos2xf(x) ,x 0

x

is continuous at x = 0, then

(A) 5

f(0)2

(B) [f(0)] = – 2 (C) {f(0)} = –0.5 (D) [f(0)] . {f(0)} = –1.5

where [x] and {x} denotes greatest integer and fractional part function



_______________________________________________________________________________________________________________________________________________






11. The function 1

lnxf(x) x

(A) is a constant function (B) has a domain (0,1) (e, )

(C) is such that x 1

Limf(x)

exist (D) is aperiodic

12. The function f(x) = (sgn x) (sin x) is

(A) discontinuous no where. (B) an even function

(C) aperiodic (D) differentiable for all x

13. Which of the following function(s) has/have the same range?

(A) 1

f(x)1 x

(B) 2

1f(x)

1 x

(C)

1f(x)

1 x

(D)

1f(x)

3 x

14. Let 2

x 1f(x)

2x 7x 5

. Then:

(A) x 1

1Limit f(x)

3 (B)

x 0

1Limit f(x)

5 (C)

xLimit f(x) 0

(D)

x 5/2Limit

does not exist

15. The function 2

| x 3 | ,x 1

f(x) x 3x 13,x 1

4 2 4

is :

(A) continuous at x = 1 (B) diff. at x = 1

(C) continuous at x = 3 (D) differentiable at x = 3



_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNCC

Integer Answer Type

1. Let f be the function defined by (x y z)(xy xz yz)

f(x,y,z)xyz

for all positive real numbers x, y and z. The

smallest possible value of f, is

2. The value of n

n

2nn 0

1lim 1

2

is

3. f(x) | x 2 | 3 is not differentiable at number of points = ?

4. Evaluate : 2 x

2

0

xe sin

2 4

dx

5. Let 1 2 3 4 5 6

1 1 x x 1f (x) x,f (x) 1 x;f (x) ,f (x) ;f (x) ;f (x)

x 1 x x 1 x

Suppose that 6 m 4f (f (x)) f (x) and

n 4 3f (f (x)) f (x) then n is ________



_______________________________________________________________________________________________________________________________________________


FIITJEE COMMON TEST

PHASE TESTI (PAPER1)

ANSWER KEY WITH Concept Code

PART – I (PHYSICS) PART – II (CHEMISTRY) PART –III (MATHS)

SECTIONA SECTIONA SECTIONA

Q.N. Ans. Con. Code Q.N. Ans. Con. Code Q.N. Ans. Con. Code

1. B P120212,213 1. B C121201 1. A M120321

2. B P120103 2. C C121207 2. D M120308

3. B P120108 3. B C121202 3. A M120311

4. B P120113 4. D C121207 4. D M120311

5. C P120306 5. D C121203 5. C M120516

6. A P120114 6. D C121206 6. C M110602

7. A P120302 7. A C121206 7. A M110611

8. D P120303 8. D C121205 8. A M120404

9. D P120115 9. B C121202 9. C M120401

10. A P120113 10. D C121205 10. D M120404

SECTION-B SECTION-B SECTION-B

11. ABCD P120205,206 11. CD C121206 11. ABC M120319

12. AD P120305 12. BC C121202 12. ABC M120322

13. AC P120114 13. AC C121206 13. BC M120317

14. ABD P120207 14. A C121202 14. ABCD M110602

15. ABD P120305 15. ABD C121206 15. ABC M120408

Paper Code

XXXX.X

CODE: Set- A


_______________________________________________________________________________________________________________________________________________


SECTION –C SECTION -C SECTION -C

1. 2 P120105 1. 6 C121202 1. 9 M120323

2. 1 P120305 2. 7 C121206 2. 2 M110606

3. 1 P120114 3. 9 C121209 3. 3 M120410

4. 2 P120216 4. 4 C121209 4. 0 M120701

5. 7 P120302 5. 0 C121206 5. 5 M120323


_______________________________________________________________________________________________________________________________________________


HINT & SOLUTIONS-PHYSICS

SECTION – A CPT1-1 SET-A

(Single Correct Choice Type)

1. eqR of the circuit = 1 2

3

1 2

R RR

R R

= 5 15 125 75 5

5 15 100 20 4

5

eq

E 20I

R 5 = 4 A

20V

15

5 A V

1.25

R1 R2 R3

Current in 21

1 2

IRR 3A

R R

P.D. across 3 3R IR 5V

(b)

2. There will be no loss of energy if the potential of the spheres is the same i.e. if

0 0

q QV

4 r 4 R

or

q Q

r R

(b)

3. Net flux in x-direction = 0

Net flux in y-direction 2A[3(1) 2] A[3(0) 2]

0

q3A

0 0q 3 A 3 , (as 2A 1m )

(b)

x

y

z

4. The electric field due to the dipole on the circumference of the ring 3

0

pE

4 R

and it is directed normal to the

plane of charged ring.

Hence force on the charged ring 3

0

pqF qE

4 R

(b) 5. Force on the conductor ABC

= Force on the conductor AC

= 5 × 10 × (5 × 10–2

) = 2.5 N

(c)

3cm

10A

A

B C 4cm

× B

3cm

10A A

B C 4cm

× B

F

6. (A)


_______________________________________________________________________________________________________________________________________________


as the potential difference across dielectric of dielectric constant 2 & 4 is not same.

7. (A)

8. (D)

0 1 3 2 3 0 1 2B.d (i i i i ) (i i )

Since for the given direction of circulation 3i entering at PSTU is positive while

3i at PQRS is negative]

9. (D)

10. Assuming ring as dipole, then dipole moment P

and E

are in same direction, so potential energy U = –PE

(A)


11. S1 closed , S2 opened , 20 10

i4

= 2.5 A

S1 opened, S2 closed , 20

i3

A

S1 and S2 both open , 20 10 5

i6 3

A

S1 and S2 both closed, i = 20 A

(a) (b) (c) (d)

12. For frame F1, the charge Q is at rest and for frame F2, the charge Q is in motion. Charge at rest or in motion

produces electric field. So both A and B will observe electric field.

Hence, choice (a) is correct.

Only moving charges produces magnetic field. So B will observe magnetic field but A will not observe any

magnetic field.

3K 6

1K 2

w w

d

d

2K 4

3K 6

1K 2 2K 4

3K 6


_______________________________________________________________________________________________________________________________________________


Hence, choice (d) is correct and choices (b) and (c) are wrong.

(a) and (d)

13. Initial stored energy 2

0 0i

AV1U

2 x

Final stored energy 2

0 0f

AV1U

2 (x dx)

so 2

f i 0 0

1 1 1U U U AV

2 x dx x

2

0 0

1 x x dxAV

2 x(x dx)

2 2

0 0 0 0

2

AV AV1 1 dx Udxdx .

2 2 x x xx

So, choice (a) is correct and choice (b) is wrong. dU U

Fdx x

2

0 0 0 00

A V A V1 1 1F . .V . qE

2 x x 2 x x 2

So magnitude of attractive force is 1

qE.2

So, choice (c) is correct and choice (d) is wrong.

(a) and (c)

14. A D A CV V V V or 20i 5 I i or i = I/5

2I I

I 2i I5 5

Current flowing from D to C.

(a) (b) (d)

20

A

5

5 20

C

D B

20 5 C

20 5 D

A B 1-2i

i 1-i

15. (a) (b) (d)

SECTION–C (Integer Type)

1. Since potential is decreasing, so q 1 is +ve and q 2 is –ve

1 2Kq Kq

a aa a

3 3

, 1

2

q 2

q 1 , 1 2q : q 2 : 1


_______________________________________________________________________________________________________________________________________________


2. 0 Lsin30

r

0

1 L

2 mv

qB

0mv 2 2L

2qB 2 1 2

1m L = 1

r

300

300

2m/s

2m/s

r

X = 0 X = L

3. 31 2

0 0 0

2q (2L x)2q L 2q x0

2A 2A 2A

… (i)

31 2dqdq dq

Idt dt dt

… (ii)

From (i), 1 2 3 3q L q x 2q L q x 0

L x 2L–x

+q1

–q1

+q2

–q2

–q3 +q3

v

I

3 31 22 3

dq dqdq dq dx dxL x q 2 L x q 0

dt dt dt dt dt dt

2 3

vI (q q )

3L = 1 mA

4. Let at any time t charge flown through the plate B to plate A is q and instantaneous current is I.

I

A B

–Q0+q

– q

R

From loop theorem 02q QIR 0

2C

02q 2 C QdqR

dt 2C

0

dq dt

2 C Q 2q 2RC

Now for charge on plate A to be zero q = Q0.

Integrating 0Q t

00 0

dq dt

2 C Q 2q 2RC

= 0

0

2 C Qt RCln

2 C Q

Putting the value of C, Q0, and R

We get t = 2 seconds.


_______________________________________________________________________________________________________________________________________________


5. B = 0INln (b / a)7 T

2(b a)

;

CChheemmiissttrryy HHiinntt aanndd ssoolluuttiioonnss

SECTION – A


1. (B)

2. (C) 2 2CH CH CH N C

3. (B)

4. (D) Acid character

> > > >

5. (D)

6. (D) This is abnormal benzoin.

CN

H Exchange

+

OCH3

COOH

CH3

COOHCOOH

Cl

COOH

NO2

COOH

OC

O

HO

C

O-

H

CN

OC

O-

H+ O

C-

OH

CNO

C

O-

C

H

CNOH

O

H Exchange

OC

-

OH

CN


_______________________________________________________________________________________________________________________________________________


CN

7. (A)

Sol. This is retro aldol

OH

Intramolecular

aldol

2H O

8. (D)

3 3 2CHCl OH HOH : CCl Cl : CCl

OH

2:CCl

2

2NaOH

H O2NaCl

H

9. (B) H

Stable Carbocation

10. (D)


11. (C,D)

OC

O

CH

OHO

OH

O

O-

O

CH3 C

O

CH-

CH2

CH2

C O

CH3

OH

O

O

OH

CHO

O-

CHO

O-

CHCl2

O-

OH

CH3 CH CH OH CH3 CH2 CH+

OH


_______________________________________________________________________________________________________________________________________________


12. (B,C) Polar forms are more stable in polar solvents.

13. (A, C)

Sol. 3 2CHCl OH CCl

OH

2CCl

& H

KOH

14. (A)

2 6

2 2

(i)B H ,THF

(ii)H O ,NaOH

Tscl t BuO

15. (A,B,D)

Sol. (a) + (b) +

N

H

NN

Cl

Cl

Cl

(Y)

N

Cl

Cl

N

H

CCl2 N

H

CHCl2N

CHO

H

(X)

CH3CH3

HH

OH

syn addition

CH3

HH

OTs

TsOh+t BuOH+

CH3

H

Anti el imination

OH


_______________________________________________________________________________________________________________________________________________


(c) + MeCoCl

(d) 3AlCl CO

3 3 3Me C COCl Me C CO Me C


1. (6) + + +

I II III IV

Fraction 1st + Fraction II

nd

2. (7) 2

3 2H OCH CHO OH CH CHO

+ → repeat infor 2moretimer

COCH3

CMe3

Fractional Distillation

(I+II) III & II

CH

H

O

C CH2

O

H

OH

OH

OH

OH

CH

OH

CH2

H

C

O

H

Aldol

C

OH

OH

OH

CHO

Aldol

CH3

CH2CH3

Cl H

H Cl

CH3

CH2CH3

H Cl

Cl H

CH3

CH2CH3

Cl H

Cl H

CH3

CH2CH3

H Cl

H Cl


_______________________________________________________________________________________________________________________________________________


HCO HCHO

Cannizaro reaction

So, 3-Aldol & 4 HCHO

3+ 4 =7

3. (9)

OH

O

H

OH

OH

H

H

OH

CH2OH

H

O

H

OH

OH

H

CH2OH

H CH2OH

*

**

*

*

**

*

*


_______________________________________________________________________________________________________________________________________________


4. (4)

4NaBH

CHO

CH2OH

H OH

H OH

H OH

H OH

(I)

CH2OH

CH2OH

H OH

H OH

H OH

H OH

Meso

CHO

CH2OH

H OH

OH H

OH H

H OH

(II)

CH2OH

CH2OH

H OH

OH H

OH H

H OH

Meso

( )


_______________________________________________________________________________________________________________________________________________


So, in total 4 stereoisomers are reduced to meso products.

5. (0)

MMAATTHHSS HHiinntt aanndd ssoolluuttiioonnss

SECTION – A PAPER - 1


1. {y} {y} |x|h(x) ln(f(x) g(x)) lne {y} [y] y e sgnx

x

|x|

x

e if x 0

h(x) e sgnx 0 if x 0

e if x 0

x

x

e if x 0

h( x) 0 if x 0

e if x 0

h(x) h( x) 0 for all x

2. (A) 4 3 2f(x) x 2x x 1 → A polynomial of degree even will always be into say

2n 2n 1 2n 2

0 1 2 2nf(x) a x a x a x ..... a

x x

Limit f(x) Limit

02n 1 2 2n

0 2 2n0

if a 0a a a[x a .....

if a 0x x x

Hence it will never approach /

(B) 3f(x) x x 1 2f '(x) 3x 1 - injective as well as surjective

( )


_______________________________________________________________________________________________________________________________________________


(C) 2f(x) 1 x neither injective nor surjective (minimum value =1)

3 2f(x) x 2x x 1 2f '(x) 3x 4x 1 D > 0

Hence f(x) is surjective but not injective.

3. Note that f is bijective hence 1f exist

When y 4

32x 7x 9 0

22x (x 1) 2x(x 1) 9(x 1) 0

2(x 1)(2x 2x 9) 0

x 1 only A ; as 22x 2x 9 0 has not other roots.

4. h 0

cosh 1g'(0 ) lim 0

h

h 0

h b 1g'(0 ) lim

h

for existence of line b 1 thus g'(0 ) 1

Hence g can not be made differentiable for any value of b.

5. Given 2

2

d y dyy 0

dxdx

now dy 1

dxdx

dy

2 2

2 2 2

d y d 1 d 1 dy 1 d x 1. . .

dx dx dxdx dy dxdx dydxdy dy dydy

2

2 2

2 3

d x

d y dy

dx dx

dy

(putting in (1))

2

2

3

d x

dyd yy 0

dxdx

dy

2 2

2

dx d xy 0

dy dy

C


_______________________________________________________________________________________________________________________________________________


6. (A) This is false . f(x) x;g(x) cosecx

now x 0limf(x) g(x)

exists =1 also x 0Limf(x) 0

exist but x cLimg(x)

does not exist.

(B) This is false. Let f be defined as 1 if x 0

f(x)2 if x 0

. Let g(x) 0 . Then, f(x)g(x) 0 , and so

x 0Limf(x) g(x)

exits, while x 0Limf(x)

does not.

(C) This is true. Notice that g (f g) f. Therefore, by the limit theorem,

x c x c x cLim g(x) Lim(f(x) g(x)) Limf(x)

(D) This is false.

7. 2 2 2 2

3n

1 n 2 (n 1) 3 (n 2) ............. n (n (n 1))lim

n

r 2 2 2 2 2 2 2N n(1 2 ....n ) (1.2 2.3 3.4 ...... (n 1)n )

n

2 2

r 2

n n (r 1).r

n

2 3 2 2 3 2

r 1

n n (r r ) n n n n

2 3(n 1) n n

2 3

3n

(n 1) n nLim

n

n

(n 1)n(n 1)(2n 1)lim 1

6n(n 1)n(n 1)

4

4 1

13 3 A

Alternatively 2 2 2 2 2 2

3 3 2 3 3

1 n 2 (n 1) ..... n .1 1 (n 1) 2 (n 1) ..... n (n 1)1 1 1

1 2 3 ..... n n

2

3

(n 1) nl 1

n

8. 2x bx 25

f(x) .(x 2)(x 5)

for existence of limit 25 5b 25 0 b 10

now (x 5)(x 5)

f(x)(x 2)(x 5)

and

x 5Limf(x) 0

(A) s


_______________________________________________________________________________________________________________________________________________


9. f(2 ) 8; f(2 ) 16

10. x

2x 0

x e 1 (1 cos2x) 1 5Lim 2 ;

2 2x

hence for continuity

5f(0)

2

[f(0)] 3; 5 1

{f(0)}2 2

hence 3

[f(0)]{f(0)} 1.52

SECTION-B


11. xlog ey x e (constant) A and C

as x 1

Limf(x) e

12. sinx x 0

f(x)sinx x 0

13. Domain is R { 1}; Range = R {0}

Domain is x R; Range (0,1]

Domain is [0, ); Range (0,1]

Domain is ( ,3); Range (0, )]

14. (A,C,D)

15. 2

x 3 if x 3

f(x) 3 x if 1 x 3

x 3x 13if x 1

4 2 4

h 0 h 0

f(1 h) f(1) 3 (1 h) 2f '(1 ) Limit Limit 1

h h


_______________________________________________________________________________________________________________________________________________


2

2

h 0 h 0

(1 h) 3 13(1 h) 2

(1 h) 6(1 h) 54 2 4f '(1 ) Limit Limith 4h

2

h 0

h 2h 6hLimit 1

4h

f is continuous at x=1


1. (x y z)(xy xz yz) 1 1 1 x y y z z x

f(x,y,z) (x y z) 3xyz x y z y x z y x z

minf(x,y,z) 9 ]

2.

2 n n 12 2 2 n

n n

1 1 1 1 1 11 1 1 1 ..... 1 1

2 2 2 2 2 2lim lim 211

1122

Ans. ]

3.

4. 2x x

2

0

xI e sin dx

2 4

put

xt

2

t t t

0 0 0

I 2 e sin t dt 2 e sintcos costsin dx 2 e (sint cost)dt4 4 4

t

02 e sint 0

Ans.]

5. Given 6

x 1f (x)

x

……….(1)

6 m 4

1f (f (x)) f (x)

1 x

(given)

m6 m

m

f (x) 1 1f (f 9x))

f (x) 1 x

(using given relation 6

x 1f (x) )

x

-1 2 5


_______________________________________________________________________________________________________________________________________________


Put mf (x) k

k 1 1

k 1 x

k kx 1 x k x 1

kx

m 6

x 1f (x) f (x)

x

m = 6

again m 4 3

1f (f (x)) f (x)

x

m

1 1f ;

1 x x

let

1t

1 x

t tx 1

t 1x

t

m

tf (t)

t 1

n 5

xf (x) f (x)

x 1

Hence n 5 Ans.]



Maximum Marks: 198

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

You are not allowed to leave the Examination Hall before the end of the test.

BA

TC

HE

S –

12

14

FIITJEE

CPT1 - 2

CODE: Set - A

PAPER - 2


_______________________________________________________________________________________________________________________________________________


INSTRUCTIONS

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet

before attempting the paper. Wrong CODE or no CODE will give wrong results.

C. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Parts.

3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.

4. Each part is further divided into one section: Section-A

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.

D. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and

write in ink your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

(i) Section-A (01 – 08) contains 8 multiple choice questions which have only one correct answer. Each question

carries +3 marks for correct answer and – 1 marks for wrong answer.

Section-A (09 – 14) contains 3 paragraphs. Based upon paragraph, 2 multiple choice

questions have to be answered. Each question has only one correct answer and carries +3 marks for correct

answer and – 1 mark for wrong answer.

Section-A (15 – 20) contains 6 multiple choice questions which have one or more than one correct

answer. Each question carries +4 marks for correct answer. There is no negative marking.


_______________________________________________________________________________________________________________________________________________


Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________


_______________________________________________________________________________________________________________________________________________


Useful Data Chemistry:

Gas Constant R = 8.314 J K1 mol1

= 0.0821 Lit atm K1 mol1

= 1.987 2 Cal K1 mol1

Avogadro's Number Na = 6.023 1023

Planck’s Constant h = 6.626 10–34 Js

= 6.25 x 10-27 erg.s

1 Faraday = 96500 Coulomb

1 calorie = 4.2 Joule

1 amu = 1.66 x 10-27 kg

1 eV = 1.6 x 10-19 J

Atomic No : H=1, D=1, Li=3, Na=11, K=19, Rb=37, Cs=55, F=9, Ca=20, He=2, O=8,

Au=79.

Atomic Masses: He=4, Mg=24, C=12, O=16, N=14, P=31, Br=80, Cu=63.5, Fe=56, Mn=55,

Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6

Useful Data Physics:

Acceleration due to gravity g = 10 2m/ s


_______________________________________________________________________________________________________________________________________________


PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS

SSEECCTTIIOONNAA



of which ONLY ONE is correct.

1. A point charge + q is fixed at point B. Another point charge + q at A of

mass m vertically above B at height h is dropped from rest. Choose the

correct statement

(a) It will collide with B

(b) It will execute S.H.M

(c) It will go down only if 2

0

q

4 < mgh

2

h

A

B

+q

+q

(d) go down up to a point and then come up.

2. In the given diagram, the potential difference between A and

B is V1, when switch is open. The potential difference

between A and B when switch is closed is V2. Then

S

Q0

A

C

+ + + +

– – – –

(a) 01

QV

2C , 0

2

QV

C (b)

1V zero , 2V zero

(c) 01

QV

2C ,

2V zero (d) 01

QV

2C , 0

2

QV

2C

3. There is a uniform magnetic field perpendicular to the

plane of paper. A positive charged particle enters in the

region, perpendicularly and collides inelastically at point Q

to the rigid wall MN. If Co-efficient of restitution e = ½ then

particle

(a) Retraces its path (b) Strikes at point O

(c) Strikes at point M (d) strikes at point N

a

N M O

a/2

Q

a/2


B

Q0

2C

– – – –

+ + + +


_______________________________________________________________________________________________________________________________________________


4. The potentiometer wire AB is 600 cm long. At what distance

from A should the jockey J touch the wire to get zero deflection

in the galvanometer?

(a) 320 cm (b) 120 cm

(c) 20 cm (d) 450 cm

E r

A B J

r

R=15r

E/2 G

5. A miliammeter of range 10mA and resistance 9 is joined in a

circuit as shown. The meter gives full scale deflection for current I

when A and B are used as its terminals, i.e. current enters at A and

leaves at B (C is left isolated). The value of I is

(a) 100 mA (b) 900 mA

(c) 1 A (d) 1.1 A

9 ,10mA

0.1 0.9

A B C

6. A capacitor of capacitance ‘C’ is connected with a battery of emf ε as shown. After full charging a dielectric of

same size of capacitor and dielectric constant k is inserted then choose correct statements. (capacitor is always

connected to battery)

(a) electric field between plates of capacitor remain same

(b) charge on capacitor is Cε

(c) energy on capacitor decreased

(d) electric field between plates of capacitor increased.

7. The electric field in a region is given by ˆ Ê 4i j

N/C. Work done by this field is zero when a particle is

moved along the line

(a) y + 4x = 2 (b) 4y + x = 6 (c) x + y = 5 (d) x – y = 5

8. The time constant of an RC circuit shown in the figure is

(a) 0 (b) 2/3 RC

(c) 6RC/5 (d) 2 RC

R

R

C

E


C


_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNBB

Comprehension Type

This section contains 3 paragraphs. Based upon each paragraph 2 multiple choice questions have to be

answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question 9 to 10

Read the paragraph carefully and answer the following questions:

A hollow cube of side L has two parallel sides conducting and remaining four sides are non-conducting. It is filled with a liquid of dielectric constant k. A small hole of area A at the bottom of the cube is opened at t = 0 and liquid starts leaking through it. The two

conducting sides are connected by a battery of emf .

(Take: L = 9 m, 218A m

20 , k = 10, = 81 V, g = 10 m/s

2 )

L

9. The capacitance of the capacitor as a function of time is

(a) 20 (t 54t 64)9

(b) 20 (t 54t 810)

9

(c) 20 (t 54t 810)9

(d) 20 (t 54t 64)

9

10. The current through the connecting wire as a function of time is

(a) 0 (54 2t) (b)

09 (54 2t) (c) 09 (54 2t) (d) 0 (54 2t)

9



_______________________________________________________________________________________________________________________________________________



A charge particle of charge 1C and mass 10gm is moving with

velocity 10 i m/s in horizontal plane consisting of magnetic field –

0.1 k T of width 2

3m and electric field –0.1 j N/C of width d.

Particle enters the magnetic field at t = 0 perpendicularly and

follows the path as shown in the figure and strikes the wall AB

perpendicularly at A (neglect gravity)

d B

A

A

m2

3

O

E

B

y

x

11. The time t after which it strikes the wall

(a) 1.2 s (b) 0.97 s (c) 1.07 s (d) 1.98 s

12. Taking O as origin y-coordinate of A will be

(a) 3.75 m (b) 0.50 m (c) 4.25 m (d) 3.25 m


A capacitor of capacitance C 0.1F is charged by a battery of

e.m.f. E1 = 100 V and internal resistance r1 = 1 by putting switch

S in position 1 as shown in figure.

100V

0.1F

50V

r2

1

r1

1

99 1

2

E1

R

E2

13. Find out heat generated in R = 99 till steady state

(a) 500 J (b) 495 J (c) 1000 J (d) 485 J

14. Now switch is thrown to position 2. Find the work done on the battery till steady state

(a) 250 J (b) 300 J (c) 275 J (d) 325 J



_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNCC

Multiple Correct Answers Type

This section contains 6 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and

(D),

15. A charged particle enters a region which offers some resistance against its

motion and a uniform magnetic field exists in the region. The particle traces

a spiral path as shown. Then:

(a) angular velocity of particle remains constant

(b) speed of particle decreases continuously

(c) total mechanical energy of the particle remains conserved

(d) net force on the particle is always perpendicular to its direction of motion

16. Four charges, all of the same magnitude, are placed at the four corners of a square. At the centre of the square,

the potential is V and the field is E. By suitable choices of the signs of the four charges, which of the following

can be obtained?

(a) V = 0, E = 0 (b) V = 0, E 0

(c) V 0, E = 0 (d) V 0, E 0

17. In the network shown, points A, B and C are at potentials of 70 V, zero and 10 V respectively.

(a) Point D is at a potential of 40 V.

(b) The currents in the sections AD, DB, DC are in the ratio 3 : 2 : 1

(c) The currents in the sections AD, DB, DC are in the ratio 1 : 2 : 3

(d) The network draws a total power of 200 W


A

B(0 V)

20

30 30

C (10 V)

D

(70 V) 10


_______________________________________________________________________________________________________________________________________________


18. In the circuit shown in figure 1 2C C 2μF . Then charge stored in

(a) capacitor C1 is zero

(b) capacitor C2 is zero

(c) both capacitors is zero

(d) capacitor C1 is 40 C

1 2 3

3 1 2

C1 C2

120V

19. Figures shows the lines of force of the electric field of a positive charge (+q) and a negative charge (-q) respectively.

Which of the following statements are correct?

Q

P

+q

O

(a)

B

A

–q

O

(b)

(a) potential at P is greater than that at Q.

(b) potential at A is greater than that at B.

(c) potential energy at P is less than that at Q

(d) potential energy at A is greater than that at B.

20. H+, He

+ and O

++ ions having same kinetic energy pass through a region of space filled with uniform magnetic

field B directed perpendicular to the velocity of ions. The masses of the ions H+, He

+ and O

++ are respectively in

the ratio 1 : 4 : 16. As a result

(a) H+ ions will be deflected most

(b) only O++

ions will be deflected least

(c) He+ and O

++ ions will suffer same deflection

(d) All ions will suffer the same deflection



_______________________________________________________________________________________________________________________________________________


PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY

SSEECCTTIIOONNAA




1. Compound A (molecular Formula 3 8C H O) is treated with acidified

2 2 7K Cr O to form a product B3 6(MF C H O) . B

forms a shining silver mirror on warning with ammonical 3AgNO . B when treated with an aqueous solution of

2 2H NCONHNH . HCl and sodium acetate gives a product C. Identify the structure of C.

(a) 3 2 2CH CH CH NNHCONH (b)

(c) (d) 3 2 2CH CH CH NCONHNH

2. 3 2 3CH NH CHCl KOH Nitrogen containing compound is

(a) 3CH C N (b)

3 3CH NH CH (c) 3CH N C

(d) 3CH N C

3. Among cellulose, poly (vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of

attraction is weakest is

(a) Nylon (b) Poly (vinyl chloride) (c) Cellulose (d) Natural rubber.

4. The two forms of D-glucopyranose obtained from the solution of D-glucose are called.

(a) Isomers (b) Anomers (c) epimers (d) enantiomers

5. The product of acid hydrolysis of P and Q can be distinguished by

P → Q →

(a) LUCAS Reagent (b) 2, 4 –DNP

(c) Fehling’s solution (d) 3NaHSO


CH3 C NNHCONH2

CH3

CH3 C NCONHNH2

CH3

CH2

OCOCH3

CH3

CH3

OCOCH3


_______________________________________________________________________________________________________________________________________________


6. Which of the following is true for SN1 when solvent is 50% water & 50 % acetone.

(a) > > >

(b) > > >

(c) > > >

(c) > > >

7. + (X) 3

3

CH COONa

H O

The compound (X) is

(a) 3CH COOH (b)

2BrCH COOH (c) 3 2(CH CO) O (d) HC C COOH

8. When propionic acid is treated with aq 3 2NaHCO ,CO is liberated. The carbon of 2CO comes from

(a) Methyl group (b) Carboxylic group (c) Methylene group (d) bicarbonate


Cl

Cl Cl

Ph Cl

Cl

Ph Cl

Cl Cl

Cl

Ph Cl

Cl Cl

Cl

Ph ClCl

Cl

Me CHO Me CH CHCOOH


_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNBB

Comprehension Type




A water insoluble organic mixture contained following compounds.

1. Benzoic acid 2. Salicylaldehyde 3. p-hydroxybenzaldehyde 4. Naphthylanine

5. Naphthalene

The following sequence of reagents are used to separate this mixture

1+2+3+4+5

aq HCl (step X)

[Insoluble] [soluble]*

aq 3NaHCO (step-Y)

[ Insoluble] [soluble]*

aq NaOH

(step-Z)

[Insoluble]*

[soluble]


_______________________________________________________________________________________________________________________________________________


Fill up the serial No. of starred comp. obtained in steps X, Y, Z, W respectively and answer the following

questions

X Y Z W


Steam distillation (step-W)

[distilled]* [left behind]


_______________________________________________________________________________________________________________________________________________


9. Soluble compound at step – Y is

(a) Benzoic acid (b) p-hydroxybenzaldehyde

(c) naphthylamine (d) Naphthalene

10. Insoluble compound at step-Z is

(a) p-hydroxybenzaldehyde (b) Salicylaldehyde

(c) Naphthylamine (d) Naphthalene


Observe the esterificaiton mechanisms for primary and tertiary alcohols.

Type- 1 2 4

||conc.H SO

3 3 2 2 3 2 2 3

O

CH COOH CH CH CH OH CH C OCH CH CH

Mechanism : H

step I

pr O H

step 2

2

Step 3

HH O

Type – 2

+ 2 4conc. H SO

Mechanism

H

Step 1

+

2H O


CH3 C OH

O

CH3 COH

OH+

CH3 COH

OH+

CH3 C

OH

OH

O+

Pr H

CH3 C

O

OCH2CH2CH3

CH3 COH

O

CH3 C

CH3

OH

CH3

CH3 C

CH3

O

CH3

C

O

CH3

CH3 C

CH3

OH

CH3

CH3 C

CH3

CH3

+

CH3 C

CH3

O

CH3

C

O

CH3

CH3 C

O

O H


_______________________________________________________________________________________________________________________________________________


11. 2 4

18conc. H SO

3 2 5CH COOH C H OH (P)

2 4

18conc.H SO

3 3 3CH COOH (CH ) C OH (P)

In the above reactions (P) & (Q) are respectively

(a) ,

(b) ,

(c) ,

(d) ,

12. 3CH COOH 2 4conc.H SO

(X)

3CH COOH 2 4conc.H SO(Y)

(a) (X) solution is optically active while (Y) solution is optically inactive

(b) Both (X) & (Y) solutions are optically active

(c) Both (X) & (Y) solutions are optically inactive

(d) (X) solution is optically inactive while (Y) solution is optically active


CH3 C

O

O C CH3

CH3

CH3

18 CH3 C

O

OC2H5

CH3 C

O

O C CH3

CH3

CH3

CH3 C

O

OC2H5

18

C2H5 C

O

O CH3

18

CH3 C

O

O C CH3

CH3

CH3

CH3 C

O

O C2H5

18

CH3 C

O

O C CH3

CH3

CH3

18

H

CH3

D OH

CH3

C

C2H5

Ph OH


_______________________________________________________________________________________________________________________________________________



Read the following reaction sequence

2ClH NaOEt/ NBS NaOH

hvP Q R S T

Then answer the following question.

13. Compounds ‘T’ is

(a) (b) (c) (d)

14. When ‘S’ is treating with strong base, product obtained is

(a) (b) (c) (d)


O

OH

OH

OH

OH

OH

OH

OH

OH

OH

Br

OHOHOH


_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNCC



(D),

15. The correct statement(s) about the following reaction sequence is/are

2 3 3 2 4 3 2 4 2 2Cl /FeCl Conc.HNO /Conc.H SO conc.HNO conc.H SO , NH NH , (R)

1 2 3 4 5(P) (Q)

(a) ‘R’ gives an aldol condensation reaction on heating with NaOH solution

(b) The compounds ‘Q’ gives a yellow p.pt in acetone

(c) step (4) is an aromatic nucleophillic substitution reaction

(d) the end product is a mixture of three compounds.

16. Which of the following products is/are correctly mentioned in the following reactions

(a) NaOD

3HCHO HCOONa CH OD

(b) NaOH

2HCDO DCOONa CH DOH

(c) NaOEt

2HCDO DCOOEt DCH ONa

(d) NaOD

2 3D CO DCOONa CD OD

17. trans-2-methyl cyclohexanol + acetyl chloride X

X NaOH(aq) Y sodium acetate

(a) X is (b) X is

(c) Y is (d) Y is


CH N NH NO2

O2N

CH3

H

H

OCOCH3

H

CH3

H

OCOCH3

H

CH3

H

OH

CH3

H

H

OH


_______________________________________________________________________________________________________________________________________________


18. The correct statements about peptides are

(a) A dipeptide has one peptide linkage between two amino acids.

(b) By convension N-Terminus is kept at left and C-terminus at right in the structure of a peptide.

(c) If only one amino acid is available for reaction, than only one dipeptide can be formed.

(d) A polypeptide with more than hundred amino acid (mol. Mass > 10,000) is called a protein

19. Salicin (structure given below) is a glycoside, found in the bark of willow tree, used in relieving pain.

Observe the following reaction of salicin.

dil HCl

CarbohydrageP Q

The correct statement(s) is (are) :

(a) P is D-Glucose

(b) Q is 2-hydroxybenzyl alcohol

(c) Q can be converted to a modern analgesic (pain-killer), aspirin

(d) The above reaction occurs through a carbocation

20. Lysine a amino acid has 1 2 3pKa 2.18, pKa 8.95, pKa 10.53

The isoelectric point of Lysine will be

(a) 6.35 (b) 9.74 (c) 2.77 (d) 10.76


O

H

OH

CH2OH

H

OH

H

H

OH

OCH2OH


_______________________________________________________________________________________________________________________________________________


PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS

SSEECCTTIIOONNAA




1. 1 1

0

tan xdx

x

(A) /4

0

sinxdx

x

(B) /2

0

xdx

sinx

(C) /2

0

1 xdx

2 sinx

(D) /4

0

1 xdx

2 sinx

2. The set of values of 'a' which satisfy the equation 2

2 2 2

0

4(t log a)dt log

a

is

(A) a R (B) a R (C) a 2 (D) a 2

3. The value of the function x

2

1

f(x) 1 x (ln t 2lnt)dt where f’ (x) vanishes is :

(A) 1e (B) 0 (C) 12e (D) 1 + 2 1e

4. 2 3/2

(2x 1)dx

(x 4x 1)

(A) 3

2 1/2

xC

(x 4x 1)

(B)

2 1/2

xC

(x 4x 1)

(C) 2

2 1/2

xC

(x 4x 1)

(D)

2 1/2

1C

(x 4x 1)

5. If 4 2

2

x x 1y

x 3x 1

and

dyax b

dx then the value of a + b is equal to

(A) cot 5

8

(B) cot

5

12

(C) tan

5

12

(D) tan

5

8



_______________________________________________________________________________________________________________________________________________


6. If 2 2 2x y R (R 0) then

3

2

y"k

1 y '

where k in terms of R alone is equal to

(A) 2

1

R (B)

1

R (C)

2

R (D)

2

2

R

7. If the function 2t 3x x

f(x) ,x 4

where 't' is a parameter has a minimum and a maximum then the range of

values of 't' is

(A) (0, 4) (B) (0, ) (C) (– , 4) (D) (4, )

8. A particle moves along the curve 3/2y x in the first quadrant in such a way that its distance from the origin

increases at the rate of 11 units per second. The value of dx/dt when x = 3 is

(A) 4 (B) 9

2 (C)

3 3

2 (D) none

SSEECCTTIIOONNBB

Comprehension Type




Read the paragraph carefully and answer the following questions:

If , (where ) are the points of discontinuity of the function g(x) f(f(f(x))), where 1

f(x)1 x

, and

2P(a,a ) is any point on xy-plane.

9. The points of discontinuity of g(x) is

(a) x 0, 1 (b) x 1 only (c) x 0 only (d) x 0,1

10. The domain of f(g(x)) is

(a) x R (b) x R {1} (c) x R {0,1} (d) x R {0,1, 1}



_______________________________________________________________________________________________________________________________________________



If nf(x) (x ) g(x), then n 1f '( ) f "( ) .... f ( ) 0 where f(x) and g(x) are polynomials.

For a polynomial f(x) with rational coefficients, answer the following questions.

11. If f(x) touches x-axis at only one point, then the point of touching is

(a) always a rational number (b) may or may not be a rational number

(c) never a rational number (d) none of these

12. If f(x) is of degree 3 and touches x-axis, then

(a) all the roots of f(x) are rational (b) only one roots is rational

(c) both (a) and (b) may be possible (d) none of these


Let us consider the integrals of the following forms 1/2

2f x, mx nx p

Case 1 : If m 0 , then put 2mx nx p u x m

Case 2 : If p 0 , then put 2mx nx p ux p

Case 3 : If quadratic equation 2mx nx p 0 has real roots and there put 2mx nx p (x )u or

(x )u

13. If 2

dxI

x 9x 4x 6

to evaluate I, one of the most proper substitution could be

(a) 29x 4x 6 u 3x (b) 29x 4x 6 3u x

(c) 1

xt

(d) 2 19x 4x 6

t

14.

152

2

x 1 xdx

1 x

is equal to

(a)

162x 1 x

c10

(b)

2

1c

15 1 x x

(c)

2

15c

1 x x

(d)

15

2x 1 xc

15



_______________________________________________________________________________________________________________________________________________


SSEECCTTIIOONNCC



(D),

15. 1 cosec x dx equals

(A) 12sin sinx c (B) 12cos cosx c

(C) 1c 2sin (1 2sinx) (D) 1cos (1 2sinx) c

16. A continuous and differentiable function ' f ' satisfies the condition ,

x

2

0

f(t)dt f (x) 1 for all real ‘x’. Then :

(A) ' f ' is monotonic increasing x R

(B) ' f ' is monotonic decreasing x R

(C) ' f ' is non monotonic

(D) the graph of y = f (x) is a straight line.

17. Let x

0

sintf(x) dt(x 0)

t then f (x) has :

(A) Maxima if x n where n = 1, 3, 5,.....

(B) Minima if x n where n = 2, 4, 6,......

(C) Maxima if x n where n = 2, 4, 6,......

(D) The function is monotonic

18. The value of

1 2

20

2x 3x 3dx

(x 1) x 2x 2

is :

(A) 12ln2 tan 24

(B) 1 1

2ln2 tan4 3

(C) 12ln2 cot 3 (D) 1ln4 cot 24


_______________________________________________________________________________________________________________________________________________


19. The value of the definite integral, /2

0

sin5xdx

sinx

is

(A) 0 (B) 2

(C) (D) 2

20. The extremum values of the function 1 1

f(x) ,sinx 4 cosx 4

where x R is :

(A) 4

8 2 (B)

2 2

8 2 (C)

2 2

4 2 1 (D)

4 2

8 2



_______________________________________________________________________________________________________________________________________________


FIITJEE COMMON TEST

PHASE TESTI (PAPER2)

ANSWER KEY WITH Concept Code

PART – I (PHYSICS) PART – II (CHEMISTRY) PART –III (MATHS)

SECTIONA SECTIONA SECTIONA

Q.N. Ans. Con. Code Q.N. Ans. Con. Code Q.N. Ans. Con.

Code

1. C P120101 1. A C121206 1. C M120702

2. D P120105 2. D C121208 2. B M120704

3. D P120305 3. D C121211 3. D M120606

4. A P120208 4. B C121209 4. B M120702

5. C P120212 5. C C121206 5. B M120307

6. A P120214 6. B C121202 6. B M120516

7. A P120104 7. C C121207 7. C M120608

8. A P120216 8. D C121207 8. A M120508

SECTION B SECTION B SECTION B

9. B P120115 9. A C121212 9. D M120405

10. C P120115 10. D C121212 10. C M120316

11. B P120313 11. B C121207 11. A M120307

12. C P120313 12. A C121207 12. A M120318

13. B P120216 13. B C121203,204 13. A M120701

14. A P120216 14. B C121203,204 14. D M120705

Paper Code

XXXX.X

CODE: Set - A


_______________________________________________________________________________________________________________________________________________


SECTION –C SECTION –C SECTION –C

15. AB P120305 15. BC C121202,206 15. AD M120705

16. ABCD P120104,P120105 16. ABCD C121206 16. AD M120604

17. ABD P120207 17. AD C121203 17. AB M120607

18. BD P120205,P120215 18. ABCD C121210,211 18. ACD M120704

19. A P120105 19. ABCD C121209,205 19. B M120702

20. AC P120305 20. B C121210 20. AC M120612

HINT & SOLUTIONS-PHYSICS

SECTION – A


1. For charge + q at A to come down, Fe < mg

2

2

0

qmg

4 h

(c)

2. Charge flow is zero after closing the switch, so, 01 2

QV V

2C

(d)

3. After collision velocity becomes v/2 so radius becomes a/2 and hence diameter is a and O will be the centre. So

particle strikes at point N.

D

4. In case of zero deflection in galvanometer

AJ

EV

2 , AJ

EiR

2 ,

E 15r EAJ

15r r 600 2

AJ = 320 cm

(a)


_______________________________________________________________________________________________________________________________________________


5. 3 310 10 9.9 0.1 i 10 10

or I = 1A

(c)

9 10mA

0.1 0.9

A B C

6. P.D. same and electric field same

(a)

7. Work done will be zero when displacement is perpendicular to the field. The field makes an angle

1

1

1tan

4

with positive x-axis

while the line y + 4x = 2 makes an angle

1

2 tan 4 with positive x-axis

0

1 2 90

i.e. the line y + 4x = 2 is perpendicular to E

.

(a)

8. (a)

Comprehension #1

9. 2 dyL A 2gy

dt

(y is height of liquid)

y t1

22

L 0

Ay dy 2g dt

L

22

2

A 2g t ty L 3

92L

0 0(L y)L k yLC

L L

= 0 (L y ky) = 20 (t 54t 810)

9

(b)

10. q C , dq

idt

, 0i 9 (54 2t)

(c)

Comprehension #2


_______________________________________________________________________________________________________________________________________________


SOLUTION

In magnetic field

mv

R 1qB

m

2 m

TqB

0.2

In electric field

Acceleration a qE

m =10 m/s

2

P

A

O

600

R/2

R/2

R

300

R/2 R

2

3

Now, PA' maximum height 2 2v sin

2a

3.75m

y-co-ordinate of A ' is 4.25 m

T' time elapsed in E

is half the time of flight v sin 3

a 2

time t = T

T'6 0.97 sec

11. (b)

12. (c)

Comprehension #3

13. When switch in position 1 and steady state is reached q0 = CE1 = 10 C W1 = Energy supplied by battery = q0E1 = 1000 J

Energy stored on the capacitor 2

01

qU

2C = 500 J

H1 = W1 – U1 = 500 J

99

99H 500

100 = 495 J

(b) 14. Position (2), in steady state q =5C

2 2 0W E (q q) = 250 J

(a)

Multiple Choice Questions

15. Time period of revolution of particle in magnetic field is given by 2 m

TqB

Since for a given particle, m and q are constant. So, in constant magnetic field T is constant


_______________________________________________________________________________________________________________________________________________


Angular velocity 2

T

Hence, angular velocity of particle is constant.

Hence, choice (a) is correct.

Due to resistive force, particle experiences a retardation and an energy is lost during motion against it. Hence

speed and total mechanical energy, both decrease continuously.

Hence, choice (b) is correct and (c) is wrong.

Since, speed of electron is decreasing continuously, therefore it is experiencing a tangential retardation. It is

possible only when the component of resultant force opposite to the direction of motion has non-zero values.

This implies, net force on electron cannot be perpendicular to its direction of motion.

Hence, choice (d) is wrong.

(a) and (b)

16. (a) (b) (c) (d)

17. Let VD be the potential of D, then

C DA D B DV VV V V V

010 20 30

VD = 40 V

Also, ratio of current in AD, DB and DC are 70 40 40 40 10

: :10 20 30

i.e. 3 : 2 : 1

Also total power network draws, 2P I R 200 W

(a) (b) (d)

18. Now, potential difference across C1 is 20 V and across C2 is zero.

charge stored in C1 is 40 C and in C2 is zero.

(b) and (d)

3 1 2

C1 C2

120V

20V 40V 60V

1 2 3

40V 20V 60V

19. (a)

20. m

rq

H He 0r : r : r 1 4 16

: : 1: 2 : 21 1 2

Radius is smallest for H+, so it is deflected most

(a)(c)


_______________________________________________________________________________________________________________________________________________


HINT & SOLUTIONS-CHEMISTRY

SECTION – A CPT1-2 SET-A


1. (A)

2. (D)

3. (D)

4. (B)

5. (C)

6. (B) The stability of carbocation

3° > benzylic > 2° > 1°

7. (C) Perkin reaction

8. (D)

Comprehension #1

9. (A)

10. (D)

Comprehension #2

11. (B) P is by type 1, Q is type – 2

12. (A) X→ Type 1 , Y=Type-2

↓ ↓

Hence configuration racemic product

is retained is obtained.

Comprehension #3

13. (B)

14. (B)

OH+

OH

+

OH

H+

OH

(P)

OH

Cl

(Q)


_______________________________________________________________________________________________________________________________________________


Sol. Ring

Expansion

2Cl

hv

NaOH NBS

Multiple Choice Questions

15. (B,C)

16. (A,B,C,D) See mechanism of cannizaro reaction

17. (A,C)

18. (A,B,C,D)

Dipeptide is formed by iamide linkage b/w 2-amino acid moleculus.

OH

(R)

OH

Br

(S)

OH

OH

(T)

EtO-


_______________________________________________________________________________________________________________________________________________


19. (A,B,C,D)

H Cl

2H O +

20. (B)

Pl 2 3pKa pKa 8.95 10.539.74

2 2

O

H

OH

CH2OH

H

OH

H

H

OH

OCH2OH O

H

OH

CH2OH

H

OH

H

H

OH

O+

CH2OH

H

CH2OH

OH

Q

O

H

OH

CH2OH

H

OH

H

H

OH

+

Carbocation

O

H

OH

CH2OH

H

OH

H

H

OH

H

OH

D Glucose

D Glucose


_______________________________________________________________________________________________________________________________________________


HINT & SOLUTIONS-MATHEMATICS


1. 1 1

0

tan xI dx

x

2x tan ;dx sec d

/4 /4 /42

0 0 0

.sec 2I d d d ; 2 y

tan sin cos sin2

/2 /2

0 0

1 y 1 xdy dx

2 siny 2 sinx

(C)

2.

22

2

2 2

0

tlog a t 2 log (a )

2

2 2(2 2log a) 2 2log a

2 22log a 2log a a R

3. 2f '(x) 1 ln x 2lnx 0 2(1 lnx) 0 1

e

Hence

11 ee

2 2 1

1

1

1 1 1 1 1f 1 (ln t 2lnt)dt 1 t ln t 1 1 2e

e e e e e

(D)

4. 2 3

2 3/2 3/2 3/2

3

2 2

2x 1 2x 1 2x xdx dx dx

(x 4x 1) 4 1 4 1x 1 1

x xx x

Now put 2

2

1 41 t

xx

5. 2 2 2 2 2

2 2

(x 1) 3x (x 1 3x)(x 1 3x)y

x 3x 1 x 1 3x


_______________________________________________________________________________________________________________________________________________


dy

2x 3dx

a 2 & b 3

a b 2 3 5

tan cot12 12

6. 2x 2yy' 0

x yy' 0 x

y 'y

…...(1)

21 yy'' (y ') 0

21 (y ')

y ''y

now 2

2 3/2 3 2 2 2 22

2

y '' 1 (y ') 1 1 1 1k

R(1 (y ') ) y 1 (y ') x y xy 1 (y ') y 1y

7. 2t 3x x

f(x) ;x 4

2

2

(x 4)(3 2x) (t 3x x )f '(x)

(x 4)

for maximum or minimum, f '(x) 0

2 22x 11x 12 t 3x x 0

2x 8x (12 t) 0

For one M and m,

D 0

64 4(12 t) 0

16 12 t 0 4 t or t 4

8. 2 2 2r x y ; dr dx dy

r x ydt dy dt

where x 3;y 3 3 and r 6 ; hence dx dy

6 11 3 3 3dt dt

but dy 3 dx 3 3 dx

xdt 2 dt 2 dt


_______________________________________________________________________________________________________________________________________________


Comprehension #1

9. (d)

Sol 1 x 1

f(x) x 1 f(f(x)) x 0,1.1 x x

Hence points of discontinuity are x 0,1 .

10. (c)

Sol g(X) f(f(f(x))) x,x R {0,1}

1

f(g(x)) x 0,1.1 x

Comprehension #2

11. (a)

Sol If f(x) touches x-axis at only one irrational point, then 2f(x) (x ) g(x), where is irrational.

coefficients of f(x) can’t be rational

for f(x) with rational coefficients, then point of touching is rational.

12. (a)

Sol. The point of touching has to be rational

the two roots of f(x) 0 are rational third root is also rational.

Comprehension #3

13. (a)

Sol. As m 9 0 , hence we can substitute 29x 4x 6 u 3x .

14. (d)

Sol. Here as per notations given, we can substitute 21 x (u x) as m 1 0 and p 1 0 .

15 15

14 15 2u 1 1I du u du u c x 1 x c.

u 15 15

Multiple Correct Type

15. 2 2

2

(1 sinx)(1 sinx) cosx cosx dtI

sinx(1 sinx) sinx(1 sinx) 1 1 1sinx t

4 2 2

16. Differentiating f(x) 2f(x).f '(x) 1

f '(x) ; f(x) 02

Hence x

f(x) c.2

Put x 0 ; f(0) c; but 2f (0) 1


_______________________________________________________________________________________________________________________________________________


f(0) 1

Hence x

f(x) 12

17. sinx

f '(x) ;x

2

xcosx sinxf ''(x)

x

Now f ''(2m ) we have f ''(x) 0 & f ''((2m 1) ) we have f ''(x) 0

18. Numerator 22(x 2x 2) (x 1)

19. sinnx sin(n 2)x 2cos(n 1)xsinx

sinnx sin(n 2)x

dx 2cos(n 1)dx dxsinx sinx

/2 /2 /2 /2 /2

0 0 0 0 0

sin5x sin3x sin3xdx 2cos4xdx dx 0 dx dx

sinx sinx sinx 2

20. f '(x) 0 (sinx cosx)(non zeroquantity) 0

tanx 1 x 3 / 4 or 7 / 4 .

Global Min = x 2n (3 / 4); global max x 2n (7 / 4)

4 4

M ; m8 2 8 2

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QP. Code : xxxx.x PHYSICS, CHEMISTRY & MATHEMATICS - Fiitjee … paper class 12.pdf · 2017. 9. 23. · National Admissions Office : FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai,