STAGE -1TEST PAPERS-11 (PHYSICS)
STAGE
TEST PAPERS (PHYSICS)
1
PAPER - 1
Time : 1.00 Hr Max. Marks : 60
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded in this section.
3. For each question in Section II, you will awarded 4 marks If you darken ALL the bubble (s) correspoding to the correct answer (s) ONLY . In all other cases zero (0)marks will be awarded. No negative marks will be awarded for incorrect answers in this section.
4. For each question In Section III, You will be awarded 4 marks if you darken the bubble corresponding to the correct answer ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect anwers in this section.
SECTION-1
Only One option correct type
This section contains 10 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A particle of mass m is projected from the ground with an initial speed u at an angle with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is :
(A)
4 (B)
4
(C)
4
(D) 4
2. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
2
one-third the size of the object. The wavelength of light inside the lens is 3
space. The radius of the curved surface of the lens is :
times the wavelength in free
(A) 1 m (B) 2 m (C) 3 m (D) 6 m
3. The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The vernier scale has 50 division equivalent to 2.45 cm. The 24th division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is :
(A) 5.112 cm (B) 5.124 cm (C) 5.136 cm (D) 5.148 cm
4. The work done on a particle of mass m by a force, K
x ˆi
3 / 2
y
3 / 2 ˆj (K being a constant of
x2 y2 x2 y2
appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is :
2K
(A) a
K
(B) a
K
(C) 2a
(D) 0
5. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by a applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is :
(A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00
6. A ray of light travelling in the direction 1 ˆi
2
3ˆj is incident on a plane mirror. After reflection, it travels along
the direction
1 ˆi
2
3ˆj. The angle of incidence is :
(A) 30º (B) 45º (C) 60º (D) 75º
7. Two rectangular blocks, having indentical dimensions, can be arranged either in configuration or in configu- ration as shown in the figure, On of the blocks has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9s to transport a certain amount of heat from the hot end to the cold end in the configuration . The time to transport the same amount of heat in the configuration is :
Configuration Configuration
x
(A) 2.0 s (B) 3.0 s (C) 4.5 s (D) 6.0 s
8. A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30mV and the speed of light is 3 × 10 ms–1. The final momentum of the object is :
(A) 0.3 × 10–17 kg ms–1 (B) 1.0 × 10–17 kg ms–1
(C) 3.0 × 10–17 kg ms–1 (D) 9.0 × 10–17 kg ms–1
9. In the Young's double slit experiment using a monochromatic light of wavelength , the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is :
(A) 2n 1
2
(B) 2n 1
4
(C) 2n 1
8
(D) 2n 1
16
10. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is: (A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9
SECTION-2
ONE OR MORE OPTION CORRECT TYPE
This section contains 5 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
11. Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities and
respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere,
1
along the line joining the centres of the spheres, is zero. The ratio 2 can be ;
(A) –4 (B) 32
25
32
(C) 25 (D) 4
12. A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m–1) x] cos [(628 s–1)t]. Assuming = 3.14, the correct statement(s) is (are) :
(A) The number of nodes is 5.
(B) The length of the string is 0.25 m.
(C) The maximum displacement of the midpoint of the string its equilibrium position is 0.01 m.
(D) The fundamental frequency is 100 Hz.
13. In the circuit shown in the figure, there are two parallel plate ca- pacitors each of capacitance C. The switch S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and then S3 is pressed. After some time.
(A) the charge on the upper plate of C1 is 2CV0 (B) the charge on the upper plate of C1 is CV0
(C) the charge on the upper plate of C2 is 0 (D) the charge on the upper plate of C2 is –CV0
14. A particle of mass M and positive charge Q, moving with a constant velocity →
4 ˆi ms1, enters a region of
uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10
milliseconds with a velocity →
2
3 ˆi ˆj ms–1. The correct statement(s) is (are)
(A) The direction of the magnetic field is –z direction.
(B) The direction of the magnetic field is +z direction
50M
(C) The magnitude of the magnetic field 3Q units.
(D) The magnitude of the magnetic field is
100M
3Q
units.
15. A solid sphere of radius R and density is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3. The complete arrangement is placed in a liquid of density 2 and is allowed to reach equilibrium. The correct statement(s)
is (are) (A) the net elongation of the spring is
4R3g 3k
(B) the net elongation of the spring is
8R3g 3k
(C) the light sphere is partially submerged. (D) the light sphere is completely submerged.
SECTION-3
INTEGER VALUE CORRECT TYPE
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive)
16. A uniform circular disc of mass 50kg and radius 0.4 m is rotating with an angular velocity of 10 rad/s–1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s–1) of the system is :
17. The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is :
18. A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane, At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the
l1
ratio l2 is :
19. A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms–1) of the particle is zero, the speed (in ms–1) after 5s is :
20. A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80s after preparation of the sample is :
PAPER - 2
Time : 1.00 Hr Max. Marks : 66
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. In Section I (Total Marks: 24), for each question you will be awarded 3 marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
3. In Section ll (Total Marks: 18), contain three paragraphs each describing theory. There are six multiple choice questions relating to three paragraph with two questions from each paragraph. For each question you will be awarded 3 marks if you give the correct answer and zero marks if no answer is given. In all other cases, minus one (-1) mark will be awarded.
4. In Section Ill (Total Marks: 24), for each question you will be awarded 4 marks if you give the correct answer(s) ONLY and zero marks otherwise. There are no negative marks in this section.
SECTION – 1
ONE OR MORE OPTIONS CORRECT TYPE
This section contains 8 multiple coice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct
1. Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are) :
(A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4 .
(B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2 .
(C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is .
(D) The energy of the mass m remains constant.
2. A particle of mass m is attached to one end of a mass–less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collies elastically with a rigid wall. After this collision :
(A) the speed of the particle when it returns to its equilibrium position is u0 .
(B) the time at which the particle passes through the equilibrium position for the first time is t .
(C) the time at which the maximum compression of the spring occurs is t .
(D) the time at which the particle passes througout the equilibrium position for the second time is t .
3. A steady current flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current . Consider a point P at a distance r from the common axis. The correct statement(s) is (are)
(A) In the region 0 < r < R, the magnetic field is non–zero.
(B) In the region R < r < 2R, the magnetic field is along the common axis.
(C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis.
(D) In the region r > 2R, the magnetic field is non–zero.
4. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement(s) is (are) :
(A) If the wind blows from the observer to the source, f2 > f1 .
(B) If the wind blows from the source to the observer, f2 > f1 .
(C) If the wind blows from the observer to the source, f2 < f1 .
(D) If the wind blows from the source to the observer, f2 < f1 .
5. Using the expression 2d sin = , one calculates the values of d by measuring the corresponding angles
in the range 0 to 90º. The wavelength is exactly knowns and the error in is constant for all values of . As
increases from 0º :
(A) the absolute error in d remains constant. (B) the absolute error in d increases.
(C) the fractional error in d remains constant. (D) the fractional error in d decreases.
6. Two non–conducting spheres of radii R1 and R2 and carrying uniform volume charge densities + and –, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region :
(A) the electrostatic field is zero
(B) the electrostatic potential is constant
(C) the electrostatic field is constant in magnitude
(D) the electrostatic field has same direction
7. The figure below shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation.
(A) the rate at which heat is absorbed in the range 0–100 K varies linearly with temperature T.
(B) heat absorbed in increasing the temperature from 0–100 K is less than the heat required for increasing the temperature from 400–500 K.
(C) there is no change in the rate of heat absorbtion in the range 400–500 K.
(D) the rate of heat absorption increases in the range 200–300 K.
8. The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a0, where a0 is the Bohr radius. Its orbital
3h
angular momentum is 2 . It is given that h is Planck constant and R is Rydberg constant. The possible
wavelength(s), when the atom de-excites, is (are) :
(A)
9
32R
9
(B) 16R
9
(C) 5R
4
(D) 3R
SECTION – 2 PARAGRAPH TYPE
This section contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D).
Paragraph for Questions 09 and 10
A small block of mass 1kg is released from rest at the top of a rough track. The track is a circular arc of radius 40m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 150 J. (Take the acceleration due to gravity, g = 10 m s–2)
9. The speed of the block when it reaches the point Q is :
(A) 5 ms–1 (B) 10 ms–1 (C) 10 ms–1 (D) 20 ms–1
10. The magnitude of the normal reaction that acts on the block at the point Q is :
(A) 7.5 N (B) 8.6 N (C) 11.5 N (D) 22.5 N
Paragraph for Questions 11 and 12
A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with a power factor unity. All the currents and voltages mentioned are rms values.
11. If the direct transmission method with a cable of resistance 0.4 km–1 is used, the power dissipation (in %) during transmission is :
(A) 20 (B) 30 (C) 40 (D) 50
12. In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at 200V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is : (A) 200 : 1 (B) 150 : 1 (C) 100 : 1 (D) 50 : 1
Paragraph for Questions 13 and 14
A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity . This can
Q
be considered as equivalent to a loop carrying a steady current 2 . A uniform magnetic field along the
positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionally constant .
13. The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is :
(A) BR (B) BR (C) BR (D) 2BR
4 2
14. The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is :
(A) –BQR2 (B)
BQR2 2
BQR2
(C) (D) BQR
2
Paragraph for Questions 15 and 16
The mass of a nucleus A X is less that the sum of the masses of (A – Z) number of neutrons and Z number
of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table
below :
15. The correct statement is :
(A) The nucleus 6Li can emit an alpha particle
(B) The nucleus 210P can emit a proton
84 0
(C) Deuteron and alpha particle can undergo complete fusion.
(D) The nuclei 70 Zn and 82Se can undergo complete fusion.
30 34
16. The kinetic energy (in keV) of the alpha particle, when the nucleus 210P at rest undergoes alpha decay, is:
84 0
(A) 5319 (B) 5422 (C) 5707 (D) 5818
SECTION – 3
Matching List Type
This section contains 4 multiple choice questions. Each questions has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
17. A right angled prism of refractive index is placed in a rectangular block of refractive index , which is
surrounded by a medium of refractive index , as shown in the figure, A ray of ligth 'e' enters the rectangular
block at normal incidence. Depending upon the relationships between , and , it takes one of the four
possible paths 'ef', 'eg', 'eh' or 'ei'.
1 2 3
Match the paths in List with conditions of refractive indices in List and select the correct answer using the codes given below the lists :
List Ι List ΙΙ
P. e f 1. >
Q.
R. e g e h 2. > and/
2 1 3
3. =
1 2
S. e i 4. < < and >
2 1 2 2 2 3
Codes :
P
Q
R
S
(A) 2 3 1 4
(B) 1 2 4 3
(C) 4 1 2 3
(D) 2 3 4 1
18. Match List with List and select the correct answer using the codes given below the lists :
List Ι List ΙΙ
P. Boltzmann constant 1. [ML2T–1]
Q. Coefficient of viscosity 2. [ML–1T–1]
R. Planck constant 3. [MLT–3K–1]
S. Thermal conductivity 4. [ML2T–2K–1]
Codes :
P Q R S
(A) 3 1 2 4
(B) 3 2 1 4
(C) 4 2 1 3
(D) 4 1 2 3
19. One mole of a monatomic ideal gas is taken along two cyclic processes E F G E and E F H
E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.
Match the paths in List with the magnitudes of the work done in List and select the correct answer using the codes given below the lists.
List Ι List ΙΙ
P. G E 1. 160 P0V0 ln2
Q. G H 2. 36 P0V0
R. F H 3. 24 P0V0
S.
Codes : F G
P
Q
R 4.
S 31 P0V0
(A) 4 3 2 1
(B) 4 3 1 2
(C) 3 1 2 4
(D) 1 3 2 4
20. Match List of the nuclear processes with List containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :
List Ι List ΙΙ
P. Alpha decay 1. 15O 15 N .......
8 7
Q. + decay 2. 238U 234 Th .......
92 90
R. Fission 3. 185Bi 184 Pb .......
83 82
S. Proton emission 4. 239Pu 140 La .......
94 57
Codes :
P Q
R
S
(A) 4 2 1 3
(B) 1 3 2 4
(C) 2 1 4 3
(D) 4 3 2 1
A nswers
PAPER - 1
1. (A) 2. (C) 3. (B) 4. (D) 5. (C) 6. (A) 7. (A)
8. (B) 9. (B) 10. (D) 11. (B,D) 12. (B,C) 13. (B,D) 14. (A,C)
15. (A,D) 16. 8 17. 1 18. 5 19. 5 20. 4
PAPER - 2
1. (B,D) 2. (A,D) 3. (A, D) 4. (A, B) 5. (D) 6. (C, D) 7. A,B,C,D
8. (A, C) 9. (B) 10. (A) 11. (B) 12. (A) 13. (B) 14. (B)
15. (C) 16. (A) 17. (D) 18. (C) 19. (A) 20. (C)
STAGE SOLUTIONS TO TEST PAPERS (PHYSICS)
2
1. At the highest point
PAPER - 1
v = u0 cos (by applying momentum conservation in horizontal direction)
1 2
v = u0 cos (by applying momentum conservation in vertical direction)
2 2
= 45°
u2 sin2
(H = 0 )
2. v = 8 m (magnification = 1 3
v
= u )
u = –24m
1 3
1 1
f 2
1
R
R = 3m
3. 50 VSD = 2.45 cm
2.45
1 VSD = 50
cm = 0.049 cm
Least count of vernier = 1MSD – 1 VSD
= 0.05 cm – 0.049 cm
= 0.001 cm
Thickness of the object = Main scale reading + vernier scale reading × least count
= 5.10 + (24) (0.001)
= 5.124 cm.
4. suppose x = r cos y = r sin
force on particle is K r cos ˆi r sin ˆj
r 3
force is in radial direction so work done by this force along given path (circle) is zero.
F
5. Y =
A
𝑙1
L
...(i)
F
4A
Y = 𝑙 2
2L
...(ii)
𝑙1 = 2
𝑙 2
6. Angle between given rays is 120° so angle of incidence is 30°
7. In configuration 1 equivalent thermal resistance is 3R
2
R
In configuration 2 equivalent thermal resistance is 3
Thermal Resistance time taken by heat flow from high temperature to low temperature
8. Change in momentum = 1.0 × 10–17 kg × m/s
power total time speed of light
P t
= c
9. For half of maximum intensity 2 = + + 2 cos
(Phase difference) = , 3 , 5 .........
2 2 2
, 3 , 5 2n 1
Path difference is 4 4 4
4
10. P1 =
1RT M1
...(i)
P2 =
2RT M2
...(ii)
by (i) and (ii)
1 8
2 9
11. At point P
If resultant electric field is zero then
KQ1 KQ2 R
4R2 8R3
1
2 = 4
At point Q
If resultant electric field is zero then
KQ1 KQ2 0
4R2 25R2
1 32
2 = – 25
( must be negative)
12. (A) There are 5 complete loops.
Total number of nodes = 6
(B) = 628 sec–1
2
k = 62.8 m–1 =
1
10
vw = k =
628
62.8
= 10 ms–1
L = 5 0.25
2
(C) 2A = 0.01 = maximum amplitude of antinode
(D) f =
v 2𝑙
10
2 0.25
= 20 Hz.
13. When switch S1 is released charge on C1 is 2CV0 (on upper plate )
When switch S2 is released charge on C1 is CV0 (on upper plate ) and charge on C2 is CV0 (on upper plate) When switch S3 is released charge on C1 is CV0 (on upper plate ) and charge on C2 is –CV0 (on upper plate)
14. Component of final velocity of particle is in positive y direction.
Centre of circle is present on positive y axis. so magnetic field is present in negative z-direction Angle of deviation is 30° because
v y
tan = v x =
= 6
t =
= QB t
M
M
B = Qt
50M
B =
3Q
15. On small sphere
4 R3()g kx 4 R3(2)g
..(i)
3 3
on second sphere (large)
4 R3(3)g 4 R3(2)g kx
...(ii)
3 3
by equation (i) and (ii)
4R3g
x = 3k
16.
=
1 4
= 2 = 5
1
× 10 rad/s = 8 rad/s
17. KEmax = hv –
eV = hv –
V h
st
e e
y = m x + C
h
So slope will be e , and it will be same for both the metals.
So ratio of the slopes = 1
18. To complete the vertical circle
=
𝑙1
𝑙 2 = 5
19. E = P.t = 0.5W × 5s = 2.5 J =
1 mv2 v = 5 m/s
2
20.
0.693
1386
= 5 × 10–4
Number decayed = N0 – N (t)
N0 – N(t)
% age Decayed = N0
× 100
= (1–e–t) × 100
t × 100
= 5 × 10–4 × 80 × 100
= 4
PAPER - 2
1. Apply energy conservation
GM.2m 1 mv 2 0 0
L 2
M M
v
L m L
2. Dispalcement x = A sint
A
velocity v = Acos t = 2
At the time of collision
cost = 1
2
t =
t =
3
2
3 = 3
2
for (C) time = 3
=
for (D) time =
=
+
(So it is incorrect)
+ (So it is correct)
3.
(A) For 0 < r < R B 0
(D) For r > 2R B 0
4.
If wind blows from source to observer
(v w) u
f
2 (v w) u
f > f
If wind blows from observer to source
(v w) u
f
2 (v w) u
f > f
5. 2d sin =
d = 2 sin
differntiate
(d) = 2
(cosec)
(d) =
(d) =
(– coseccot )
2
– cos
2sin2
as = increases ,
Alternate solution
cos 2sin2
decreases
d
2 sin
𝑙n d 𝑙n 𝑙n2 𝑙n sin
(d) d
= 0 – 0 –
1
sin
cos()
Fractional error |+(d)| = |cot | Absoulute error d = (dcot)
d cos
2 sin sin
d
cos sin2
6. For electrostatic field,
→ → →
EP E1 E2
C P (–) C P
= 30 30
= 30
→
(C1P PC2 )
EP 3
C1C2
For electrostatic potential, Since electric field is non zero so it is not equipotential.
7. q = mCT
dq mc dT
dt dt
dq
R = rate of absortion of heat = dt C
(i) in 0 – 100 k
C increases, so R increases but not linearly
(ii) q = mCT as C is more in (400 k – 500 k) then (0 – 100 k) so heat is increasing.
(iii) C remains constant so there no change in R from (400 k – 500 k)
(iv) C is increases so R is increases in range (200 k – 300 k)
8. Rn = 4.5 a0
3h
L = mvr = 2
[as n = 3, z= 2]
1 Rz
n2
n2
f 1
1 R41 1 4R 8 9
31
1
9 9
31
32R
1 R41 1 3 4R 1
21
1
4 4
21 3R
1 R4 1 1
5 4R 9
32
4
9 36
32 5R
R 1
9. Mg = 2 – 150 = 2 MV2
1
1 × 10 × 20 – 2 V2 V = 10 m/s
10.
N Mg
2
M(10)2
40
N = 7.5 N.
11. P = 600 × 1000 = 4000 × I I = 150 A
dH
dt = (150)2 × 0.4 ×20 × 2
which is 30% of 600kW
12.
Np 40,000 = 200
Ns 200 1
13. E.dl = – A dB dt
E. 2R = –R2B
BR
E = 2
Alternate :
d
E2R = dt
dB
= – R2 dt
E = R dB BR
2 dt 2
14. Megnetic dipole moment M = J
M = J (i)
J Q dB . R R.
t dt 2
J QB R2
2
so M
QBR2
2
Alternate :
M Q L 2m
M = Q R2
2
QR2
= *
2
induced electric field is oppsite. to the so the charge is retarded.
= – t
= – QB 1
(a = QE/m), =
QE = Q x BR = QB )
2
Q'R2
t
QB R2
mR R 2m 2m
Mf = 2
= Q
2m 2
QR2 Q2BR2 QR2
BQR2
m = Mf – Mi = 2
4m 2
=
2
15. (A) 3Li7 He4 H3
m = [MLi MHe MH3 ]
= [6.01513 – 4.002603 – 3.016050]
= – 1.003523u
m is negative so reaction is not possible.
(B) 84Po210 83Bi209 1P1
m is negative so reaction is not possible.
(C) 1H2 2He4 3Li6
m is Positive so reaction is possible.
(D) 30 Zn70 34Se82 64Gd152
m is Positive so reaction is not possible.
16. 84Po210 2He4 82Pb206
m = [ M – M – M ] = 0.008421 u
He Pb
Q = 0.008421×932 MeV = 5422 KeV
K 210 5422KeV 214
= 5320 KeV
17. For e i 45° >
c
sin 45° > sin
2
> 1
> 22
For e f
angle of refraction is lesser than angle of incidence, so >
and then >
For e g , =
for e h, < <
22 and 2 > 3
18. (p) U =
1 kT
2
ML2T–2 = [k] K [K] = ML2T–2K–1
(q) F = A dv
dx
MLT–2
[]
L2LT–1L–1
= ML–1
T–1
(r) E = h ML2T2 = [h] T–1 [h] = ML2 T–1
dQ kA
ML2T–3L
–3 –1
(s) dt
[k] =
𝑙
L2K
= MLT K
19.
Vf 32V0
In FG work done in isothermal proces is nRT ln V = 32 P0 V0 ln V
= 32 P0V0 ln 2 = 160 P
5
V0 ln 2
i
0
In G E, W = P
V = P (31 V ) = 31 P V
0 0 0 0 0
In G H work done is less than 31 P V i.e., 24 P V
0 0
In F H work done is 36 P V
20. (p) In decay mass number decreses by 4 and atomic number decreases by 2.
(q) In + decay mass number remains unchanged while atomic number decreases by 1.
(r) In Fission, parent nucleus breaks into almost two equal fragments.
(s) In proton emission both mass number and atomic number decreases by 1.
STAGE
SIMILAR TEST PAPERS (PHYSICS)
3
PAPER - 1
Time : 1.00 Hr Max. Marks : 70
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded in this section.
3. For each question in Section II, you will awarded 4 marks If you darken ALL the bubble (s) correspoding to the correct answer (s) ONLY . In all other cases zero (0)marks will be awarded. No negative marks will be awarded for incorrect answers in this section.
4. For each question In Section III, You will be awarded 4 marks if you darken the bubble corresponding to the correct answer ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect anwers in this section.
SECTION-1
ONLY ONE OPTION CORRECT TYPE
This section contains 10 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A particle of mass m is projected from the ground with an initial speed u at an angle with the vertical. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is :
(A)
4 (B)
4
(C)
4
(D) 2
2. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
2
half the size of the object. The wavelength of light inside the lens is 3 times the wavelength in free space. The radius of the curved surface of the lens is :
1
(A) 3
2
m (B) 3
4
m (C) 3
8
m (D) 3 m
3. The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The vernier scale has 50 division equivalent to 2.40 cm. The 24th division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is :
(A) 5.112 cm (B) 5.124 cm (C) 5.136 cm (D) 5.148 cm
4. The power delievered to particle of mass m by a force, K
x ˆi
3 / 2
y
3 / 2 ˆj (K being a constant
x2 y2 x2 y2
of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is :
2K
(A) a
K
(B) a
K
(C) 2a
(D) 0
5. One end of a horizontal thick copper wire of length L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by a applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is :
(A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00
6. A ray of light travelling in the direction 1 ˆi
2
3ˆj is incident on a plane mirror. After reflection, it travels along
the direction
1 ˆi
2
3ˆj. The angle of incidence is :
(A) 30º (B) 45º (C) 60º (D) 75º
7. Two rectangular blocks, having indentical dimensions, can be arranged either in configuration or in configuration as shown in the figure, one of the blocks has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 27s to transport a certain amount of heat from the hot end to the cold end in the configuration . The time to transport the same amount of heat in the configuration is :
Configuration Configuration
x
(A) 2.0 s (B) 3.0 s (C) 4.5 s (D) 6.0 s
8. A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 90mW and the speed of light is 3 × 108 ms–1. The final momentum of the object is :
(A) 0.3 × 10–17 kg ms–1 (B) 1.0 × 10–17 kg ms–1
(C) 3.0 × 10–17 kg ms–1 (D) 9.0 × 10–17 kg ms–1
9. In the Young's double slit experiment using a monochromatic light of wavelength , the phase difference (in terms of an integer n) corresponding to any point having half the peak intensity is :
(A) 2n 1
2
(B) 2n 1
4
(C) 2n 1
8
(D) 2n 1
16
10. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 3 : 4. The ratio of their densities is: (A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9
SECTION-2
ONE OR MORE OPTION CORRECT TYPE
This section contains 5 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
11. Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities and
respectively, touch each other. The net electric field at a distance 3 R from the centre of the smaller sphere,
2
1
along the line joining the centres of the spheres, is zero. The ratio 2
can be ;
(A) –4 (B) – 8 (C) 32 (D) 27
9 25 8
12. A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m–1) x] cos [(628 s–1)t]. Assuming = 3.14, the correct statement(s) is (are) :
(A) The number of nodes is 6.
(B) The length of the string is 0.25 m.
(C) The maximum displacement of the midpoint of the string its equilibrium position is 0.01 m.
(D) The fundamental frequency is 20 Hz.
13. In the circuit shown in the figure, there are two parallel plate ca- pacitors each of capacitance C. The switch S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and then S3 is pressed. After some time.
(A) the charge on the upper plate of C1 is 2CV0
(B) the charge on the upper plate of C1 is CV0
(C) the charge on the upper plate of C2 is 0
(D) the charge on the upper plate of C2 is –2CV0
14. A particle of mass M and positive charge Q, moving with a constant velocity →
4 ˆi ms1, enters a region of
uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after
10 milliseconds with a velocity → 3 ˆi ˆj ms–1. The correct statement(s) is (are) :
(A) The direction of the magnetic field is –z direction.
(B) The direction of the magnetic field is +z direction
50M
(C) The magnitude of the magnetic field 3Q units.
(D) The magnitude of the magnetic field is
100M
4Q
units.
15. A solid sphere of radius R and density is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3. The complete arrangement is placed in a liquid of density 2 and is allowed to reach equilibrium. The correct statement(s)
4R3g
is (are) (A) the net elongation of the spring is 3k
(B) the light sphere is completely submerged in the equillibrium condition.
(C) the light sphere is partially submerged.
(D) If the spring is cut, then just after cutting the spring, acceleration of light sphere is g in upward direction.
SECTION-3
INTEGER VALUE CORRECT TYPE
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive)
16. A uniform circular disc of mass 37.5 kg and radius 0.4 m is rotating with an angular velocity of 8 rad/s–1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s–1) of the system is :
17. The work functions of Cesium and platinum are 1.9ev and 5.6 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is :
18. A bob of mass m, suspended by a string of length 𝑙1 , is given a minimum velocity required to complete a full circle in the vertical plane, At the highest point, it collides elastically with another bob of mass m suspended
by a light rod of length 𝑙 2 , which is initially at rest. The string is mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the
𝑙1
ratio
𝑙 2
is :
19. A particle of mass 1 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms–1) of the particle is zero, the speed (in ms–1) after 4s is :
20. A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 40s after preparation of the sample is :
PAPER - 2
Time : 1.00 Hr Max. Marks : 66
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. For each question in Section I and Section II , you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY and zero (0) marks if no bubbles are darkend. In all other cases, minus one (–1) mark will be awarded in these sections.
3. For each question in Section III, you will be awarded 4 marks If you darken ALL the bubble (s) correspond- ing to the correct answer (s) ONLY In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect answer (s) in this section.
SECTION – 1
ONE OR MORE OPTIONS CORRECT TYPE
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
1. A very small groove is made in the earth, and a particle of mass m0 is placed at R/2 distance from the centre. Find the escape speed of the particle from that place.
(A) The minimum initial speed of the mass m to escape the gravitational field of the two bodies is 4 .
(B) The minimum initial speed of the mass m to escape the gravitational field of the two bodies is 2 .
(C) The minimum initial speed of the mass m to escape the gravitational field of the two bodies is .
(D) The energy of the mass m remains constant.
2. A particle of mass m is attached to one end of a mass–less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collies elastically with a rigid wall. After this collision :
(A) the speed of the particle when it returns to its equilibrium position is u0 .
(B) the time at which the particle passes through the equilibrium position for the first time is .
(C) the time at which the maximum compression of the spring occurs is .
(D) the time at which the particle passes throughout the equilibrium position for the second time is t .
3. A steady current flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite long hollow cylindrical conductor radius 2R. The two conductors carry equal steady current in opposite directions. Consider a point P at a distance r from the common axis. The correct statement(s) is (are) :
(A) In the region 0 < r < R, the magnetic field is zero.
(B) In the region R < r < 2R, the magnetic field is along the common axis.
(C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis.
(D) In the region r > 2R, the magnetic field is non–zero.
4. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with speed w at an acute angle with road One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement(s) is (are) :
(A) If the wind blows from the observer to the source, f2 > f1 .
(B) If the wind blows from the source to the observer, f2 > f1 .
(C) If wind blows from the observer to the source, f2 < f1 .
(D) If wind blows from the source to the observer, f2 < f1 .
5. Using the expression 2d sin = , one calculates the values of d by measuring the corresponding angles
in the range 0 to 90º. The wavelength is exactly known and the error in is constant for all values of . As
varied from 90º to 0°
(A) the absolute error in d remains constant. (B) the absolute error in d increases.
(C) the fractional error in d remains constant. (D) the fractional error in d increases.
6. Two non–conducting spheres of radii R1 and R2 and carrying uni- form volume charge densities + and –, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region :
(A) In the cavity the electrostatic field is zero
(B) In the cavity the electrostatic potential is constant
(C) At all points in the overlapping region, the electrostatic field is constant in magnitude
(D) At all points in the overlapping region, the electrostatic field has same direction
7. The figure below shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation.
(A) the rate at which heat is absorbed in the range 0–100 K varies non linearly with temperature T.
(B) heat absorbed in increasing the temperature from 0–100 K is less than the heat required for increasing the temperature from 400–500 K.
(C) there is no change in the rate of heat absorbtion in the range 400–500 K.
(D) the rate of heat absorption increases in the range 200–300 K.
8. The radius of the orbit of an electron in a Hydrogen-like atom is 2 a0, where a0 is the Bohr radius. Its orbital
h
angular momentum . It is given that h is Planck constant and R is Rydberg constant. The possible
wavelength(s), when the atom de-excites, is (are)
(A)
9
32R
9
(B) 16R
1
(C) 3R
4
(D) 3R
SECTION – 2 PARAGRAPH TYPE
This section contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D).
Paragraph for Questions 09 and 10
A small block of mass 2kg is released from rest at the top of a rough track. The track is a circular arc of radius 20m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 100 J. (Take the acceleration due to gravity, g = 10 m s–2)
9. The speed of the block when it reaches the point Q is :
(A) 5 ms–1 (B) 10 ms–1 (C) 10 ms–1 (D) 20 ms–1
10. The magnitude of the normal reaction that acts on the block at the point Q is :
(A) 7.5 N (B) 8.6 N (C) 11.5 N (D) 20 N
Paragraph for Questions 11 and 12
A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with a power factor unity. All the currents and voltages mentioned are rms values.
11. If the direct transmission method with a cable of resistance 0.53 km–1 is used, then approximate power dissipation (in %) during transmission is :
(A) 20 (B) 30 (C) 40 (D) 50
12. In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 15. If the power to the consumers has to be supplied at 200V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is : (A) 200 : 1 (B) 150 : 1 (C) 300 : 1 (D) 50 : 1
Paragraph for Questions 13 and 14
A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity . This can
Q
be considered as equivalent to a loop carrying a steady current 2 . A uniform magnetic field along the
positive z-axis is now switched on, which increases at a constant rate from 0 to B in 0.5 second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionally constant .
13. The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is :
(A) BR (B) BR (C) BR (D) 2BR
4 2
14. The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is :
(A) –BQR2 (B)
BQR2 2
BQR2
(C) (D) BQR
2
Paragraph for Questions 15 and 16
The mass of a nucleus A X is less that the sum of the masses of (A – Z) number of neutrons and Z number
of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below :
1H
1 1.007825u 2 H
1 2.014102u 3 H
1 3.016050u 4He
2 4.002603u
6Li
3 6.015123u 7Li
3 7.016004u 70 Zn
30 69.925325u 82 Se
34 81.916709u
152 Gd
64 151.919803u 206 Pb
82 205.974455u 209 Bi
83 208.980388u 210 Po
84 209.982876u
15. The correct statement is :
(A) The nucleus 6Li can emit an alpha particle
(B) The nucleus 210P can emit an particle
84 0
(C) Alpha particle can undergo complete fission
(D) The nuclei 70 Zn and 82Se can undergo complete fusion.
30 34
16. The kinetic energy (in MeV) of the alpha particle, when the nucleus 210P at rest undergoes alpha decay, is:
84 0
(A) 7.8484 (B) 7.7017 (C) 7.2121 (D) 7.4848
SECTION – 3 MATCHING LIST TYPE
This section contains 4 multiple choice questions. Each questions has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
17. A white light ray is incident on a glass prism & four refracted rays A, B, C, D are as shown. Match the refracted rays with the colors given (1 & D are due to total internal Reflection.)
List - I (Rays) List - II (color)
P. Ray A 1. Red
Q. Ray B 2. green
R. Ray C 3. yellow
S. Ray D 4. blue
Codes :
P Q R S
(A) 4 3 2 1
(B) 4 2 1 3
(C) 1 3 2 4
(D) 2 1 4 3
18. Match List with List and select the correct answer using the codes given below the lists :
List Ι List ΙΙ
P. Boltzmann constant 1. [ML2T–1]
Q. Coefficient of viscosity 2. [ML–1T–1]
R. Planck constant 3. M-1L3T–2
S. Universal Gravitational constant 4. [ML2T–2K–1]
Codes :
P Q R S
(A) 3 1 2 4
(B) 3 2 1 4
(C) 4 2 1 3
(D) 4 1 2 3
19. One mole of a monoatomic ideal gas is taken along two cyclic processes E FGE and E F H
E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.
Match the paths in List with the magnitudes of the work done in List and select the correct answer using the codes given below the lists.
List Ι List ΙΙ
P. H E 1. 160 P0V0 ln2
Q. G H 2. 36 P0V0
R. F H 3. 24 P0V0
S.
Codes : F G
P
Q
R 4.
S 7 P0V0
(A) 4 3 2 1
(B) 4 3 1 2
(C) 3 1 2 4
(D) 1 3 2 4
20. Match List of the nuclear processes with List containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :
List Ι List ΙΙ
P. Alpha decay 1.
226 Ac 226 Th +
89 90
Q. –
decay 2.
238U 234 Th .......
92 90
R. Fission 3.
185Bi 184 Pb .......
S. Proton emission 4.
83
236
92
82
137
53
+ ......
Codes :
P Q R S
(A) 4 2 1 3
(B) 1 3 2 4
(C) 2 1 4 3
(D) 4 3 2 1
A nswers
PAPER - 1
1. (A) 2. (D) 3. (D) 4. (D) 5. (D) 6. (A) 7. (D)
8. (C) 9. (B) 10. (D) 11. (B,D) 12. (A,B,C,D) 13. (B,D)
14. (A,D) 15. (A,B,D) 16. 6 17. 1 18. 4 19. 2 20. 2
PAPER - 2
1. B,D 2. A,B,C,D 3. (A, B) 4. (A, B) 5. (D) 6. A, B,C, D
7. A,B,C,D 8. (C) 9. (B) 10. (D) 11. (C) 12. (A) 13. (C)
14. (B) 15. (B) 16. (B) 17. (C) 18. (C) 19. (A) 20. (C)
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