SECTION-I (PHYSICS)
Single Correct Type Questions Statement-II: Resistivity is an intrinsic
1. A vernier scale has M + 2 divisions that align property of the material of the wire.
perfectly with M divisions of the main scale. (1) If both statement-I and statement-II are
If each division on the main scale measures b true and the statement-II is correct
units, what is the least count of this explanation of the statement-I.
instrument? (2) If both statement-I and statement-II are
(1)
b
(2)
( M + 2) b true but statement-II is not the correct
( M + 2) M explanation of statement-I.
Mb 2b (3) If statement-I is true but the statement-II
(3) (4) is false.
M +2 M +2
(4) If statement-I is false but the statement-II
2. In a typical semiconductor material, what is is true.
the correct relationship between the mobility
of conduction electrons, denoted by n , and 5. A simple pendulum of length 1 m, hanging from
an inclined wall, is made to oscillate from an
the mobility of valence holes, denoted by p ? angle 2° with the vertical as shown in figure.
(1) n p (2) n p
(3) n = p (4) n 0, p 0
3. Two identical wheels of radius r are rotating
on parallel axles. They spin with the same
constant angular speed Ω but in opposite
directions. At t = 0 , point P on the first wheel
and point Q on the second are at their
minimum separation, lying on the line
connecting the axles. Which graph best If collision with the wall is elastic, time period of
oscillation will be (Use g = π2)
represents the magnitude of the relative
velocity, vr , between points P and Q over one
2 4
(1) s (2) s
3 3
rotational period T ?
1
(3) 2s (4) s
3
6. A block of mass 5 kg rests on a horizontal
surface with a coefficient of kinetic friction of
0.4 . It is connected by an ideal string passing
over a frictionless pulley to another hanging
(1) (2) block of mass 5 kg. What is the magnitude of
the acceleration of the center of mass of this
two-block system? (Assume g = 10 m/s2 )
(3) (4)
4. Consider the following two statements
regarding the electrical resistance of a
conductor. 3 2
(1) m/s2 (2) 3 m/s2
Statement-I: The resistance of a wire is given 2
by R = l / A . If the length l of the wire is 3
(3) m/s2 (4) 3 2 m/s2
halved, its resistivity is also halved. 2
[3]
, 7. The first spectral line of the Paschen series in (1) F = 160 mm, d = 200 mm
the hydrogen spectrum has a wavelength of (2) F = 160 mm, d = 120 mm
1875 nm. What is the approximate wavelength (3) F = 10 mm, d = 50 mm
of the second line in this series? (4) F = 200 mm, d = 160 mm
(1) 1282 nm (2) 1875 nm
(3) 1094 nm (4) 2150 nm 11. A straight conducting rod of mass M and
length L slides with a constant velocity down
8. Binding energy per nucleon vs mass number a frictionless inclined plane. The plane is
curve for nuclei is shown in the figure W, X, Y and tilted at an angle with the horizontal. A
Z are four nuclei indicated on the curve. The constant current I flows through the rod. The
process that would release energy is
entire setup is placed in a uniform horizontal
magnetic field of magnitude B , which is
directed parallel to the base of the incline.
Determine the magnitude of the magnetic
field B. (B is perpendicular to PQ line and
parallel to base)
(1) Y→2Z (2) W→X + Z
(3) W→2Y (4) X→Y+Z
9. Two coherent light sources with intensities I A Mg Mgsin
(1) B = (2) B =
and I B produce an interference pattern. The IL IL
ratio of the maximum intensity to the Mgtan Mg
(3) B = (4) B =
minimum intensity in the pattern is found to IL ILcos
be . What is the ratio of the intensities of the
12. In the circuit shown, two capacitors with
sources, I A / I B (assuming I A I B )?
capacitances C A and C B are initially charged
2 2
+1 +1 to potentials 2V0 and V0 respectively, with the
(1) (2)
−1 −1 polarities as indicated. At t = 0 , the switch S
+1 −1 is closed, connecting them in series with an
(3) (4)
−1 +1 inductor L . What is the charge on capacitor
C A at the instant the current in the inductor
10. To create a beam expander, a collimated light reaches its maximum value?
beam of diameter 2 mm is passed through a
combination of two convex lenses. The first
lens has a focal length of 40 mm. If the final
emergent beam is also collimated and has a
diameter of 8 mm, what are the focal length CA ( 2CA + CB )V0
F of the second lens and the separation d (1)
CA + CB
between the lenses?
CB ( 2CA + CB )V0
(2)
CA + CB
(3) ( 2CA − CB )V0
C ACBV0
(4)
C A + CB
[4]
Single Correct Type Questions Statement-II: Resistivity is an intrinsic
1. A vernier scale has M + 2 divisions that align property of the material of the wire.
perfectly with M divisions of the main scale. (1) If both statement-I and statement-II are
If each division on the main scale measures b true and the statement-II is correct
units, what is the least count of this explanation of the statement-I.
instrument? (2) If both statement-I and statement-II are
(1)
b
(2)
( M + 2) b true but statement-II is not the correct
( M + 2) M explanation of statement-I.
Mb 2b (3) If statement-I is true but the statement-II
(3) (4) is false.
M +2 M +2
(4) If statement-I is false but the statement-II
2. In a typical semiconductor material, what is is true.
the correct relationship between the mobility
of conduction electrons, denoted by n , and 5. A simple pendulum of length 1 m, hanging from
an inclined wall, is made to oscillate from an
the mobility of valence holes, denoted by p ? angle 2° with the vertical as shown in figure.
(1) n p (2) n p
(3) n = p (4) n 0, p 0
3. Two identical wheels of radius r are rotating
on parallel axles. They spin with the same
constant angular speed Ω but in opposite
directions. At t = 0 , point P on the first wheel
and point Q on the second are at their
minimum separation, lying on the line
connecting the axles. Which graph best If collision with the wall is elastic, time period of
oscillation will be (Use g = π2)
represents the magnitude of the relative
velocity, vr , between points P and Q over one
2 4
(1) s (2) s
3 3
rotational period T ?
1
(3) 2s (4) s
3
6. A block of mass 5 kg rests on a horizontal
surface with a coefficient of kinetic friction of
0.4 . It is connected by an ideal string passing
over a frictionless pulley to another hanging
(1) (2) block of mass 5 kg. What is the magnitude of
the acceleration of the center of mass of this
two-block system? (Assume g = 10 m/s2 )
(3) (4)
4. Consider the following two statements
regarding the electrical resistance of a
conductor. 3 2
(1) m/s2 (2) 3 m/s2
Statement-I: The resistance of a wire is given 2
by R = l / A . If the length l of the wire is 3
(3) m/s2 (4) 3 2 m/s2
halved, its resistivity is also halved. 2
[3]
, 7. The first spectral line of the Paschen series in (1) F = 160 mm, d = 200 mm
the hydrogen spectrum has a wavelength of (2) F = 160 mm, d = 120 mm
1875 nm. What is the approximate wavelength (3) F = 10 mm, d = 50 mm
of the second line in this series? (4) F = 200 mm, d = 160 mm
(1) 1282 nm (2) 1875 nm
(3) 1094 nm (4) 2150 nm 11. A straight conducting rod of mass M and
length L slides with a constant velocity down
8. Binding energy per nucleon vs mass number a frictionless inclined plane. The plane is
curve for nuclei is shown in the figure W, X, Y and tilted at an angle with the horizontal. A
Z are four nuclei indicated on the curve. The constant current I flows through the rod. The
process that would release energy is
entire setup is placed in a uniform horizontal
magnetic field of magnitude B , which is
directed parallel to the base of the incline.
Determine the magnitude of the magnetic
field B. (B is perpendicular to PQ line and
parallel to base)
(1) Y→2Z (2) W→X + Z
(3) W→2Y (4) X→Y+Z
9. Two coherent light sources with intensities I A Mg Mgsin
(1) B = (2) B =
and I B produce an interference pattern. The IL IL
ratio of the maximum intensity to the Mgtan Mg
(3) B = (4) B =
minimum intensity in the pattern is found to IL ILcos
be . What is the ratio of the intensities of the
12. In the circuit shown, two capacitors with
sources, I A / I B (assuming I A I B )?
capacitances C A and C B are initially charged
2 2
+1 +1 to potentials 2V0 and V0 respectively, with the
(1) (2)
−1 −1 polarities as indicated. At t = 0 , the switch S
+1 −1 is closed, connecting them in series with an
(3) (4)
−1 +1 inductor L . What is the charge on capacitor
C A at the instant the current in the inductor
10. To create a beam expander, a collimated light reaches its maximum value?
beam of diameter 2 mm is passed through a
combination of two convex lenses. The first
lens has a focal length of 40 mm. If the final
emergent beam is also collimated and has a
diameter of 8 mm, what are the focal length CA ( 2CA + CB )V0
F of the second lens and the separation d (1)
CA + CB
between the lenses?
CB ( 2CA + CB )V0
(2)
CA + CB
(3) ( 2CA − CB )V0
C ACBV0
(4)
C A + CB
[4]
