OPTICS, MODERN

AND
THERMAL PHYSICS
Challenge for JEE Main Exam
Video Solution

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 Optics, Modern & Thermal Physics QUESTION BANK
PHYSICS
PHYSICS

1. A point source of light S, placed at a distance 60 4. An object ' O ' is placed at a distance of 100 cm
cm infront of the centre 50 cm of a plane mirror in front of a concave mirror of radius of
of width 50 cm , hangs vertically on a wall. A
man walks infront of the mirror along a line curvature 200 cm as shown in the figure. The
parallel to the mirror at a distance 1.2 m from it object starts moving towards the mirror at a
(see in the figure). The distance between the speed 2 cm/s. The position of the image from
extreme points where he can see the image of
the mirror after 10 s will be at _____ cm.
the light source in the mirror is ______ cm.

2. As shown in the figure, a plane mirror is fixed

at a height of 50 cm from the bottom of tank
!
containing water µ = &"'. The height of water
5. A concave mirror for face viewing has focal
in the tank is 8 cm . A small bulb is placed at
length of 0.4 m . The distance at which you hold
the bottom of the water tank. The distance of
the mirror from your face in order to see your
image of the bulb formed by mirror from the
image upright with a magnification of 5 is
bottom of the tank is ______ cm.
(A) 0.16 m (B) 1.60 m
(C) 0.32 m (D) 0.24 m
6. A vessel of depth ' d ' is half filled with oil of
refractive index n# and the other half is filled
with water of refractive index n$ . The apparent
depth of this vessel when viewed from above
3. A light ray is incident, at an incident angle θ# ,
on the system of two plane mirrors M# and M$ will be
having an inclination angle 75∘ between them (A)
$&((! )(" )
(B)
&((! )(" )
(! )(" $(! ("
(as shown in figure).
&( ( &(! ("
(C) $(( !)(" ) (D) ((
! " ! )(" )

7. Consider a light travelling in air is incident into

a medium of refractive index √2n. The incident
angle is twice that of refracting angle. Then, the
angle of incidence will be
(
After reflecting from mirror M# it gets reflected (A) sin+# (√n) (B) cos +# ;<$ =
back by the mirror M$ with an angle of
reflection 30∘ . The total deviation of the ray (C) sin+# (√2n) (D) 2cos +# ;<$=
(

will be _____ degree.

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8. If a wave gets refracted into a denser medium, 13. A convex lens has power P. It is cut into two
then which of the following is true? halves along its principal axis. Further one piece
(out of the two halves) is cut into two halves
(A) wavelength, speed and frequency decreases.
perpendicular to the principal axis (as shown in
(B) wavelength increases, speed decreases and
figure). Choose the incorrect option for the
frequency remains constant.
reported pieces.
(C) wavelength and speed decreases but
frequency remains constant.
(D) wavelength, speed and frequency increases.
9. There is a small source of light at some depth
below the surface of water (refractive index =
4/3 ) in a tank of large cross sectional surface , ,
(A) Power of L# = $ (B) Power of L$ = $
area. Neglecting any reflection from the bottom
,
(C) Power of L" = $ (D) Power of L# = P
and absorption by water, percentage of light that
14. The graph shows how the magnification m
emerges out of surface is (nearly) [Use the fact
produced by a thin lens varies with image
that surface area of a spherical cap of height h
distance v. What is the focal length of the lens
and radius of curvature r is 2πrh]
used?
(A) 34% (B) 17%
(C) 21% (D) 50%
10. Two convex lenses of focal length 20 cm each
are placed coaxially with a separation of 60 cm
between them. The image of the distant object
formed by the combination is at ______ cm
from the first lens - /
(A) . (B) .
11. A parallel beam of light is allowed to fall on a
/" . /"
transparent spherical globe of diameter 30 cm (C) -
(D) -.
15. A convex lens, of focal length 30 cm , a
and refractive index 1.5 . The distance from the
concave lens of focal length 120 cm , and a
centre of the globe at which the beam of light plane mirror are arranged as shown. For an
object kept at a distance of 60 cm from the
can converge is _____ mm.
convex lens, the final image formed by the
12. For an object placed at a distance 2.4 m from a combination is a real image at a distance of
lens, a sharp focused image is observed on a
screen 𝐒 placed at a distance 12 cm form the
lens. A glass plate of refractive index 1.5 and
thickness 1 cm is introduced between lens and
screen such that the glass plate faces parallel to
the screen. By what distance should the object
be shifted so that a sharp focused image is
observed again on the screen? (A) 60 cm from the convex lens
(B) 60 cm from the concave lens
(A) 0.8 m (B) 3.2 m
(C) 70 cm from the convex lens
(C) 1.2 m (D) 5.6 m (D) 70 cm from the concave lens
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16. A prism of refractive index µ and angle of prism 19. In a compound microscope, the magnified
A is placed in the position of minimum angle of virtual image is formed at a distance of 25 cm
deviation. If minimum angle of deviation is also from the eye- piece. The focal length of its
A, then in terms of refractive index, value of A objective lens is 1 cm . If the magnification is
is 100 and the tube length of the microscope is 20

(A) 2cos +# &$'

0
(B) sin+# &$'
0 cm , then the focal length of the eye-piece lens
(in cm ) is _____ .
+# 0 +# 0+#
(C) cos & $' (D) sin I< $
J 20. A compound microscope consists of an
objective lens of focal length 1 cm and an eye
17. Monochromatic light is incident on a glass
piece of focal length 5 cm with a separation of
prism of angle A. If the refractive index of the
10 cm . The distance between an object and the
material of the prism is µ, a ray, incident at an
objective lens, at which the strain on the eye is
angle θ, on the face AB would get transmitted
(
minimum is !1 cm. The value of n is ______ .
through the face AC of the prism provided
21. The interference pattern is obtained with two
coherent light sources of intensity ratio 4 : 1 .
2 )2 3
And the ratio 2#$% +2#&' is 4. Then, the value of x
#$% #&'

will be equal
(A) 3
(B) 4
(C) 2
(D) 1
22. In the Young's double slit experiment, the

# distance between the slits varies in time as

(A) θ > cos +# Nµsin IA + sin+# &0'JP
d(t) = d1 + a1 sinωt , where d1 , ω and a1 are
# constants. The difference between the largest
(B) θ < cos +# Nµsin IA + sin+# &0'JP
fringe width and the smallest fringe width
# obtained over time is given as
(C) θ > sin+# Nµsin IA − sin+# &0'JP
!"
(A)
#
#! $%!
(D) θ < sin+# Nµsin IA − sin+# &0'JP
!"
18. In normal adjustment, for a refracting telescope, (B) a
#"! &
the distance between objective and eye-piece is
'!"%!
30 cm . The focal length of the objective, when (C)
(#"! )%"! *
the angular magnification of the telescope is 2 ,
'!"(#! )
will be (D)
(#"! )%"! *
(A) 20 cm (B) 30 cm
(C) 10 cm (D) 15 cm
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23. In the given figure, P and Q are two equally 27. A Young's double-slit experiment is performed
intense coherent sources emitting radiation of
using monochromatic light of wavelength λ The
wavelength 20 m . The separation between P
and Q is 5 m and the phase of P is ahead of that intensity of light at a point on the screen, where
of Q by 90∘ . A, B and C are three distinct points the path difference is λ, is K units. The intensity
of observation, each equidistant from the 5
of light at a point where the path difference is :
midpoint of PQ. The intensities of radiation at
A, B, C will be in the ratio is given by
(;
, where n is an integer. The value
#$

of n is ____ .
28. An unpolarised light beam of intensity 2I1 is
passed through a polaroid P and then through
another polaroid Q which is oriented in such a
(A) 0: 1: 4 (B) 2: 1: 0 way that its passing axis makes an angle of 30∘
(C) 0: 1: 2 (D) 4: 1: 0
relative to that of P . The intensity of the
24. In a double slit experiment, when a thin film of
emergent light is
thickness t having refractive index µ is
2( 2(
(A) (B)
introduced in front of one of the slits, the ! $
"2( "2(
maximum at the centre of the fringe pattern (C) !
(D) $

shifts by one fringe width. The value of t is (λ is 29. A source of light is placed in front of a screen.

the wavelength of the light used) Intensity of light on the screen is I . Two
5 5 polaroids P# and P$ are so placed in between the
(A) (0+#) (B) ($0+#)
source of light and screen that the intensity of
$5 5
(C) (0+#) (D) $(0+#)
light on screen is I/2. P$ should be rotated by an
25. In Young's double slit experiment, one of the
angle of _____ (degrees) so that intensity of light
slit is wider than other, so that the amplitude of "2
on the screen becomes 9
the light from one slit is double of that from
other slit. If I6 be the maximum intensity, the 30. A system of three polarizers P# , P$ , P" is set up

resultant intensity I when they interfere at phase such that the pass axis of P" is crossed with

difference ϕ is given by respect to that of P# . The pass axis of P$ is

2# 7 2# 7 inclined at 60∘ to the pass axis of P" . When a
(A) "
&1 + 2cos $ $ ' (B) 3
&1 + 4cos $ $ '
2# 7 2# beam of unpolarized light of intensity I1 is
(C) 8
&1 + 8cos $ $ ' (D) 8
(4 + 5cos ϕ)
incident on P# , the intensity of light transmitted
26. In a Young's double slit experiment, the path by the three polarizers is I. The ratio ( I1 /I )
difference, at a certain point on the screen, equals (nearly)
#
between two interfering waves is 9
th of (A) 10.67 (B) 5.33
wavelength. The ratio of the intensity at this (C) 1.80 (D) 16.00
point to that at the centre of a bright fringe is 31. The angle of incidence at which reflected light
in totally polarized for reflection from air to
close to
glass (refractive index n), is
(A) 0.80 (B) 0.94 (A) sin+# (n) (B) sin+# (1/n)
(C) 0.85 (D) 0.74 (C) tan+# (1/n) (D) tan+# (n)
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32. When radiation of wavelength λ is incident on a 35. Given below are two statements: one is labelled
metallic surface, the stopping potential of as Assertion A and the other is labelled as
ejected photoelectrons is 4.8 V . If the same Reason R.
surface is illuminated by radiation of double the Assertion A: The photoelectric effect does not
previous wavelength, then the stopping potential takes place, if the energy of the incident
becomes 1.6 V . The threshold wavelength of radiation is less than the work function of a
the metal is metal.
(A) 4λ (B) 8λ Reason R: Kinetic energy of the photoelectrons
(C) 2λ (D) 6λ is zero, if the energy of the incident radiation is
33. The variation of stopping potential (V1 ) as a equal to the work function of a metal.

function of the frequency ( v ) of the incident In the light of the above statements, choose the

light for a metal is shown in figure. The work most of appropriate answer from the options

function of the surface is given below.

(A) Both A and R are correct and R is the
correct explanation of A
(B) Both A and R are correct but R is not the
correct explanation of A
(C) A is correct but R is not correct
(D) A is not correct but R is correct.
36. From the photoelectric effect experiment,
following observations are made. Identify which
of these are correct.
A. The stopping potential depends only on the
(A) 2.98 eV
work function of the metal
(B) 2.07 eV
B. Saturation current increases as the intensity
(C) 1.36 eV
of incident light increases.
(D) 18.6 eV
C. The maximum kinetic energy of a photo
34. Let K# and K $ be the maximum kinetic energies
electron depends on the intensity of the incident
of photoelectrons emitted when two
light.
monochromatic beams of wavelength λ# and λ$ ,
D. Photoelectric effect can be explained using
respectively are incident on a metallic surface.
wave theory of light
If λ# = 3λ$ , then Choose the correct answer from the options
;"
(A) K# > " given below.

(B) K# <
;" (A) B, C only
"
;"
(B) A, C, D only
(C) K# = " (C) B only
;!
(D) K $ = " (D) A, B, D only

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 6
37. What should be the order of arrangement of de- 43. Particle A of mass mA = $
moving along the x-
Broglie wavelength of electron (λ< ) , an α - axis with velocity v1 collides elastically with
particle ( λ= ) and proton ( λ> ) given that all another particle B at rest having mass mB = " .
6

have the same kinetic energy?

If both particles move along the x-axis after the
(A) λ< > λ> > λ= (B) λ< = λ> > λ=
collision, the change Δλ in de-Broglie
(C) λ< = λ> = λ= (D) λ< < λ> < λ=
wavelength of particle A , in terms of its de-
38. The ratio of the de-Broglie wavelengths of
Broglie wavelength (λ1 ) before collision is
proton and electron having same kinetic energy:
"
(Assume m> = m< × 1849) (A) Δλ = 2λ1 (B) Δλ = $ λ1
3
(A) 1: 43 (B) 1: 30 (C) Δλ = $ λ1 (D) Δλ = 4λ1
(C) 1: 62 (D) 2: 43
39. Proton (P) and electron (e) will have same de- 44. An electron (mass m ) with initial velocity vi⃗ =

Broglie wavelength when the ratio of their i⃗ = −E1 k̂. If λ1

v1 ı̂ + v1 ȷ̂ is in an electric field E

momentum is (assume, m> = 1849M< ): is initial de-Broglie wavelength of electron, its

(A) 1: 1 (B) 1: 1849 de- Broglie wavelength at time t is given by

5( 5(
(C) 1: 43 (D) 43: 1 (A) (B)
) " * " +" ) " * " +"
C#) "( " C$)
40. The de-Broglie wavelength of a particle having # ,( # " ," (

kinetic energy E is λ. How much extra energy 5( 5( √$

(C) (D)
) " * " +" ) " * " +"
must be given to this particle so that the de- C#)
"#" ,"
C#)
# " ,"
( (
Broglie wavelength reduces to 75% of the
45. The ratio for the speed of the electron in the 3rd
initial value?
?
orbit of He) to the speed of the electron in the
(A) E (B) 8 E
3rd orbit of hydrogen atom will be
#: #
(C) E (D) 8 E
8 (A) 1: 1 (B) 1: 2
41. The de Broglie wavelengths for an electron and
(C) 4: 1 (D) 2: 1
a photon are λ< and λ> respectively. For the
46. Find the ratio of energies of photons produced
same kinetic energy of electron and photon,
due to transition of an electron of hydrogen
which of the following presents the correct
atom from its (i) second permitted energy level
relation between the de Broglie wavelengths of
to the first level, and (ii) the highest permitted
two
energy level to the first permitted level.
(A) λ> ∝ λ$< (B) λ> ∝ λ<
(A) 3: 4 (B) 4: 3
#
(C) λ> ∝ gλ< (D) λ> ∝ <5 (C) 1: 4 (D) 4: 1
)

42. An electron moving with speed v and a photon 47. The time period of revolution of electron in its
moving with speed c , have same de-Broglie ground state orbit in a hydrogen atom is
wavelength. The ratio of kinetic energy of 1.6 × 10+#: s. The frequency of revolution of
electron to that of photon is the electron in its first excited state (in s +# ) is
@ ".
(A) ". (B) @ (A) 5.6 × 10#$ (B) 1.6 × 10#!
$. @
(C) @
(D) $. (C) 7.8 × 10#! (D) 6.2 × 10#3
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48. The energy levels of an hydrogen atom are 52. The graph which depicts the results of
shown below. The transition corresponding to Rutherford gold foil experiment with α-particles
emission of shortest wavelength is is θ : Scattering angle
Y : Number of scattered α-particles detected
(Plots are schematic and not to scale)

(A) D (B) A
(C) B (D) C
49. A small particle of mass m moves in such a way
# (A)
that its potential energy U = $ mω$ r $ where ω

is constant and r is the distance of the particle

from origin. Assuming Bohr's quantization of
momentum and circular orbit, the radius of nth
orbit will be proportional to
#
(A) √n (B) (
(C) n$ (D) n
(B)
50. A particle of mass m moves in a circular orbit in
#
a central potential field U(r) = $ kr $ . If Bohr's

quantization conditions are applied, radii of

possible orbitals and energy levels vary with
quantum number n as
#
(A) r( ∝ n$ , E( ∝ (" (B) r( ∝ √n, E( ∝ n
# (C)
(C) r( ∝ √n, E( ∝ ( (D) r( ∝ n, E( ∝ n
51. Choose the correct option from the following
options given below
(A) In the ground state of Rutherford's model
electrons are in stable equilibrium. While in
Thomson's model electrons always experience a
net-force.
(B) An atom has a nearly continuous mass
distribution in a Rutherford's model but has a (D)
highly non-uniform mass distribution in 53. gd# and gd$ are the impact parameters
Thomson's model.
corresponding to scattering angles 60∘ and 90∘
(C) A classical atom based on Rutherford's
model is doomed to collapse. respectively, when an α particle is approaching
(D) The positively charged part of the atom a gold nucleus. For d# = xd$ , the value of x
possesses most of the mass in Rutherford's
will be
model but not in Thomson's model.
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54. An unstable heavy nucleus at rest breaks into 58. Statement-1: Energy is released when heavy
two nuclei which move away with velocities in nuclei undergo fission or light nuclei undergo
the ratio of 8: 27. The ratio of the radii of the fusion. Statement-2: For heavy nuclei, binding
nuclei (assumed to be spherical) is energy per nucleon increases with increasing Z
(A) 3: 2 (B) 2: 3 while for light nuclei it decreases with
(C) 4: 9 (D) 8: 27
increasing Z.
55. Read the following statements.
(A) Statement-1 is true, statement-2 is false.
(A) Volume of the nucleus is directly
(B) Statement-1 is false, statement-2 is true.
proportional to the mass number.
(C) Statement-1 is true, statement-2 is true;
(B) Volume of the nucleus is independent of
statement-2 is a correct explanation for
mass number.
statement-1.
(C) Density of the nucleus is directly
(D) Statement-1 is true, statement-2 is true;
proportional to the mass number.
statement-2 is not a correct explanation for
(D) Density of the nucleus is directly
statement-1.
proportional to the cube root of the mass
59. Two deuterons undergo nuclear fusion to form a
number.
Helium nucleus. Energy released in this process
(E) Density of the nucleus is independent of the
is (given binding energy per nucleon for
mass number.
deuteron = 1.1MeV and for helium = 7.0MeV)
Choose the correct option from the following
(A) 25.8 MeV (B) 32.4 MeV
options
(C) 30.2 MeV (D) 23.6 MeV
(A) (A) and (D) only. (B) (A) and (E) only.
?
60. If the binding energy per nucleon in " Li and
(C) (B) and (E) only. (D) (A) and (C) only.
!
$ He nuclei are 5.60 MeV and 7.06 MeV
56. If M1 is the mass of an oxygen isotope
#?
respectively, then in the reaction:
9 O , M> and ME are the masses of a proton
p + ?" Li → 2 !$ He, energy of proton must be
and a neutron respectively, the nuclear binding
(A) 39.2 MeV (B) 28.24 MeV
energy of the isotope is (C) 17.28 MeV (D) 1.46 MeV
(A) (MF − 17ME )c $ 61. In a reactor, 2kg of 8$ U
$"3
of fuel is fully used
(B) (MG − 8M, )c $ up in 30 days, the energy released per fission is
(C) (MF − 8M, − 9ME )c $ 200 MeV . Given that the Avogadro number,
(D)MF c $ N = 6.023 × 10$: per kilo mole and 1eV =
57. Nucleus A is having mass number 220 and its 1.6 × 10+#8 J. The power output of the reactor
binding energy per nucleon is 5.6 MeV . It splits is close to
in two fragments ' B ' and ' C ' of mass numbers (A) 35 MW (B) 60 MW
105 and 115 . The binding energy of nucleons in (C) 125 MW (D) 54 MW
62. If the potential barrier across a p − n junction is
' B ' and ' C ' is 6.4 MeV per nucleon. The
0.6 V . Then the electric field intensity, in the
energy Q released per fission will be
depletion region having the width of 6 ×
(A) 0.8 MeV (B) 275 MeV
(C) 220 MeV (D) 176 MeV 10+: m, will be _______ × 103 N/C.
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63. Choose the correct statement about Zener diode: 66. For the following circuit given inputs A and B,
(A) It works as a voltage regulator in reverse choose the correct option for output 'Y'
bias and behaves like a simple pn junction diode
in forward bias.
(B) It works as a voltage regulator in both
forward and reverse bias.
(C) It works as a voltage regulator only in
forward bias.
(D) It works as a voltage regulator in forward
bias and behaves like a simple pn junction diode
in reverse bias.
64. Given below are two statements : one is labeled
as Assertion (A) and the other is labeled as
Reason (R)
Assertion (A): Photodiodes are preferably
operated in reverse bias condition for light (A)

intensity measurement.
Reason (R): The current in the forward bias is
more than the current in tiie reverse bias for ap-
(B)
n junction diodes.
In the light of the above statement, choose the
correct answer from the options given below:
(A) A is false but R is true (C)
(B) Both A and R are true but R is NOT the
correct explanation of A
(C) A is true but R is false
(D) Both A and Rare true and R is the correct (D)
explanation of A 67. For the forward biased diode characteristics
65. In a semiconductor, the number density of shown in the figure, the dynamic resistance at
intrinsic charge carriers at 27∘ C is 1.5 × 10#: / IH = 3 mA will be _________ Ω.
m" . If the semiconductor is doped with impurity
atom, the hole density increases to 4.5 × 10$$ /
m" . The electron density in the doped
semiconductor is ______ × 108 /m" .

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68. If each diode has a forward bias resistance of 70. For the circuit shown below, calculate the value
25Ω in the below circuit, of II .

(A) 0.15 A (B) 0.05 A

(C) 25 mA (D) 0.1 A
71. The zener diode has a VI = 30 V. The current
passing through the diode for the following
Which of the following options is correct?
2! 2"
circuit is _____ mA .
(A) 2 = 1 (B) 2 = 1
" -

2 2
(C) 2! = 2 (D) 2- = 1
" .

69. Identify the semiconductor devices whose

characteristics are given below, in the order (i),
(ii), (iii), (iv) 72. The truth table of the circuit shown is

(A) (B)

(A) Simple diode, Zener diode, Solar cell, Light

dependent resistance
(B) Zener diode, Simple diode, Light dependent (C) (D)
resistance, Solar cell 73. A non-isotropic solid metal cube has
(C) Solar cell, Light dependent resistance, Zener coefficients of linear expansion as 5 ×
diode, Simple diode 10+3 ∘ C +# along the x-axis and 5 × 10+: ∘ C +#
(D) Zener diode, Solar cell, Simple diode, Light along the y and the z-axis. If the coefficient of
dependent resistance. volume expansion of the solid is C × 10+: ∘ C +#
then the value of C is _______ .
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74. An external pressure P is applied on a cube at linear expansion of the metal is α, and its
∘
0 C so that it is equally compressed from all Young's modulus is Y, the force that one part of
sides. K is the bulk modulus of the material of the wheel applies on the other part is
the cube and α is its coefficient of linear
expansion. Suppose we want to bring the cube
to its original size by heating. The temperature
should be raised by
, ,
(A) "=; (B) =;
"=
(C) ,; (D) 3PKα

75. Two different wires having lengths L# and L$ (A) SYαΔT (B) πSYαΔT
and respective temperature coefficient of linear (C) 2SYαΔT (D) 2πSYαΔT
expansion α# and α$ are joined end-to-end. 78. M grams of steam at 100∘ C is mixed with 200 g
Then the effective temperature coefficient of of ice at its melting point in a thermally
linear expansion is insulated container. If it produces liquid water at
=! J! )=" J"
(A) J! )J"
(B) 2√α# α$ 40∘ C [heat of vaporization of water is 540cal/g
=! )=" = = J" J! and heat of fusion of ice is 80cal/g, the value of
(C) (D) 4 = !)=" "
$ ! " (J" )J! )
M is _____ .
76. A compressive force, F is applied at the two
79. An ice cube of dimensions 60 cm × 50 cm ×
ends of a long thin steel rod. It is heated,
20 cm is placed in an insulation box of wall
simultaneously, such that its temperature
thickness 1 cm . The box keeping the ice cube at
increases by ΔT. The net change in its length is
0∘ C of temperature is brought to a room of
zero. Let ℓ be the length of the rod, A its area of
temperature 40∘ C. The rate of melting of ice is
cross-section, Y its Young's modulus, and a its
approximately (Latent heat of fusion of ice is
coefficient of linear expansion. Then, F is equal
3.4 × 103 J kg +# and thermal conductivity of
to
insulated wall is 0.05 W m+# ∘ C +# )
AK
(A) ℓ$ YαΔT (B) =LM
(A) 61 × 10+" kg s +#
(C) AYαΔT (D) ℓAYαΔT (B) 61 × 10+3 kg s +#
77. A wooden wheel of radius R is made of two (C) 208 kg s +#
semicircular parts (see figure). The two parts are (D) 30 × 10+3 kg s +#
held together by a ring made of a metal strip of 80. Two identical metal wires of thermal
cross sectional area S and length L. L is slightly conductivities K# and K $ respectively are
less than 2πR. To fit the ring on the wheel, it is connected in series. The effective thermal
heated so that its temperature rises by ΔT and it conductivity of the combination is
just steps over the wheel. As it cools down to ;! );" $;! ;"
(A) $;! ;"
(B) ;
! );"
surrounding temperature, it presses the
; ; ;! );"
semicircular parts together. If the coefficient of (C) ; !);" (D) ;! ;"
! "

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81. A cylinder of radius R is surrounded by a 84. Thermodynamic process is shown below on a
cylindrical shell of inner radius R and outer P − V diagram for one mole of an ideal gas. If
radius 2R . The thermal conductivity of the V$ = 2V# then the ratio of temperature T$ /T# is
material of the inner cylinder is K# , and that of
the outer cylinder is K $ . Assuming no loss of
heat, the effective thermal conductivity of the
system for heat flowing along the length of the
cylinder is
$;! )";" ;! );"
(A) 3
(B) $
;! )";" # #
(C) K# + K $ (D) (A) $ (B)
! √$

82. The temperature θ at the junction of two (C) 2 (D) √2

insulating sheets, having thermal resistances R# 85. Which of the following is an equivalent cyclic
and R $ as well as top and bottom temperatures process corresponding to the thermodynamic
θ# and θ$ (as shown in figure) is given by cyclic given in the figure?

N! O! )N" O"
(A) O! )O"
N" O" +N! O!
(B) O" +O!
N! O" +N" O!
(C) where, 1 → 2 is adiabatic.
O" +O!

N! O" )N" O! (Graphs are schematic and are not to scale)

(D) O! )O"

83. A rod CD of thermal resistance 10.0 K W +# is

joined at the middle of an identical rod AB as
shown in figure. The ends A, B and D are
maintained at 200∘ C 100∘ C and 125∘ C
respectively. The heat current in CD is P watt.
The value of P is _____ . (A)

(B)
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 88. n moles of an ideal gas with constant volume
heat capacity CQ undergo an isobaric expansion
by certain volume. The ratio of the work done in
the process, to the heat supplied is
(O !(O
(A) R (B) R
/ +(O / +(O

(O !(O
(C) R (D) R
/ )(O / )(O

89. Following figure shows two processes A and B

(C) for a gas. If ΔQ A and ΔQ B are the amount of
heat absorbed by the system in two cases, and
ΔUA and ΔUB are changes in intemal energies,
respectively, then

(D)
86. Starting with the same initial conditions, an
ideal gas expands from volume V# to V$ in three
different ways. The work done by the gas is W#
if the process is purely isothermal, W$ , if the
(A) ΔQ A > ΔQ B- , ΔUA > ΔUB
process is purely adiabatic and W" if the process
(B) ΔQ A = ΔQ B , ΔUA = ΔUB
is purely isobaric. Then, choose the correct
(C) ΔQ A < ΔQ B , ΔUA < ΔUB
option.
(D) ΔQ A > ΔQ B , ΔUA = ΔUB
(A) W# < W$ < W" (B) W$ < W" < W#
90. A rigid diatomic ideal gas undergoes an
(C) W" < W# < W$ (D) W$ < W# < W"
adiabatic process at room temperature. The
87. A monoatomic ideal gas, initially at temperature
relation between temperature and volume for
T# is enclosed in a cylinder fitted with a
this process is TV 4 = constant, then x is
frictionless piston. The gas is allowed to expand $ "
(A) " (B) 3
adiabatically to a temperature 𝐓$ by releasing
$ 3
the piston suddenly. If l# and l$ are the lengths (C) 3 (D) "

of the gas column, before and after the 91. The pressure P# and density d# of diatomic gas
M ?
expansion respectively, then the value of M! will &γ = 3' changes suddenly to P$ (> P# ) and d$
"

be respectively during an adiabatic process. The

"
P - P temperature of the gas increases and becomes
(A) &P"' (B) P!
! " _______ times of its initial temperature.
"
P! - P &
(C) &P ' (D) P" (given &" = 32'
" ! !

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92. A sample of gas with γ = 1.5 is taken through 96. Sound travels in a mixture of two moles of
an adiabatic process in which the volume is helium and n moles of hydrogen. If rms speed
compressed from 1200 cm" to 300 cm" . If the of gas molecules in the mixture is √2 times the
initial pressure is 200 kPa . The absolute value speed of sound, then the value of n will be
of the workdone by the gas in the process = (A) 1 (B) 2
_____ J. (C) 3 (D) 4
93. A cylindrical container of volume 4.0 × 97. When an air bubble of radius r rises from the
10+" m" contains one mole of hydrogen and bottom to the surface of a lake, its radius
3S
two moles of carbon dioxide. Assume the becomes .Taking the atmospheric pressure to
!
temperature of the mixture is 400 K . The
be equal to 10 m height of water column, the
pressure of the mixture of gases is depth of the lake would approximately be
+# +#
[Take gas constant as 8.3 J mol K ] (ignore the surface tension and the effect of
(A) 24.9 × 10" Pa
(B) 249 × 10# Pa temperature)
(C) 24.9 × 103 Pa (A) 11.2 m (B) 10.5 m
(D) 24.9 Pa (C) 9.5 m (D) 8.7 m
94. The rms speed of oxygen molecule in a vessel at
98. A gas has n degrees of freedom. The ratio of
!
3 "
particular temperature is &1 + 4' v, where v is specific heat of gas at constant volume to the
specific heat of gas at constant pressure will be
the average speed of the molecule. The value of
( ()$
$$ (A) ()$ (B)
x will be: (take π = ?
) (
( (
(A) 27 (B) 8 (C) $()$ (D) (+$

(C) 28 (D) 4 99. Which statements are correct about degrees of

95. Given below are two statements: freedom?
Statement I: The average momentum of a (A) A molecule with n degrees of freedom has
molecule in a sample of an ideal gas depends on n$ different ways of storing energy.
temperature. (B) Each degree of freedom is associated with
#
Statement II: The rms speed of oxygen RT average energy per mole.
$
molecules in a gas is v. If the temperature is (C) A monatomic gas molecule has 1 rotational
doubled and the oxygen molecules dissociate degree of freedom where as diatomic molecule
into oxygen atoms, the rms speed will become has 2 rotational degrees of freedom.
2v. (D) CH! has a total of 6 degrees of freedom.
In the light of the above statements, choose the Choose the correct answer from the options
correct answer from the options given below. given below.
(A) Both statement I and statement II are true. (A) (B) and (C) only
(B) Both statement I and statement II are false. (B) (B) and (D) only
(C) Statement I is true but statement II is false. (C) (A) and (B) only
(D) Statement I is false but statement II is true. (D) (C) and (D) only
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100. The mean free path of molecules of a certain
gas at STP is 1500d , where d is the diameter of
the gas molecules. While maintaining the
standard pressure, the mean free path of the
molecules at 373 K is approximately:
(A) 750d (B) 1098d
(C) 2049d (D) 1500d

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 ANSWER KEY

1. 150 2. 98 3. 210 4. 400 5. C 6. B 7. D 8. C 9. B 10. 100

11. 225 12. B 13. A 14. B 15. A 16. A 17. C 18. A 19. 6.25 20. 50
21. B 22. C 23. B 24. A 25. C 26. C 27. 9 28. C 29. 30 30. A
31. D 32. A 33. B 34. B 35. B 36. B 37. A 38. A 39. A 40. B
41. A 42. D 43. D 44. C 45. D 46. A 47. C 48. A 49. A 50. B
51. C 52. A 53. 3 54. A 55. B 56. C 57. D 58. A 59. D 60. C
61. B 62. 1 63. A 64. B 65. 5 66. A 67. 25 68. C 69. A 70. C
71. 6 72. A 73. 60 74. A 75. A 76. C 77. C 78. 40 79. B 80. B
81. D 82. D 83. 2 84. D 85. B 86. D 87. A 88. C 89. D 90. C
91. 4 92. 480 93. C 94. C 95. D 96. B 97. C 98. A 99. B 100. C

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