aiot-02 english (1)
TRANSCRIPT
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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)
Question No. 31 to 60 consist ofFour (4) marks for each correct response.
PART C CHEMISTRY (120 marks)
Question No. 61 to 90 consist ofFour (4) marks for each correct response.
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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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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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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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.
(3) Angular momentum of negative point charge
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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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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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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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.
(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
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.
(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
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) .
(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.
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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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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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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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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.
(3) Angular momentum of negative point charge
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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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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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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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.
(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
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.
(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
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) .
(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.
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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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PART- B
SECTION - I
Straight Objective Type
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),
(2), (3) and (4), out of which ONLY ONE is
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
(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
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.
(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
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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.
(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
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.
(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
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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