STAGE-1 TEST PAPERS-6 (PHYSICS)
STAGE
TEST PAPERS (PHYSICS)
1
Time : 1.00 Hr Max. Marks : 81
GENERAL INSTRUCTIONS
1. There are 23 questions in this paper.
2. For each question in Section I , 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. For each question in Section II, you will be awarded 4 Marks if you give the correct answer(s) and
zero Mark if no answer is given. No negative Mark will be awarded for an incorrect answer.
4. For each question in Section III , 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.
5. For each question in Section IV , you will be awarded 4 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.
Useful Data :
Planck's constant h = 4.1 × 10–15 eV.s Velocity of light c = 3 × 108 m/s
SECTION - I
Straight Objective Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. An ideal gas is expanding such that PT2 = constant. The coefficient of volume expansion of the gas is
(A)
1 (B)
T
2 (C)
T
3 (D) 4
T T
2. Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60ΒΊ).
In the position of minimum deviation, the angle of refraction will be
(A) 30ΒΊ for both the colours (B) greater for the violet colour
(C) greater for the red colour (D) equal but not 30ΒΊ for both the colours
3. A spherically symmetric gravitational system of particles has a mass density
0
for for
r R r R
where 0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance r (0 < r < ) from the centre of the system is represented by
V V V
(A)
(B) (C)
(D)
R r R r R r
4. Which one of the following statement is WRONG in the context of X-rays generated from a X-ray tube?
(A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases.
(B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target.
(C) Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube.
(D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube.
5. Student , and perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length = 0.1 cm Least count for time = 0.1 s
Student Length of the
pendulum (cm) Number of
oscillations (n) Total time for
(n) oscillations (s) Time period
(s)
64.0 8 128.0 16.0
64.0 4 64.0 16.0
20.0 4 36.0 9.0
g
If E, E and E are the percentage errors in g, i.e., g 100 for students , and , respectively,
(A) E = 0 (B) E is minimum
(C) E = E (D) E is maximum
6. Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then
Figure :
(A) P1 > P2 > P3 (B) P1 > P3 > P2
(C) P2 > P1 > P3 (D) P3 > P2 > P1
SECTION - II
Multiple Correct Answers Type
This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B),
(C) and (D) out of which ONE OR MORE is/are correct.
7. In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).
(A) If d = , the screen will contain only one maximum
(B) If < d < 2, at least one more maximum (besides the central maximum) will be observed on the screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase
(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase
8. A particle of mass m and charge q, moving with velocity V enters Region normal to the boundary as shown in the figure. Region
has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region is π. Choose the correct choice(s). Figure :
(A) The particle enters Region only if its velocity V > qπB
m
(B) The particle enters Region only if its velocity V < qπB
m
(C) Path length of the particle in Region is maximum when velocity V = qπB
m
(D) Time spent in Region is same for any velocity V as long as the particle returns to Region
9. Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.
Figure :
B/A
8
6
4
2
0
100 200 A
(A) Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release energy
(B) Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy
(C) Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into two equal fragments
(D) Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into two equal fragments
10. Two balls, having linear momenta
→ pΛi
and
→ pΛi , undergo a collision in free space. There is no
external force acting on the balls. Let → and → be their final momenta. The following option(s) is(are)
NOT ALLOWED for any non-zero value of p , a1, a2, b1, b2, c1 and c2.
(A)
→
p'1
→
a1
Λi b1
Λ
Λj c1 kΛ
Λ
(B)
→
p'1
→
c1 kΛ
Λ
p'2 a2 i b2 j p'2 c2 k
(C)
→
p'1
→
a1
Λi b1 Λ
Λj c1 kΛ Λ Λ
(D)
→
p'1
→
a1
Λi b1 Λj Λ Λ
p'2 a2 i b2 j c1 k
SECTION - III
p'2 a2 i b1 j
Reasoning Type
This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
11. Statement-1 : The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.
Statement-2 : In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains con- stant.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
12. Statement-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identi- cal dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach, the bottom of the inclined plane first.
Statement-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
13. Statement-1 : An astronaut in an orbiting space station above the Earth experiences weightlessness. Statement-2 : An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
14. Statement-1 : In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
Statement-2 : Resistance of a metal increases with increase in temperature.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
SECTION - IV
Linked Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
C15-17 : Paragraph for Question Nos. 15 to 17
5
A small spherical monoatomic ideal gas bubble is trapped inside a liquid of density (see figure).
3 π
Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T0, the height of the liquid is H and the atmospheric pressure is P0 (Neglect surface tension).
Figure :
15. As the bubble moves upwards, besides the buoyancy force, the following forces are acting on it.
(A) Only the force of gravity
(B) The force due to gravity and the force due to the pressure of the liquid
(C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
(D) The force due to gravity and the force due to viscosity of the liquid
16. When the gas bubble is at a height y from the bottom, its temperature is -
P gH 2 / 5 P g(H y) 2 / 5
(A) T0 0 π (B) T0 0 π
P0 πgy P0 πgH
P gH 3 / 5 P g(H y) 3 / 5
(C) T0 0 π (D) T0 0 π
P0 πgy P0 πgH
17. The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)
(P0 πgH)2 / 5
πnRgT0
(A)
πnRgT0
(P
gy)7 / 5
(B) (P
gH)2 / 5 [P
g(H y)]3 / 5
0 π
0 π
0 π
(P0 πgH)3 / 5
πnRgT0
(C)
πnRgT0
(P
gy)8 / 5
(D) (P
gH)3 / 5 [P
g(H y)]2 / 5
0 π
0 π
0 π
C18-20 : Paragraph for Question Nos. 18 to 20
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10 m/s2)
Figure :
A
18. The speed of the block at point B immediately after it strikes the second incline is -
(A)
(C)
m/s (B)
m/s (D)
m/s m/s
19. The speed of the block at point C, immediately before it leaves the second incline is
(A)
(C)
m/s (B)
m/s (D)
m/s
m/s
20. If collision between the block and the incline is completely elastic, then the vertical (upward) compo- nent of the velocity of the block at point B, immediately after it strikes the second incline is
(A)
m/s (B)
m/s
(C) 0 (D) – m/s
C21-23 : Paragraph for Question Nos. 21 to 23
In a mixture of H – He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.
21. The quantum number n of the state finally populated in He+ ions is :
(A) 2 (B) 3
(C) 4 (D) 5
22. The wavelength of light emitted in the visible region by He+ ions after collisions with H atoms is (A) 6.5 × 10–7 m (B) 5.6 × 10–7 m
(C) 4.8 × 10–7 m (D) 4.0 × 10–7 m
23. The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is :
(A)
1 (B) 1
4 2
(C) 1 (D) 2
PAPER - 2
Time : 1.00 Hr Max. Marks : 81
GENERAL INSTRUCTIONS
1. There are 22 questions in this paper.
2. For each question in Section I , 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. For each question in Section II , you will be awarded 3 Marks if you give the correct answer and zero Mark
if noanswer is given. In all other cases, minus one (–1) Mark will be awarded.
4. For each question in Section III, you will be awarded 4 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.
5. For each question in Section IV, you will be awarded 6 Marks if you give ALL the correct answer(s) or awarded 1 Mark each for correct answer in any row. No negative Mark will be awarded for an
incorrect answer.
SECTION - I
Straight Objective Type
This section contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
y
1. A transverse sinusoidal wave moves along a string in the positive
x-direction at a speed of 10 cm/s. The wavelength of the wave is
0.5 m and its amplitude is 10 cm. At a particular time t, the snap-
shot of the wave is shown in figure. The velocity of point P when its x
displace ment is 5 cm is
(A)
(C)
3 Λj m/s (B) –
50
3 Λi m/s (D) –
50
3 Λj
50
3 Λi
50
m/s
m/s
q
2. Consider a system of three charges ,
q and 2q
placed at
3 3 3
points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60ΒΊ
q
(A) The electric field at point O is 80 R2 directed along the negative x-axis
(B) The potential energy of the system is zero
(C) The magnitude of the force between the charges at C and B is
q
(D) The potential at point O is 12 0 R
q2 540 R2
3. A radioactive sample S1 having an activity of 5Ci has twice the number of nuclei as another sample S2 which has an activity of 10Ci. The half lives of S1 and S2 can be
(A) 20 years and 5 years, respectively (B) 20 years and 10 years, respectively
(C) 10 years each (D) 5 years each
4. A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispheri cal soap bubble as shown in figure. Just after opening the valve. Figure :
(A) Air from end 1 flows towards end 2. No change in the
volume of the soap bubbles 2 1
(B) Air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases
(C) No change occurs
(D) Air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases.
5. A block (B) is attached to two unstreched springs S1 and S2 with spring constants k and 4 k, respectively (see figure ). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure ) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B.
The ratio Figure :
y is
x
(A) 4 (B) 2
(C)
1 (D) 1
2 4
6. A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A,
` satisfies
(A) =
(B)
4 4 2
(C) 3 (D) 3
2 4 4
7. A parallel plate capacitor C with plates of unit area and separation
d is filled with a liquid of dielectric constant K = 2. The level of C
d
liquid is 3 initially. Suppose the liquid level decreases at a d d R
constant speed V, the time constant as a function of time t is 3
Figure :
(A)
6 0 R
5d 3V t
6 0 R
(B)
(15d 9V t) 0 R 2d2 – 3d V t – 9V 2t2
(15 d – 9V t) 0 R
(C) 5d– 3V t (D) 2d2 3d V t – 9V 2t2
8. A vibrating string of certain length π under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is
(A) 344 (B) 336
(C) 117.3 (D) 109.3
9. A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and
IV are n , n0 , n0 and n0 , respectively. The angle of incidence for which the beam just misses entering
0 2 6 8
Region IV is Figure
3
(A) sin 4
1
(B) sin–1 8
1
(C) sin–1 4
1
(D) sin–1 3
SECTION - II
Reasoning Type
This section contains 4 reasoning type questions, Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
10. Statement-1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
→ →
Statement-2 : If the observer and the object are moving at velocities V1 and V2 respectively with reference
→ →
to a laboratory frame, the velocity of the object with respect to the observer is V2 V1 .
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
11. Statement-1 : The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
Statement-2 : Soft iron has a high magnetic permeability and cannot be easily magnetized or demagne- tized.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
12. Statement-1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
Statement-2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the
Q
surface is given by
4 0 R .
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
13. Statement-1 : It is easier to pull a heavy object than to push it on a level ground.
Statement-2 : The magnitude of frictional force depends on the nature of the two surfaces in contact.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
SECTION - III
Linked Comprehension Type
This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
C14-16 : Paragraph for Question Nos. 14 to 16
The nuclear charge (Ze) is non–uniformly distributed within a nucleus of radius R. The charge density (r) [charge per unit volume] is de- pendent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
Figure :
14. The electric field at r = R is :
(A) independent of a (B) directly proportional to a
(C) directly proportional to a2 (D) inversely proportional to a
15. For a = 0, the value d (maximum value of as shown in the figure) is :
(A)
3Ze2
4R3
4Ze
(B)
3Ze
R3
Ze
(C) 3R3 (D) 3R3
16. The electric field within the nucleus is generally observed to be linearly dependent on r. This implies :
(A) a = 0 (B) a = R
2
2R
(C) a = R (D) a = 3
C17-19 : Paragraph for Question Nos. 17 to 19
A uniform thin cylindrical disc of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disc is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disc rolls without slipping
with velocity
Figure :
→
V0 V0 Λi . The coefficient of friction is .
17. The net external force acting on the disc when its centre of mass is at displacement x with respect to its equilibrium position is
(A) –kx (B) –2kx
(C) – 2kx
3
(D) – 4kx
3
18. The centre of mass of the disc undergoes simple harmonic motion with angular frequency equal to
(A) (B)
(C) (D)
19. The maximum value of V0 for which the disc will roll without slipping is
(A) g
(C) g
(B) g
(D) g
SECTION - IV
Matrix - Match Type
This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements in Column Ξ are labelled as A,B,C and D whereas statements in Column ΞΞ are labelled as p,q,r and s. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r , B-p, B-s, C-r, C-s and D-q, then the answer should be written as: A p, r; Bp, s; C r,s; Dq.
20. Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4×4 matrix given in the ORS.
Column I Column II
(A) Potential energy of a simple pendulum (p) (y–axis) as a function of displacement (x–axis)
(B) Displacement (y–axis) as a function of time (q) (x–axis) for a one dimensional motion at zero or
constant acceleration when the body is moving along the positive x–direction.
(C) Range of a projectile (y–axis) as a function (r) of its velocity (x–axis) when projected at a fixed angle.
(D) The square of the time period (y–axis) of a (s) simple pendulum as a function of its length (x–axis).
21. Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
Column I Column II
(A) An insulated container has two chambers (p) The temperature of the gas
decreases
separated by a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened.
(B) An ideal monoatomic gas expands to twice its (q) The temperature of the gas increases
original volume such that its pressure P
where V is the volume of the gas.
1 , or remains constant
V 2
(C) An ideal monoatomic gas expands to twice its (r) The gas loses heat
original volume such that its pressure P
where V is its volume
1
V 4 / 3 ,
(D) An ideal monoatomic gas expands such that its (s) The gas gains heat pressure P and volume V follows the behaviour
shown in the graph
22. An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
Column I Column II
(A) (p) Real image
(B) (q) Virtual image
(C) (r) Magnified image
(D) (s) Image at infinity
A nswers
PAPER - 1
1. (C) 2. (A) 3. (C) 4. (B) 5. (B)
6. (C)
(D) 7. (A), (B) 8. (A), (C), (D) 9. (B), (D) 10. ( A ) ,
11. (A) 12. (D) 13. (A) 14. (D) 15. (D)
16. (B) 17. (B) 18. (B) 19. (B) 20. (C)
21. (C) 22. (C) 23. (A)
PAPER - 2
1.
(A)
2.
(C)
3.
(A)
4.
(B)
5.
(C)
6. (D) 7. (A) 8. (A) 9. (B) 10. (B)
11. (C) 12. (B) 13. (B) 14. (A) 15. (B)
16. (C) 17. (D) 18. (D) 19. (C)
20.
(A) (p);
(B) (q,s);
(C) (s);
(D) (q)
21. (A)(q); (B)(p,r); (C)(p,s); (D)(q,s)
22. (A) (p,q,r,s), (B) (q), (C) (p,q,r,s), (D) (p,q,r,s)
1. PT2 = C
using PV = nRT in PT2 = C
nRT 2
T
V
C T3 V 3 ln T ln V
Differentiating we get 3 dT = dV
T V
Coefficient of volume expansion () =
1 dV 3
V dT = T
2. For minimum deviation
i = e and r1 = r2 = A/2 = 30ΒΊ
which is independent of nature of light.
Both the lights are set for minimum deviation so angle of refraction will be 30° for both colours.
3. = for r < R
= 0 for r > R
Case I for r < R
mV 2
FC = r
mg r
R
mV 2
r
(g = acceleration due to gravity at surface of sphere)
V =
Case II for
GMm r 2
g r for r < R
R
r > R
mV2
=
r
V = g R So
r
4.
hc
min = eV
Cut off wavelength depends on the energy of the accelerated electrons and is independent of nature of
target.
5. The least count of length π = 0.1 cm The least count of time t = 0.1 s
g
% error of g = g
× 100
42π
42π 2
g π t
T = 2
g =
T2
= t2 .n
g = π 2 t
g
0.1
2 0.1 100
For student 100 g
64.0
128.0
E1 =
0.2
64.0
100 = 20
64
g
0.1
0.1
For student 100 g
2 100
64.0 64.0
E2 =
0.3
64.0
100
30
= 64
g
0.1
0.1
For student 100 g
= 2 100
20.0 36.0
0.1 0.1 100 19
E1 is least.
E3 = 20.0 18.0 = 18
6. The given three circuits R1, R2 and R3
are equivalent to the following three circuits.
32
P1 = 1
= 9 W , P2 =
32
1/ 2
32
= 18 W , P3 = 2
= 4.5 W , P2 > P1 > P3
7. If d = , then maximum path difference will be less than . So there will be only central maximum on the screen.
If < d < 2, then the maximum path difference will be less than 2.
So there will be two more maximum on screen corresponding to path difference x =
So (A) and (B) are correct.
Intensity of dark fringe becomes zero when intensities
of two slits are equal. Initial intensity at both the slits are unequal so
there will some brightness at dark fringe. Hence when intensity of both slits is made same the intensity at dark on screen shall decrease to zero. So both (C) and (D) are false.
mV
8. The radius of circle of path of the charged particle is R = qB
mV
For particle to enter region R > π. or qB
> π
For path length of particle in region to be maximum
qπB
π = R or V = m
The period of revolution of charged particle is = qB
m
The time spent in region II is t =
m , which is same
qB
for all the cases when it returns to region I.
9. (A) For 1 < A < 50, on fusion mass number for compound nucleus is less than 100.
B/A remains same. Hence no energy is released
(B) For 51 < A < 100, on fusion mass no. of compound nucleus is between 100 and 200. B/A increases. Hence energy is released.
(C) On fission for 100 < A < 200, the mass no. for fission nuclei will be between 50 to 100. B/A decreases. Hence no energy is released.
(D) On fission for 200 < A < 260, the mass no. for fission nuclei will be between 100 to 130, B/A will increase. Hence energy is released.
10.
P1 pΛi
P2 pΛi
As there is no external force so momentum will remain conserved
→ → → →
P1 P'2 P1 P2
Now from option
P1 P2 0
(A)
→ →
P1 P2
= (a1
a2
) Λi (b1
b2
)Λj c1kΛ
(B) P1 P2
(C) P1 P2
(D) P1 P2
= (c1 c 2 )kΛ
= (a1 a2 ) Λi (b1 b2 )Λj
= (a1 a2 ) Λi 2b1 Λj
and it is given that a b c , a , b , c , 0
1 1 1 2 2 2
in case of A and D it is not possible to get P1 P2 = 0 Hence Ans. (A) and (D)
11. As the stream falls down, its speed will increase and cross-section area will decrease. Thus it will become narrow.
Similarly as the stream will go up, speed will decrease and cross-section area will increase. Thus it will become broader.
Hence statement-1 is correct and statement-2 is correct explanation also.
12. The acceleration of centre of mass of either cylinder
gsin
a = K 2
1 R2
where K is radius of gyration.
So acceleration of centre of hollow cylinder is less than that of solid cylinder.
Hence time taken by hollow cylinder will be more. So statement-1 is wrong.
F F
mv 2
mv 2
13.
Gravity
normal = r
(along the radial direction), if Fgravity = r
then Fnormal = zero.
14. R π2 = π1X, As temperature increases, value of unknown resistance increases.
15. The forces on the bubble (except buoyancy force) are – gravity and viscous.
16. The gas in the bubble is insulated. Hence the process is adiabatic. For adiabatic process
1
T pf
= constant T = T ×
1
f i pi
p
1
5 / 31 2
T = T
× P0 πg(H y)
= T P0 πg(H y)
5 / 3
= T P0 πg(H y) 5
f 0
P0 πgH
0 P0
πgH
0 P0
πgH
nRTf . g
2
P0 πg(H y) 5
π.g
17. F = V . .g = Pf
π = nR. T0
P0 πgH
× P0
πg(H y)
π.n.R gT0
= (P0 gH)2 / 5.[P g(H y)]3 / 5
π 0 π
18. At point B there is perfectly inelastic collision so component of velocity to incline plane becomes zero and component parallel to second surface is retained
velocity immediately after it strikes second incline
V = 2gh cos 30
= × 3 =
2
V = m/s
19. At point ‘C’
V 2 V 2 2gh
V 2 = 45 + 2 × 10 × 3
VC =
C B C
m/s
20. The block coming down from incline AB makes an angle 30° with incline BC. If the block collides with incline BC elastically, the angle of block after collision with the incline shall be 30°.
Hence just after collision with incline BC the velocity of block shall be horizontal. So immediately after the block strikes second inclined, its vertical component of velocity will be zero.
3
21. E =
× 13.6 eV = Energy released by H atom. Let He+ go to nth state.
4
So energy required
1 1
E = 13.6 × 4
He 4
n2 eV
3
1 1
E = E
He H 4
× 13.6 = 13.6 × 4
n2
n = 4
22. The wavelength corresponding to transition from n = 4 to n = 3 in He+ corresponds to visible region. Its wavelength is :
hc = 13.6 × 4 1
9
1
16
4.110 15 3 108
or (m)
= 13.6 4 7
9 16
=
4.110 15 3 108
13.6 4 7
m or = 4.68 × 10–7 m.
9 16
K TE
TE Z 2
23. K.E. = – T.E.
H = H
For same ‘n’
H H 1
= =
KHe
TEHe
TE 2
e He
1. V =
V = 2f
C
VP = 2
2
= 0.5
× 0.1
VP =
3 j m/s
50
2. Net electric field due to both charges q/3, will get cancelled.
2q
Electric field due to
will be directed in –ve axis
3
2q
E = 3
R2
q
E = 6 R2
q 2
q 2q q 2q
K K K
P.E. of system =
3 3 3 3 3
2R
P.E. of system 0
2Rsin60
2Rcos 60
Force between B and C
K 2q q
3 3
4 2Kq2
2q2
1 q2
F =
(2Rsin 60)2
= 9 4 3R2
9 3 40R2
(attractive) = 54 0 R2
K q q 2q
3 3 3
Potential at O : V =
= 0
R
3. Given that N = 5Ci
1 1
N = 10Ci
2 2
N = 2 N
2 2 1 1
Also N1 = 2N2
Then N = 2 (2N )
2 2 1 2
= 4
2 1
4T
4. Pressure inside tube = P = P0 + r
P < P
(since r2
> r1)
Hence pressure on side 1 will be greater than side 2. So air from end 1
flows towards end 2.
5.
As springs and supports (m1 and m2) are having negligible mass. Whenever springs pull the massless supports, springs will be in natural length. At maximum compression, velocity of B will be zero.
And by energy conservation.
1 (4K) y2 =
2
1 Kx2
2
y 1
x 2
6. V2 = U2 – 2g (L – L cos)
5gL 4
= 5gL – 2gL (1 – cos)
5 = 20 – 8 + 8 cos
7
cos = – 8
3 < <
4
7. Time constant = = RC
A0 KA0
C C d x x
1 2
C = =
C1 C2
KA0
A0 d x
A0 x
d R
d
C = x K (d x)
x = 3
– Vt
= RK A 0
d Vt d Vt
K d
3 3
A = 1 K = 2
3 2R0
= d 3Vt 6d 2d 6Vt
6R 0
= 5d 3Vt
8. As string and tube are in resonance f1 = f2
| f1 – n | = 4 Hz.
When T increases, f1 also increases. It is given that beat frequency decreases to 2 Hz.
n – f = 4
n = 4 + f1
as f1 = f2
n = 4 + f2
f2 =
3V
4π
3 340
= 4 (3 / 4)
= 340
n = 344
9. As the beam just suffers TIR at interface of region and IV.
n sin =
n0 sin =
n0 sin =
n0 sin 90
0 2 1 6 2 8
1
sin = 8
1
= sin–1 8
10. Statement-1 is based on visual experience.
Statement-2 is formula of relative velocity. But it does not explains statement-1. The correct explanation of statement-1 is due to visual perception of motion (due angular velocity). The object appears to be faster when its angular velocity is greater w.r.t. observer.
11. C = BINA
BNA
=
C
Using iron core, value of magnetic field increases. So deflection increases for same current. Hence sensitivity increases. So statement-1 is true.
Statement-2 is false as we know soft iron can be easily magnetized or demagnetized.
12. Statement-1 is true by information.
Statement-2 is true by formula. But statement-2 is not the explanation of 1.
13. Statement-1 is also practical experience based; so it is true.
Statement-2 is also true but is not the correct explanation of statement-1. Correct explanation is ''there is increase in normal reaction when the object is pushed and there is decrease in normal reaction when object is pulled".
14. Electric field at r = R
KQ
E = R2 , Q = Total charge within the nucleus = Ze
So, E =
KZe R2
So electric field is independent of a
15. Q = r 4r 2dr
for a = 0
d r
R R r
R d
r
d (R r) R
Q = R
0
(R – r) 4 r2 dr
4d R 2 R 3
4d R4
R4
dR3
= R Rr dr r dr
= R 3
4 =
0
0
3
dR3
Q = Ze = 3
or d =
3Ze
R3
16. From the formula of uniformly (volume) charged solid sphere
r
E = 3 0
For E r, should be constant throughout the volume of nucleus This will be possible only when a = R.
17. Applying equation of torque about lowest point
3 MR 2
(2Kx) R =
R =
4Kx 3M
as there is no slipping
4Kx
a = R =
3M
4Kx
Net force = Ma = 3
Which is directed opposite to displacement
4Kx
Fnet = 3
4kx
18. F
net
= 3 = –M(2x) =
1 1 MR 2 V 2 1
19.
2 MV 2 + 2
3
0
2 R
= 2 (2K)x2
= MV 2 = 2kx2 x =
2 0 max
max
At extreme position, friction will have maximum value.
2kx
max
– fmax =
4k x 3
max
max =
2
3 kx
max
or Mg = 2 k 3
Mg =
M V0
3
or V0
= g
20. (A) From nature of SHM, the graph of potential energy as function of displacement will be parabolic graph as given in option p
Hence (A) (p) ;
(s) is rejected because this is not a complete graph of U vs X.
(B) a = 0 or a = constant. (as per given condition)
V > 0 moving along positive x-axis y – displacement
1
y = ut ±
at2 for a = constant
2
y = vt for a = 0
These two conditions are satisfied by (q) and (s).
(B) (q, s)
(p) is rejected because at t = 0 the displacement is not zero and velocity has negative values.
u2 sin(2)
(C) R = g and R u2 for a fixed angle of projection.
and u = 0, R = 0
(C) (s)
(D) T = 2 T2 = 4
(D) (q)
2 π
g
y =
42
x
g
21. Column-I : Expansion of ideal gas Column-II : Thermodynamic change.
(A) Q = 0 (as boundary is non conducting)
in the case of free expansion W = 0 Q = U + W
0 = U + 0 U = 0 U = const.
(A) (q) (As temp remains constant).
1
(B) P V 2
PV2 = C n RTV = C TV = C'
Since volume increases the temperature decreases.
Q = n C T , for polytropic process, PVx = constant, C = C
R
+ 1 x
C = Cv +
R
2 1
= CV
– R
3 R – R
2
C = R Q = n R T
2 2
T is negative so Q is negative means heat is lost
So for (B) (p, r)
(C) PV4/3 = C TV1/3 = C'
So when volume increases temperature decreases
Now C = CV +
R
4 1
3
= 3 R – 3R C = – 3 R
2 2
3
Q = nCT Q = n
R(T)
2
as T is negative Q will be positive.
Hence (C) p,s
(D) T = PV nR
as product of P and V increases, so temperature increases Q = U + W U = +ve (T = +ve)
W = +ve (As volume increases)
So Q = +ve Hence gas gains heat
(D) (q, s)
22. (A) f < 0,
uf f u
v =
v
and m = –
u f
1 f / u
u / f 1 u
values of v may be positive, negative or infinity, also it can have values less than or greater than u.
(A) (p,q,r,s)
(B) In this case f is positive.
So v will be positive and less than u.
(B) (q)
(C) v =
f
1 f / u
u
u/ f 1
Here u < 0 f > 0
v may be positive, negative or infinity v may be greater than or less than u So (C) (p,q,r,s)
1 1 1
(D) (D)
( 1)
f R R
1 2
for diagram R2 > R1
f is +ve
This is same as in case (C) for the nature of image. So (D) (p,q,r,s)
STAGE
SIMILAR TEST PAPERS (PHYSICS)
3
Time : 1.00 Hr Max. Marks : 81
GENERAL INSTRUCTIONS
1. There are 23 questions in this paper.
2. For each question in Section I , 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. For each question in Section II, you will be awarded 4 Marks if you give the correct answer(s) and
zero Mark if no answer is given. No negative Mark will be awarded for an incorrect answer.
4. For each question in Section III , 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.
5. For each question in Section IV , you will be awarded 4 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.
Useful Data :
Planck's constant h = 4.1 × 10–15 eV.s Velocity of light c = 3 × 108 m/s
SECTION - I
Straight Objective Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. An ideal gas obey the relation of P1/2 V2 = constant. The coefficient of volume expansion of the gas is : (where T is the absolute temperature)
(A)
1 (B) – 1
3T 3T
1
(C) 2T
(D)
1
– 2T
2. Two light beams of different colours pass through the prism. Inside the prism, their paths are shown in the figure. Which of the following statement is wrong :
(A) The yellow light beam suffers minimum deviation.
(B) The blue light beam suffers minimum deviation.
(C) Both the beams have same magnitude of minimum deviation.
(D) Both the beams suffer deviation in clockwise sense.
3. For spherically symmetric gravitational system of particles, volume mass density is given by
0
for for
r R r R
where is positive constant. A test mass can undergo circular motion under the influence of the gravita-
tional field of particles. For radial distance r(0 < r < ), the graph is plotted for certain physical quantities of test particle. Which one of the graph is WRONG ?
centripetal acceleration
kinetic energy
(A) (B)
R r r
Linear momentum
Angular momentum
(C) (D)
4. Which one of the following statement is wrong about X-rays.
(A) Frequency of K (characteristics) X-ray of Ni is greater in comparison to K X-ray of Zn
(B) Cut off wavelength of continuous X-ray depends on the kinetic energy of the slowest electron in
the X-ray tube.
(C) For same value of applied accelerating voltage in the X-ray tube, cut off wavelength is same for Ni and Cu target.
(D) For constant applied voltage if number of electrons striking per second on the target increases, then intensity of X–ray increases.
5. In order to measure the spring constant of a spring, Man A, B and C observe the observations in an experi- ment using the same spring, but blocks of different masses as shown.
Assume that Hook’s law is valid and time
period is given by T = 2 M
k
The observations are shown in the table. Least count for mass = 1 gm
Least count for time = 0.1 sec.
Man Mass of block
M (kg) Number of
ascillations n Total time for (n)
oscillations (sec) Time period
(sec)
A 1 20 10 0.5
B 1 10 5 0.5
C 2 20 14 0.7
k 100
If e , e , e , are the percentage errors in calculation of k, i.e., for man A,B,C respectively,
A B C
then:
k
(A) eA = eB = eC (B) eB is minimum
(C) eA is maximum (D) eC is minimum
6. If the power dissipated in the resistor configuration , , is P , P , P respectively, then correct order of them is
1 2 3
(A) P1 > P2 > P3 (B) P3 > P2 > P1
(C) P1 > P2 = P3 (D) P2 > P3 > P1
SECTION - II
Multiple Correct Answers Type
This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B),
(C) and (D) out of which ONE OR MORE is/are correct.
7. In a Young’s double slit experiment, the separation between the two slits is d and the wavelength of the light is . The intensity of light falling on slit 2 is nine times the intensity of light falling on slit 1. Choose the correct choice (s).
(A) If d = 0.8 , the screen will contain only one maximum and two minimum.
(B) If 2.5 < d 3 , total seven maximum may be observed on the screen.
(C) If the intensity of light falling on slit 1 is increased to four times the intensity of the observed dark fringes will decrease and intensity of the observed bright fringes will increase.
(D) If the intensity of light falling on slit 1 is reduced, then intensity of the observed dark and bright fringes will decrease.
8. A charged particle ‘A’ having mass m , charge 2q, speed 3qBod enters the region (of width d) perpendicular
2 m
to boundary as shown in figure , where uniform magnetic field B exists perpendicular to the plane of the
paper. Another charged particle B having mass 2m, charge q, speed 3qBod
m
enters the region (width 2d)
perpendicular to boundary as shown in figure , where uniform magnetic field 2B exists normal to the plane
of the paper. Select the correct alternative /s
‘’A’’ ,
m , 2q ,
2
‘’B’’ , 2 m, q,
(A) The particle A enters in the region III
(B) The particle B enters in the region III
(C) Path length of the particle A in region II is less then path length of the particle B in region II
(D) If width of region II is increased in figure II then time spent by particle B in region II increases.
9. Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice (s) given below.
(A) Fission of a nucleus of mass number 210 will release energy when broken into two equal fragments.
(B) Fission of a nucleus of mass number 62 will release energy when broken into two equal fragments
(C) Fusion of two nuclei with mass number 21 and 40 will release energy.
(D) Fusion of two nuclei with mass number 59 and 40 will release energy.
10. A shell is fired from ground. When it reaches the top of its trajectory it's velocity is 100 i m/sec. In horizontal
direction and it explodes at that top point into two fragments having equal masses. Let v1 and V2
be their
velocity just after explosion. The following options (s) is (are) certainly not allowed for any non zero positive value of a1, a2, b1, b2, c1, and c2 .
(A)
v1 = a1 i
+ c1 k
(B)
v1 =
b1 j
+ c1 k
v2 = a2 i
v2 = b2 j
+ c2 k
(C)
v1 = a1 i
+ b1 j
(D)
v1 = a1 i
+ c1 k
v2 = – b1 j
v2 = – a1 i
– c1 k
SECTION - III
Reasoning Type
This section contains 4 reasoning type questions, Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct
11. Statement-1 : The flow of water in the shown tube is in steady state. The pressure at point B is greater than the pressure at point A.
Statement-2 : The flow of water in the shown tube is in steady state. The pressure at point B is less than the pressure at point A.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
12. Statement–1 : A ring and a disc with the same mass and same radius are simultaneously allowed to roll without slipping down an inclined plane from the same height. The friction force acting on the ring is smaller than the friction force acting on the disk.
Statement–2 : Rotational kinetic energies of both the bodies are different, but by the principle of conserva- tion of energy, the total (translational + rotational) kinetic energies of both the bodies are equal when they reach the bottom of the incline.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
13. Statement-1 : The time period of a simple pendulum in a satellite above the earth is infinity.
Statement-2 : An object, moving around the earth under the influence of the earth’s gravitational force is in a state of ‘free fall’.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
14. Statement-1 : In a Meter Bridge experiment (shown in figure), tempera- ture of unknown resistance X is decreased. For the same position of null point
can be obtained by adding a suitable resistance in parallel with resistance R.
Statement-2 : Resistance of metal decreases with increase in temperature.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
SECTION - IV
Linked Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
C15-17 : Paragraph for Question Nos. 15 to 17
7
A small spherical diatomic ideal gas bubble is trapped inside a liquid of density
(see figure).
5 π
Assume that the bubble does not exchange an heat with liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T0 , the height of the liquid is H and the atmospheric pressure is PO (Neglect surface tension).
15. Assume that acceleration ‘a’ of chamber is zero and chamber moves upward with constant velocity V as shown. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it.
(A) Only the force of gravity.
(B) The force due to gravity and the force due to the pressure of the liquid.
(C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid.
(D) The force due to gravity and the force due to viscosity of the liquid.
16. Assume that container moves upward with constant acceleration a = g metre/sec2 When the gas bubble is at a height y from the bottom of container, its temperature is -
2
P0 2gπ (H – y) 7
7
P0 2gπ (H – y) 5
(A) T0
P0 2π gH
(B) T0
P0 2π gH
3
P0 π gH 7
5
P0 2gπ (H – y) 7
(C) T (D) T
0 P0 π gy 0 P0 π gH
17. If the container moves upward with constant acceleration a = g m/sec2, The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)
(P0 2 π gH)5
πn TRgT0
(A) 2 n R g T 7 (B) 2 5
π 0
(P0 2π
gy) 5
(P0 π gH) 5 [P0 πg(H – y)] 7
(P0 π gH)5 2 π nRg T0
(C) n R g T 3
π 0 (P0 π gy)7
2 5
7 7
0 π 0 π
C18-20 : Paragraph for Question Nos. 18 to 20
A small block is moving with 20m/sec. on smooth horizontal surface AB. All the surface AB, BC, CD, are frictionless. The block strikes the inclined plane BC. The collision between the block and inclined BC is perfectly inelastic.
18. The speed of the block at point B just after it strikes the incline BC is :
m
(A) 20 sec .
m
(B) 10 sec .
(C) 10
m (D) 5 3
sec . 2
m sec .
19. The speed of the block just before it strikes incline CD is :
(A) 5
m 3
sec . (B) 5 2
m sec .
m
(C) 10 sec .
(D) 5
m sec .
20. If collision between the block and the incline is perfectly elastic, than the vertical (upward) component of velocity of block just after it strikes the plane CD is :
m
(A) 2.5 sec .
m
(B) 5 sec .
(C) 5 3 2
m
sec . (D)
m sec .
C21-23 : Paragraph for Question Nos. 21 to 23
A hydrogen atom in third excited state makes a transition to first excited state and emit photon. This emitted photon is absorbed by He+ ion which was already in seventh excited state. After absorption of photon He+ ion jumps from seventh excited state to higher excited state having quantum number nf.
21. The quantum number n of the state finally populated in He+ ion
(A) 8 (B) 10
(C) 16 (D) 20
22. Now He+ ion jumps to lower state by emitting single photon ‘P’ of visible light. The energy of this photon is as possible as close to energy of the absorbed photon by He+ ion (as mentioned in paragraph). Then wavelength of this photon ‘P’ is nearly.
(A) 6760 AΒΊ (B) 5000 AΒΊ
(C) 4480 AΒΊ (D) 3500 AΒΊ
23. The ratio of the kinetic energy of the n = 4 electron for H atom to that He+ ion is P and the ratio of the total
P1
energy of the n = 6 electron for the H atom to that of He+ ion is P . Then ratio is
2
(A) 1 (B) 9/4
(C) 4/9 (D) 4
PAPER - 2
Time : 1.00 Hr Max. Marks : 81
GENERAL INSTRUCTIONS
1. There are 22 questions in this paper.
2. For each question in Section I , 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. For each question in Section II , you will be awarded 3 Marks if you give the correct answer and zero Mark
if noanswer is given. In all other cases, minus one (–1) Mark will be awarded.
4. For each question in Section III, you will be awarded 4 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.
5. For each question in Section IV, you will be awarded 6 Marks if you give ALL the correct answer(s) or awarded 1 Mark each for correct answer in any row. No negative Mark will be awarded for an
incorrect answer.
SECTION - I
Straight Objective Type
This section contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A transverse sinusoidal wave is traveling along a string in the negative x axis. At particular time t, for the shown snap shot of wave, magnitude of displacements of point A, B and C are same. Take velocity of point in positive y direction as positive and in negative direction as negative. At given instant of time velocities of points A, B, C are VA, VB, VC respectively.
VA
Then respective values of VB
and
VA
VC are -
(A) +1, – 1 (B) +1, +2
(C) –1, 1 (D) –1, –1
2. Three point charges are located on circumference of circle of radius 2.5m as shown in figure. The electrostatic potential energy of system is
y (metre)
16 37
(A) 15 kq2 (B) 30 kq2
q
43 79
(C) 30 kq2 (D) 60 kq2
3. A radioactive sample S1 has activity A and another sample S2 has activity 3A. The half lives of S1 and S2 are 2T and 5T respectively. The ratio of number of nuclei present in S1 to S2 is -
(A) 5/2 (B) 5/6
(C) 2/15 (D) 3/1
4. The open glass tube has uniform cross-section and a valve separating the two identical ends. The valve is initially closed End 1 has planer film of soap bubble and End 2 has a soap bubble having radius of curvature ‘r’. Immediately after opening the valve.
(A) Air from end 1 flows towards end 2. The volume of soap bubble at end 2 increases.
(B) Air from end 2 flows towards end 1. The volume of soap bubble at end 2 increases.
(C) Air from end 2 flows towards end 1. The volume of soap bubble at end 2 decreases.
(D) no change occurs.
5. One of the ends of two massless springs A1 and B1 are rigidly attached to a toy car and other free ends are attached to massless small blocks A2 and B2 respectively. The natural lengths of springs A1 and B1 are 2π0 and 4π0 respectively and spring constants are 2k and k respectively (blocks A2 and B2 are not rigidly attached to wall). Now this car is taken near the wall and released from rest as shown in figure. At the moment of
release distance between the car and wall is x = π0. When x becomes 3π0, the kinetic energy of car is :
(A) 12 kπ 2 (B)
11 kπ 2
2
(C) 4kπ 2 (D) 5kπ 2
0 0
6. A small block describes the vertical circular motion inside the smooth spherical cavity of radius R. The speed at the lowest position A is just sufficient to make it reach the highest point B. The angle at which the speed of the block is three fifth of the largest speed satisfies
(A) 4
< < 3
(B) 3
3
< < 4
3
(C) 4
5
< < 6
5
(D) 6
< <
7. A parallel plate capacitor has plate area A and separation ‘d’. Initially it is completely filled with material of dielectric constant K = 3 The width x of filled material decreases at a constant speed v as shown in figure.
For time interval 0 < t <
π , time constant of circuit varies as
v
R0A
2 v t
R0A
2 v t
(A) d
3 –
π
(B) d
1 π
(C) R0A 3 2 v t
(D) R0A
2 v t
d π
1 –
d
π
8. A vibrating wire of certain length under certain tension resonates with a mode corresponding to the second overtone (fifth harmonic) of an air column of length 50 cm inside a tube closed at one end. The wire also generates 6 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the wire is slightly decreased, the number of beats increases to 8 per second. Assuming the speed of sound in air to be 340 m/sec, the frequency n of the tuning fork in Hz is -
(A) 817 (B) 833
(C) 831 (D) 819
9. Light beam is incident at an angle as shown in the figure. After refractions beam is incident on interfacing surface AC and makes an angle 45° with that surface AC. For which value of it (angle of incidence 45° with surface AC) is not certainly possible :
1
(A) sin–1 2
1
(B) sin–1 6
1
(C) sin–1 9
1
(D) sin–1 2
SECTION - II
Reasoning Type
This section contains 4 reasoning type questions, Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
10. Statement-1 : All three cars are moving on different straight tracks with same speed as shown in figure. Observer in car B, feels that car A is moving with greater speed than car C.
Statement-2 : If two objects are moving with speed V1 and V2 in opposite directions, than speed of the first object with respect to second object is V1 + V2
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
11. Statement- 1 : The sensitivity of a moving coil galvanometer can be decreased by replacing diamagnetic material in place of ferromagnetic material.
Statement- 2 : Ferromagnetic material (like soft iron) has positive susceptibility whereas diamagnetic mate- rial has negative susceptibility.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
12. Statement-1 : After closing the switch S, potential of conducting sphere becomes zero.
Statement-2 : For uniformly charged nonconducting solid sphere, potential difference between the surface
of sphere and center of sphere is kQ , where Q is the total charge of sphere and R is the radius of sphere.
2R
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
13. Statement-1 : A block is moved up the rough incline under two situations as shown in figure. In compresion to situation , the friction force acting on the block is larger in situation .
Statement- 2 : For the above shown situation, If lubricating oil is spread on rough inclined surface, then above required force F is decreased.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
SECTION - III
Linked Comprehension Type
This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
C14-16 : Paragraph for Question Nos. 14 to 16
For a neutral atom, the charge distribution within the nucleus is shown for radial distance 0 < r < r2 and
the charge distribution of atomic electrons are shown for r3 < r < r . The volume charge density (r) is
only function of radial distance r from the centre of nucleus and electric field is only along the radial direction. Total nucleus charge is Ze.
14. The electric field for r > r6 is :
(A) dependent on value of r6 (B) independent of the total nuclear charge
(C) directly proportional to r (D) inversely proportional to r
15. If r3 = r4 and r5 = r6, then magnitude of electronic density in region r4 < r < r5 is :
Ze
(A) 4 3
(B)
Ze
4 3
3 (r5 r4 )
Ze
3 r5
Ze
(C) 4 3 3
(D) 4(r 2 r 2 )
3 (r5 r4 )
16. The electric field is linearly dependent on r :
(A) for only region 0 < r < r1 (B) for only region r4 < r < r5
(C) for both the regions 0 < r < r1 and r4 < r < r5 (D) for the region r2 < r < r4
C17-19 : Paragraph for Question Nos. 17 to 19
A uniform solid sphere of mass M and radius R is attached to four identical light springs of spring constant k which are fixed to walls as shown in figure. The springs are attached symmetrically to the axle of the sphere as shown if figure The axle is massless and all the springs and the axle are in horizontal plane. The unstretched length of each spring is L. The sphere is initially at its equilibrium position with its center of mass (CM) at a
distance L from the each wall. The sphere rolls without slipping with velocity
0
= V0
Λi and angular velocity
. The coefficient of friction is .
17. The net external force acting on the sphere when its centre of mass is at displacement x with respect to its equilibrium position is
– 20
(A) –10 kx (B) 7 kx
– 2
(C) 5
– 7
kx (D) 5 kx
18. The centre of mass of the sphere undergoes simple harmonic motion time period T equal to
(A) 2
(C) 2
(B) 2
(D) 2
19. The maximum value of angular velocity about centre of mass for which sphere will roll without slipping
is
g
(A) R
g
(C) R
g
(B) R
g
(D) R
SECTION - IV
Matrix - Match Type
This section contains 3 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column-I are labelled A, B, C and D, while the statements in Column-II are labelled p, q, r and s. Any given statement in Coloumn-I can have correct matching with ONE OR MORE statement(s) in Coloumn-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s and D-q then the answer
should be written as : A p,r ; B p, s ; C r, s ; D q.
20. On the basis of results of some experiments curves are drawn in column-II in which variation of dependent quantity with independent parameter are shown. Match the graphs (in column II) with corresponding varia- tions in column-I.
Column-I Column-II
y
(A) (p)
x
A block is oscillating on smooth fixed surface as shown. The kinetic energy (on axis) versus displacement (on x-axis)
graph may be y
(B) A particle is moving under constant acceleration. (q) x Velocity (on y-axis) versus time (on x-axis) graph may be
y
(C) Range (on y-axis) of a projectile (on horizontal ground) (r) versus projection angle (on x-axis) with horizontal is best
represented by x
y
(D) A simple pendulum is taken inside the tunnel and time (s) period is noted at different depths. Time period (on y-axis)
versus gravitational acceleration (on x-axis) graph may be x
21. In column I , some thermodynamic processes are given for an ideal gas. Match the processes given in column I with corresponding thermodynamic change given in column II.
Column - I Column II
(A) An insulated container has two chambers (p) The pressure of the gas decreases. separated by a light piston. The chamber I
contains an ideal gas and the chamber II
has vacuum. Piston is frictionless.
The piston is released from shown position
(B) An ideal monoatomic gas expands to thrice (q) The internal energy of gas decreases. its original volume such that its pressure
1
P V 3 where V is the volume of gas
(C) An ideal monoatomic gas expands to twice its (r) The gas loses heat. original volume such that its
1
temperature T
where V is the volume of gas
(D) An ideal monoatomic gas expands such (s) The gas neither loses heat nor gains heat. that its temperature T and V follows the
behaviour shown in the graph and T V2
22. A real object ‘S’ is placed on the optic axis of an optical instrument as shown in column-I. The distance between the object and the instrument can be varied. Some statements are given in column-II about image. f is the magnitude of focal length of the instrument. Match the optical instruments given in column-I with the appropriate properties of images given in column-II.
Column–I Column–II
(A) (p) If image distance r from pole lies in range 0 < r < f,
then image must be virtual.
(B) (q) If image distance r from pole lies 0 < r < f, then image
must be magnified.
(C) (r) If object distance r from pole is in range f < r < 2f,
then image must be real.
(D) (s) If object distance r from the pole is in the range
2f < r < , then image must be diminished
A nswers
PAPER - 1
1. (B) 2. (C) 3. (B) 4. (B) 5. (D)
6. (D) 7. (A), (C) 8. (B), (C) 9. (C)
10. (A), (B), (D) 11. (C) 12. (D) 13. (A) 14. (C)
15. (D) 16. (A) 17. (D) 18. (B) 19. (A)
20. (A) 21. (C) 22. (A) 23. (A)
PAPER - 2
1. (C) 2. (D) 3. (C) 4. (C) 5. (D)
6. (C) 7. (A) 8. (B) 9. (D) 10. (B)
11. (A) 12. (B) 13. (B) 14. (B) 15. (C)
16. (A) 17. (B) 18. (A) 19. (D)
20.
(A)(r) ; (B)(p), (q)
; (C)(r) ; (D)(s)
21. (A)(p, s) ; (B)(p,q,r) ; (C)(p , q , s) ; (D)(p , s)
22. (A)(r, s) ; (B)(p, s) ; (C)(r, s) ; (D)(r, s)
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