aiot-02 english (1)

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IMPORTANT INSTRUCTIONS

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

Use of pencil is strictly prohibited.

2. The Test Booklet consists of90 questions.

3. There are three parts in the question paper. The distribution of marks subjectwise in each part is as under for each correct

response.

PART A PHYSICS (120 marks)

Question No. 1 to 30 consist ofFour (4) marks for each correct response.

PART B MATHEMATICS (120 marks)


PART C CHEMISTRY (120 marks)


4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question.

1 (minus one) 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.

5. No candidate is allowed to carry any textual material, printed or written, bits of papers, paper, mobile phone, any electronic

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

6. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom

of each page.

7. On completion of the test, the candiate 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.

8. Make sure that the CODE printed of the Answer Sheet is the same c as that on this booklet. In case of discrepancy, the

condidate should immediately report the matter to the Invigilator fo replacement of both the Test Booklet and the Answer Sheet.

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

10. Fill the test cities code in ORS Sheet and for details of cities code see last page this test paper booklet.

Date : 01-04-2012 Duration : 3 Hours Max. Marks : 360

ALL INDIA OPEN TEST-2 (AIOT-2)

TARGET : AIEEE 2012 0

CODE

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

DONOTBREAKTHESEA

LSWITHOUTBEING

INSTRUCTEDTODOSOB

YTHEINVIGILATOR

CLASS-XII / XIII COURSE : ALL INDIA TEST SERIES (VIKALP)

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(SPACE FOR ROUGH WORK)

ERMT3010412C0-1

PARTA

SECTION - I

Straight Objective Type

This section contains 27 multiple choice

questions. Each question has 4 choices (1),(2), (3) and (4) for its answer, out of which

ONLY ONE is correct.

1. During ground to ground projectile motion if

height(h) attained by a particle from ground

level is given by equation h = (20t 5t2)m. Then

maximum height attained by particle will be :

(1) 10 m

(2) 20 m

(3) 30 m

(4) 40 m

2. Two blocks A and B of masses 4 kg and 8 kg

respectively are placed on a smooth plane

surface. A force F of 12 N is applied on A as

shown. Then the force of contact (in N)

between A and B is :

(1) 2 (2) 4

(3) 8 (4) 12

3. A cubical block of wood of side length 20 cm,

floats in oil and water as shown in figure. The

density of oil is 0.8 g cm3 and density of water

is 1 g cm3. The mass of the block is :

(1) 2.08 kg

(2) 7.04 kg

(3) 8 kg

(4) 9.06 kg

4. An ideal gas undergoes a cyclic process abcda

which is shown by pressure- density curve.

P

d

a

b

c

1

(1) Work done by the gas in the process 'bc'

is positive

(2) Work done by the gas in the process 'cd'

is negative

(3) Internal energy of the gas at state 'a' is

greater than at state 'c'

(4) Net work done by the gas in the cycle is

positive.

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ERMT3010412C0-2

5. A rod of length 1m is sliding in a corner as

shown. At an instant when the rod makes an

angle of 60 with the horizontal plane, the

velocity of point A on the rod is 1m/s. The

angular velocity of the rod at this instant is :

(1) 2 rad/s

(2) 1.5 rad/s

(3) 0.5 rad/s

(4) 0.75 rad/s

6. A solid sphere is in pure rolling motion on an

inclined surface having inclination . Then :

//////////////////////

(1) frictional force is acting on sphere down

the inclined plane

(2) If increases, friction will decrease .

(3) Friction will decrease its angular velocity.

(4) Friction will decrease its linear velocity.

7. A pendulum consists of a wooden bob of mass

m and length . A bullet of mass m1 is fired

towards the pendulum with a speed v1 and it

emerges from the bob with speed3

v1. The bob

just completes motion along a vertical circle.

Then v1 is :

(1) g5m

m

1

(2) g5m2

m3

1

(3) g5m

m

3

2

1

(4) g5m

m1

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ERMT3010412C0-3

8. A block of unknown mass is at rest on a fixed

rough, horizontal surface. A horizontal force F

is applied to the block. The graph in the figure

shows the acceleration of the block with

respect to the applied force. The mass of the

block is

(1) 0.1 kg

(2) 0.5 kg

(3) 2.0 kg

(4) 0.2 kg

9. A block weighing 40 N travels down a smooth

fixed curved track AB joined to a rough

horizontal surface (figure). The rough surface

has a friction coefficient of 0.10 with the block.

If the block starts slipping on the track from a

point 2.0 m above the horizontal surface, the

distance it will move on the rough surface is :

(1) 40 m (2) 20 m

(3) 15 m (4) 10 m

10. A positive point charge +Q is fixed in space. A

negative point charge q of mass m revolves

around fixed charge in elliptical orbit. The fixed

charge +Q is at one focus of the ellipse. The

only force acting on negative charge is the

electrostatic force due to positive charge. Then

which of the following statement is true.

(1) Linear momentum of negative point charge

is conserved.

(2) Angular momentum of negative point charge

about fixed positive charge is not conserved.


about fixed positive charge is conserved.

(4) Angular velocity of the charge q is

conserved about +Q charge.

11. The acceleration of a certain simple harmonic

oscillator is given by

a = (35.28 m/s2) cos 4.2t

The amplitude of the simple harmonic motion

is

(1) 2.0 m (2) 8.4 m

(3) 16.8 m (4) 17.64 m

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ERMT3010412C0-4

12. Four cubes of ice at 10C each one gm is

taken out from the refrigerator and are put in

150 gm of water at 20C. The temperature of

water when thermal equilibrium is attained.

Assume that no heat is lost to the outside and

water equivalent of container is 46 gm.

(Specific heat capacity of water =1 cal/gm-C,

Specific heat capacity of ice = 0.5 cal/gm-C,Latent heat of fusion of ice = 80 cal/gm)

(1) 0C

(2) 10C

(3) 17.9C

(4) None of these

13. Uniformly charged infinite wire and uniformly

charged wire AB lies in a plane. Find the

force on infinite wire, due to wire AB.

(1) k12 n 916

(2) k12 n 925

(3)9

25k12

(4)9

16k12

14. An open organ pipe is in resonance in its 2nd

harmonic with a tuning fork of frequency f1. Now

it is closed at one end. If the frequency of the

tuning fork is increased slowly from f1

then

again a resonance is obtained when the

frequency is f2. If in this case the pipe vibrates

in nth harmonic then

(1) n = 3, f2

=4

3f1

(2) n = 3, f2

=4

5f1

(3) n = 5, f2

=4

5f1

(4) n = 5, f2

=4

3f1

15. A chord attached about an end to a vibrating

fork divides it into 6 loops, when its tension is

36 N. The tension at which it will vibrate in

4 loops is:

(1) 24 N

(2) 36 N

(3) 64 N

(4) 81 N

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ERMT3010412C0-5

16. If radius of a resistor is decreased by 0.5% by

stretching then percentage change in

resistance :

(1) 0.5 %

(2) 1%

(3) 1.5%

(4) 2%

17. The temperature of an spherical isolated black

body falls from T1to T

2in time 't'. Then time t is

(1)

12 T

1

T

1t

(2)

21

22 T

1

T

1t

(3)

31

32 T

1

T

1t

(4)

41

42 T

1

T

1t

18. The charge on capacitor in two different RC

circuits 1 and 2 are plotted as shown in figure.

Choose the correct statement(s) related to the

two circuits.

(1) Both the capacitors are charged to the

same magnitude of charge

(2) The emf's of cells in both the circuits are

equal.

(3) The emf's of the cells must be different

(4) The emf E1 is equal to E2

19. An infinitely long current carrying wire is placed

along x-axis such that it lies between x = 0 to

x = + (infinity). The current is in direction of

positive x-axis. Let B1, B

2and B

3be the

magnitude of magnetic field at points A(a, a),

B(0, a) and C(a, a) respectively. Then pick

the incorrect option.

(1) B1

> B2

> B3

(2) B2

=2

BB 31

(3) B1

: B2

: B3

= 12 : 1 : 12

(4) 21

B

BB22

31

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20. A non conducting ring of radius R and mass

m having charge q uniformly distributed over

its circumference is placed on a rough

horizontal surface. A vertical time varying

uniform magnetic field B = 4t2 is switched

on at time t=0. The coefficient of friction

between the ring and the table, if the ring

starts rotating at t =1 sec, is :

(1) g

qmR4(2) mg

qR4

(3) mgqR8

(4) mg2

qR

21. A spherical liquid drop of radius R is divided

into eight equal droplets. If surface tension is

T, then work done in the process will be

(assume isothermal condition) :

(1) 2R2 T

(2) 3R2 T

(3) 4R2

T(4) 2RT2

22. The following truth table corresponds to the

logic gate

A 0 0 1 1

B 0 1 0 1

X 0 1 1 1

(1) NAND (2) OR

(3) AND (4) XOR

23. In the following circuit readings in ammeters

A1 and A2 will be-

10

10

A1

A2

2V

(1) 0.2 A, zero

(2) Zero, 0.2 A

(3) 0.2 A, 0.2 A

(4) 0.2 A, 0.4 A

24. The value of current in two series LCR circuits

at resonance is same when connected across

a sinusoidal voltage source. Then:

(1) both circuits must be having same value

of capacitance and inductor

(2) in both circuits ratio of L and C will be

same

(3) for both the circuits XL/XC must be same

at that frequency

(4) both circuits must have same impedance

at all frequencies.

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ERMT3010412C0-7

SECTION - II

Reasoning Type

This section contains 3 reasoning type

questions. Each question has 4 choices (1),

(2), (3) and (4), out of which ONLY ONE is

correct.

25. STATEMENT1: In the photo electric effect

experiment, saturation is achieved and cross

section area of electrons beam is also uniform.

Electrons density at section (1) and section (2)

will be same.

STATEMENT2: At saturation, current

through each section will be same.

(1) Statement-1 is True, Statement-2 is True;

Statement-2 is a correct explanation for

Statement-1.


Statement-2 is NOT a correct explanation for

Statement-1

(3) Statement-1 is True, Statement-2 is False

(4) Statement-1 is False, Statement-2 is True

26. STATEMENT-1 : In alpha decay of different

radioactive nuclides, energies of alpha particles

has been compared. It is found that as energy

of alpha particle increases the half life of the

decay decreases.

STATEMENT-2 : More is the energy in any

decay process, more is the probability ofdecaying the nuclide which leads to faster rate

of decay.



Statement-1.



Statement-1



27. STATEMENT-1 : Two coherent point sources

of light having nonzero phase difference are

seperated by small distance. Then on the

perpendicular bisector of line segment

joining both the point sources, constructive

interference cannot be obtained.

STATEMENT-2 : For two waves from

coherent point sources to interfere

constructively at a point, the magnitude of

their phase difference at that point must be

2m where m is a nonnegative integer) .



Statement-1



Statement-1


(4) Statement-1 is False, Statement-2 is

True.

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ERMT3010412C0-8

SECTION - III

Comprehension Type

This section contains 1 paragraph. Based upon each paragraph, 2 multiple choice questions

have to be answered. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY

ONE is correct.

Paragraph for Question Nos. 28 to 30

Consider a transparent homogenous hemisphere of refractive index n = 2 in front of which a

small object is placed in air as shown in figure.

28. Calculate value of x so that the final image of the small object OA will be virtual :

(1) 2 R (2) 3 R (3)2

R(4) 1.5 R

29. The position of image from P after refraction from curved surface (For x = 2R)

(1) R (2) 2 R (3) 4 R (4) 1.5 R

30. The nature of final image of the object OA when x = 2 R :

(1) Erect and magnified (2) Inverted and magnified

(3) Erect and same size (4) Inverted and same size

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ERMT3010412C0-1

PARTA

SECTION - I


This section contains 27 multiple choice

questions. Each question has 4 choices (1),(2), (3) and (4) for its answer, out of which

ONLY ONE is correct.

1. During ground to ground projectile motion if

height(h) attained by a particle from ground

level is given by equation h = (20t 5t2)m. Then

maximum height attained by particle will be :

(1) 10 m

(2) 20 m

(3) 30 m

(4) 40 m

2. Two blocks A and B of masses 4 kg and 8 kg

respectively are placed on a smooth plane

surface. A force F of 12 N is applied on A as

shown. Then the force of contact (in N)

between A and B is :

(1) 2 (2) 4

(3) 8 (4) 12

3. A cubical block of wood of side length 20 cm,

floats in oil and water as shown in figure. The

density of oil is 0.8 g cm3 and density of water

is 1 g cm3. The mass of the block is :

(1) 2.08 kg

(2) 7.04 kg

(3) 8 kg

(4) 9.06 kg

4. An ideal gas undergoes a cyclic process abcda

which is shown by pressure- density curve.

P

d

a

b

c

1

(1) Work done by the gas in the process 'bc'

is positive

(2) Work done by the gas in the process 'cd'

is negative

(3) Internal energy of the gas at state 'a' is

greater than at state 'c'

(4) Net work done by the gas in the cycle is

positive.

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ERMT3010412C0-2

5. A rod of length 1m is sliding in a corner as

shown. At an instant when the rod makes an

angle of 60 with the horizontal plane, the

velocity of point A on the rod is 1m/s. The

angular velocity of the rod at this instant is :

(1) 2 rad/s

(2) 1.5 rad/s

(3) 0.5 rad/s

(4) 0.75 rad/s

6. A solid sphere is in pure rolling motion on an

inclined surface having inclination . Then :

//////////////////////

(1) frictional force is acting on sphere down

the inclined plane

(2) If increases, friction will decrease .

(3) Friction will decrease its angular velocity.

(4) Friction will decrease its linear velocity.

7. A pendulum consists of a wooden bob of mass

m and length . A bullet of mass m1 is fired

towards the pendulum with a speed v1 and it

emerges from the bob with speed3

v1. The bob

just completes motion along a vertical circle.

Then v1 is :

(1) g5m

m

1

(2) g5m2

m3

1

(3) g5m

m

3

2

1

(4) g5m

m1

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ERMT3010412C0-3

8. A block of unknown mass is at rest on a fixed

rough, horizontal surface. A horizontal force F

is applied to the block. The graph in the figure

shows the acceleration of the block with

respect to the applied force. The mass of the

block is

(1) 0.1 kg

(2) 0.5 kg

(3) 2.0 kg

(4) 0.2 kg

9. A block weighing 40 N travels down a smooth

fixed curved track AB joined to a rough

horizontal surface (figure). The rough surface

has a friction coefficient of 0.10 with the block.

If the block starts slipping on the track from a

point 2.0 m above the horizontal surface, the

distance it will move on the rough surface is :

(1) 40 m (2) 20 m

(3) 15 m (4) 10 m

10. A positive point charge +Q is fixed in space. A

negative point charge q of mass m revolves

around fixed charge in elliptical orbit. The fixed

charge +Q is at one focus of the ellipse. The

only force acting on negative charge is the

electrostatic force due to positive charge. Then

which of the following statement is true.

(1) Linear momentum of negative point charge

is conserved.


about fixed positive charge is not conserved.


about fixed positive charge is conserved.

(4) Angular velocity of the charge q is

conserved about +Q charge.

11. The acceleration of a certain simple harmonic

oscillator is given by

a = (35.28 m/s2) cos 4.2t

The amplitude of the simple harmonic motion

is

(1) 2.0 m (2) 8.4 m

(3) 16.8 m (4) 17.64 m

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ERMT3010412C0-4

12. Four cubes of ice at 10C each one gm is

taken out from the refrigerator and are put in

150 gm of water at 20C. The temperature of

water when thermal equilibrium is attained.

Assume that no heat is lost to the outside and

water equivalent of container is 46 gm.

(Specific heat capacity of water =1 cal/gm-C,

Specific heat capacity of ice = 0.5 cal/gm-C,Latent heat of fusion of ice = 80 cal/gm)

(1) 0C

(2) 10C

(3) 17.9C

(4) None of these

13. Uniformly charged infinite wire and uniformly

charged wire AB lies in a plane. Find the

force on infinite wire, due to wire AB.

(1) k12 n 916

(2) k12 n 925

(3)9

25k12

(4)9

16k12

14. An open organ pipe is in resonance in its 2nd

harmonic with a tuning fork of frequency f1. Now

it is closed at one end. If the frequency of the

tuning fork is increased slowly from f1

then

again a resonance is obtained when the

frequency is f2. If in this case the pipe vibrates

in nth harmonic then

(1) n = 3, f2

=4

3f1

(2) n = 3, f2

=4

5f1

(3) n = 5, f2

=4

5f1

(4) n = 5, f2

=4

3f1

15. A chord attached about an end to a vibrating

fork divides it into 6 loops, when its tension is

36 N. The tension at which it will vibrate in

4 loops is:

(1) 24 N

(2) 36 N

(3) 64 N

(4) 81 N

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ERMT3010412C0-5

16. If radius of a resistor is decreased by 0.5% by

stretching then percentage change in

resistance :

(1) 0.5 %

(2) 1%

(3) 1.5%

(4) 2%

17. The temperature of an spherical isolated black

body falls from T1to T

2in time 't'. Then time t is

(1)

12 T

1

T

1t

(2)

21

22 T

1

T

1t

(3)

31

32 T

1

T

1t

(4)

41

42 T

1

T

1t

18. The charge on capacitor in two different RC

circuits 1 and 2 are plotted as shown in figure.

Choose the correct statement(s) related to the

two circuits.

(1) Both the capacitors are charged to the

same magnitude of charge

(2) The emf's of cells in both the circuits are

equal.

(3) The emf's of the cells must be different

(4) The emf E1 is equal to E2

19. An infinitely long current carrying wire is placed

along x-axis such that it lies between x = 0 to

x = + (infinity). The current is in direction of

positive x-axis. Let B1, B

2and B

3be the

magnitude of magnetic field at points A(a, a),

B(0, a) and C(a, a) respectively. Then pick

the incorrect option.

(1) B1

> B2

> B3

(2) B2

=2

BB 31

(3) B1

: B2

: B3

= 12 : 1 : 12

(4) 21

B

BB22

31

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ERMT3010412C0-6

20. A non conducting ring of radius R and mass

m having charge q uniformly distributed over

its circumference is placed on a rough

horizontal surface. A vertical time varying

uniform magnetic field B = 4t2 is switched

on at time t=0. The coefficient of friction

between the ring and the table, if the ring

starts rotating at t =1 sec, is :

(1) g

qmR4(2) mg

qR4

(3) mgqR8

(4) mg2

qR

21. A spherical liquid drop of radius R is divided

into eight equal droplets. If surface tension is

T, then work done in the process will be

(assume isothermal condition) :

(1) 2R2 T

(2) 3R2 T

(3) 4R2

T(4) 2RT2

22. The following truth table corresponds to the

logic gate

A 0 0 1 1

B 0 1 0 1

X 0 1 1 1

(1) NAND (2) OR

(3) AND (4) XOR

23. In the following circuit readings in ammeters

A1 and A2 will be-

10

10

A1

A2

2V

(1) 0.2 A, zero

(2) Zero, 0.2 A

(3) 0.2 A, 0.2 A

(4) 0.2 A, 0.4 A

24. The value of current in two series LCR circuits

at resonance is same when connected across

a sinusoidal voltage source. Then:

(1) both circuits must be having same value

of capacitance and inductor

(2) in both circuits ratio of L and C will be

same

(3) for both the circuits XL/XC must be same

at that frequency

(4) both circuits must have same impedance

at all frequencies.

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ERMT3010412C0-7

SECTION - II

Reasoning Type

This section contains 3 reasoning type

questions. Each question has 4 choices (1),


correct.

25. STATEMENT1: In the photo electric effect

experiment, saturation is achieved and cross

section area of electrons beam is also uniform.

Electrons density at section (1) and section (2)

will be same.

STATEMENT2: At saturation, current

through each section will be same.



Statement-1.



Statement-1



26. STATEMENT-1 : In alpha decay of different

radioactive nuclides, energies of alpha particles

has been compared. It is found that as energy

of alpha particle increases the half life of the

decay decreases.

STATEMENT-2 : More is the energy in any

decay process, more is the probability ofdecaying the nuclide which leads to faster rate

of decay.



Statement-1.



Statement-1



27. STATEMENT-1 : Two coherent point sources

of light having nonzero phase difference are

seperated by small distance. Then on the

perpendicular bisector of line segment

joining both the point sources, constructive

interference cannot be obtained.

STATEMENT-2 : For two waves from

coherent point sources to interfere

constructively at a point, the magnitude of

their phase difference at that point must be

2m where m is a nonnegative integer) .



Statement-1



Statement-1


(4) Statement-1 is False, Statement-2 is

True.

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ERMT3010412C0-8

SECTION - III

Comprehension Type

This section contains 1 paragraph. Based upon each paragraph, 2 multiple choice questions

have to be answered. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY

ONE is correct.

Paragraph for Question Nos. 28 to 30

Consider a transparent homogenous hemisphere of refractive index n = 2 in front of which a

small object is placed in air as shown in figure.

28. Calculate value of x so that the final image of the small object OA will be virtual :

(1) 2 R (2) 3 R (3)2

R(4) 1.5 R

29. The position of image from P after refraction from curved surface (For x = 2R)

(1) R (2) 2 R (3) 4 R (4) 1.5 R

30. The nature of final image of the object OA when x = 2 R :

(1) Erect and magnified (2) Inverted and magnified

(3) Erect and same size (4) Inverted and same size

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ERMT3010412C0-9


PART- B

SECTION - I


This section contains 25 questions. Each

question has 4 choices (1), (2), (3) and (4) for

its answer, out of which ONLY ONE is correct.

31. Consider the function f(x) = x2 + bx + c where

D = b2 4c > 0. If b = 0, c < 0 then number of

points of non differentiability of |f(|x|)| are

(1) 1

(2) 2

(3) 3

(4) 4

32. )x!n(sinlim

40

n

, n N and x is a rational

number.

(1) 0

(2) 1

(3) 1/2

(4) does not exist

33. If f(x) = 5x2

ax

3

x 23 has negative point of

minima then

(1) a < 1

(2) a > 2

(3) a < 2

(4) a > 2

34. dxxsecxsinx3

is equal to

(1)2

1[sec2x tanx] + c

(2)2

1[xsec2x tanx] + c

(3)2

1[xsec2x + tanx] + c

(4) 2

1

[sec2x + tanx] + c

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35. If i = 1 then the value of

100

0n

!n)i( is

(1) 2i + 94

(2) 2i + 95

(3) 96 + 2i

(4) 98 + 2i

36. A person always prefer to drink ' juice' and

milk shake in his breakfast. In how many ways

he can drink them if there are 4 types of juice,

3 types of milk shake, two types of tea and

two types of coffee.

(1) 1681

(2) 1680

(3) 1682

(4) 1684

37. If A is 5 5 skew symmetric matrix then its

trace is equal to

(1) 5

(2) 5

(3) |A|5

(4) 1

38. The probability that a leap year will have 53

Monday or 53 Tuesday is

(1)7

1

(2)7

2

(3)7

3

(4)7

4

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39. If the product of n positive number is nn, then

their sum is

(1) a positive integer

(2) divisible by n

(3) equal to n +n

1

(4) never less than n2.

40. The locus of the centres of the circle

x2 + y2 2ax 2by + 2 = 0, where a and b are

parameters, if the tangents from the origin to

each of the circles are orthogonal.

(1) straight line

(2) parabola

(3) ellipse

(4) circle

41. If | ba

| < | ba

|, then the angle between

a

and b

lies in the interval

(1)

2,

2

(2) (0, )

(3)

,2

(4)

2

3,

2

42. If the normals at points P(t1) and Q(t

2) on the

parabola y2 = 4ax intersect at R on the curve

then

(1) t1= t

2

(2) t1

t2

= 4

(3) t1

t2

= 2

(4) t1t2

= 1

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43. The orthocentre of the triangle having sides

x y + 1 = 0, x + y + 3 = 0 and 2x + 5y 2 = 0

is

(1) (2, 1)

(2) (2,1)

(3) (2, 1)

(4) (2,1)

44. The latusrectum of the ellipse

x2 tan2 + y2 sec2 = 1 is2

1then

20 is equal to

(1)

3

(2)4

(3)12

5

(4)8

45. If sin + cos = a, then sin3 + cos3 =

(1) )a3(2

a 2

(2) )3

a(2

a 2

(3) )3a(2

a 2

(4) )2a(a 2

46. Which of the following equation is linear ?

(1) xlogx

y

dx

dy

(2) 0x4

dx

dyy 22

(3) (2x2 + y3)

dx

dy= 3y

(4) none of these

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47. If sin1

4tan sin1

y

3

6

= 0 and x2 = y

then x is equal to

(1) 2

(2) 4

(3) 2

(4) 3

48. If A and B are two events such that

0 < P(A) < 1 and 0 < P(B) < 1 and

P(A B) + P(A) P(B) = P(A) + P(B). Then

(1) A and B are dependent events.

(2) A and B are independent events.

(3) A B is a disjoint set.

(4) none of these

49. The product of r consecutive integers is

divisible by

(1) r4

(2)

1r

1k

2k

(3) r !

(4) none of these

50. If the fourth term (which is independent of x )

in the expansion of

n

x

1ax

is

2

5, then

(1) a =3

1, n = 6

(2) a =3

1, n = 5

(3) a = 2, n = 3

(4) a =21 , n = 6

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51. The domain of definition of the function

f(x) =

4

xx5log

2

10 is

(1) (1, 4)

(2) (0, 5)

(3) [1, 4]

(4) (0, 5]

52. The false statement in the following is

(1) p (~p) is a contradiction

(2) (p q) (q p) is a contradiction

(3) ~ (~p) p is a tautology

(4) p (~p) is tautology

53. Let I be the set of all non-zero integers and a

relation R is defined as (x, y) R xy = yx

for x, y I {0}, then relation R is

(1) reflexive but not symmetric

(2) symmetric but not reflexive

(3) reflexive and symmetric both

(4) equivalence relation

54. For the curve yn = an1x, if the subnormal at

any point is a constant then n =

(1) 1

(2) 2

(3) 1

(4) 2

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55. If f(x) =

x4

3,x

9

2sin3

4

3x0,1

, then

(1) f(x) is continuous at x = 0

(2) f(x) is continuous at x =

(3) f(x) is continuous at x =4

3

(4) f(x) is discontinuous at x =4

3

SECTION - II

Reasoning Type

This section contains 5 reasoning typequestions. Each question has 4 choices (1),


correct.

56. STATEMENT- 1 : ii is an imaginary number.

STATEMENT- 2 : i = 1 is an imaginary

number

(1) Statement -1 is True, Statement -2 is True; Statement -2 is a correct explanation for

Statement -1

(2) Statement-1 is True, Statement-2 is True ;

Statement-2 is NOT a correct explanation

for Statement-1

(3) Statement -1 is True, Statement -2 is False

(4) Statement -1 is False, Statement -2 is True

57. If z1 z

2and |z

1+ z

2| =

21 z

1

z

1 then

STATEMENT- 1 : z1z

2is unimodular.

STATEMENT- 2 : z1

and z2

both are

unimodular.

(1) Statement -1 is True, Statement -2 is True

; Statement -2 is a correct explanation for

Statement -1



for Statement-1


(4) Statement -1 is False, Statement -2 is

True

58. STATEMENT- 1 : The function f(x) = esinx,

x

2

3,

2is decreasing function.

STATEMENT- 2 : Composition of two

decreasing function is an increasing function.



Statement -1



for Statement-1



True

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59. STATEMENT- 1 : Angle between the tangents

drawn from any point on the directrix to

parabola y2 = 4ax is 90.

STATEMENT- 2 : Directrix is the director

circle of parabola.



Statement -1



for Statement-1



True

60. STATEMENT- 1 :

2/

02 4)x(tan1

dx.

STATEMENT - 2 :

a

0

dx)x(f =2

1

a

0

dx)]xa(f)x(f[ is valid for

2/

0

n xtan1

dxif and only if n is rational.



Statement -1



for Statement-1



True

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Name of the Candidate Roll Number

I have read all the instructions and

shall abide by them.

--------------------------------Signature of the Invigilator

I have verified all the information

filled in by the Candidate.

--------------------------------Signature of the Candidate

(Space for rough work)

Example for Filling Test Cities Code in ORS :

If your Test centre is BHAGALPUR and test code is 06 then fill in ORS :

(a)

(b)

TEST CODE TEST CENTRE TEST CODE TEST CENTRE TEST CODE TEST CENTRE

01 AGARTALA 02 AGRA 03 AHMEDABAD

04 AJMER 05 BENGALURU 06 BHAGALPUR

07 BHAGALPUR 08 BHATINDA 09 BHILAI

10 BHOPAL 11 BHUBNESHWAR 12 BIKANER

13 BOKARO 14 CHANDIGARH 15 DEHRADUN

16 DEOGARH (RANCHI IC) 17 DHANBAD 18 GANGAPUR CITY

19 GUWAHATI 20 GWALIOR 21 HARIDWAR

22 INDORE 23 JAMMU & KASHMIR (J&K) 24 JAIPUR

25 JAMSHEDPUR 26 JODHPUR 27 KANPUR

28 KOLHAPUR 29 KOLKATA 30 KOTA

31 LUCKNOW 32 MATHURA 33 MENGALURU

34 MUMBAI 35 MUZAFFARPUR 36 NAGPUR

37 NEW DELHI 38 PATNA 39 RAIPUR

40 RANCHI 41 SAKTI NAGAR (NTPC) 42 SRI GANGANAGAR

43 UDAIPUR 44 VARANASI 45 SAMASTIPUR

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