IIT JAM PHYSICS - PH 2022 Question Paper | Sourav Sir's Classes
1. JAM 2022 PHYSICS - PH
PH 2/36
Section A: Q.1 โ Q.10 Carry ONE mark each.
Q.1 The equation ๐ง 2
+ ๐งฬ 2
= 4 in the complex plane (where ๐งฬ is the complex
conjugate of ๐ง) represents
(A) Ellipse
(B) Hyperbola
(C) Circle of radius 2
(D) Circle of radius 4
Q.2 A rocket (๐โฒ) moves at a speed
๐
2
m/s along the positive x-axis, where c is the
speed of light. When it crosses the origin, the clocks attached to the rocket and
the one with a stationary observer (๐) located at ๐ฅ = 0 are both set to zero. If ๐
observes an event at (๐ฅ, ๐ก), the same event occurs in the ๐โฒ frame at
(A) ๐ฅโฒ
=
2
โ3
(๐ฅ โ
๐๐ก
2
) and ๐กโฒ
=
2
โ3
(๐ก โ
๐ฅ
2๐
)
(B) ๐ฅโฒ
=
2
โ3
(๐ฅ +
๐๐ก
2
) and ๐กโฒ
=
2
โ3
(๐ก โ
๐ฅ
2๐
)
(C) ๐ฅโฒ
=
2
โ3
(๐ฅ โ
๐๐ก
2
) and ๐กโฒ
=
2
โ3
(๐ก +
๐ฅ
2๐
)
(D) ๐ฅโฒ
=
2
โ3
(๐ฅ +
๐๐ก
2
) and ๐กโฒ
=
2
โ3
(๐ก +
๐ฅ
2๐
)
2. JAM 2022 PHYSICS - PH
PH 3/36
Q.3 Consider a classical ideal gas of ๐ molecules in equilibrium at temperature ๐.
Each molecule has two energy levels, โ๐ and ๐. The mean energy of the gas is
(A) 0
(B) ๐๐ tanh (
๐
๐๐ต๐
)
(C) โ๐๐ tanh (
๐
๐๐ต๐
)
(D) ๐
2
Q.4 At a temperature ๐, let ๐ฝ and ๐ denote the volume expansivity and isothermal
compressibility of a gas, respectively. Then
๐ฝ
๐
is equal to
(A)
(
๐๐
๐๐
)
๐
(B)
(
๐๐
๐๐
)
๐
(C)
(
๐๐
๐๐
)
๐
(D)
(
๐๐
๐๐
)
๐
3. JAM 2022 PHYSICS - PH
PH 4/36
Q.5 The resultant of the binary subtraction 1110101 โ 0011110 is
(A) 1001111
(B) 1010111
(C) 1010011
(D) 1010001
Q.6 Consider a particle trapped in a three-dimensional potential well such that
๐(๐ฅ, ๐ฆ, ๐ง) = 0 for 0 โค ๐ฅ โค ๐, 0 โค ๐ฆ โค ๐, 0 โค ๐ง โค ๐ and ๐(๐ฅ, ๐ฆ, ๐ง) = โ
everywhere else. The degeneracy of the 5th
excited state is
(A) 1
(B) 3
(C) 6
(D) 9
4. JAM 2022 PHYSICS - PH
PH 5/36
Q.7 A particle of mass ๐ and angular momentum ๐ฟ moves in space where its
potential energy is
๐(๐) = ๐๐2
(๐ > 0) and ๐ is the radial coordinate.
If the particle moves in a circular orbit, then the radius of the orbit is
(A)
(
๐ฟ2
๐๐
)
1
4
(B)
(
๐ฟ2
2๐๐
)
1
4
(C)
(
2๐ฟ2
๐๐
)
1
4
(D)
(
4๐ฟ2
๐๐
)
1
4
5. JAM 2022 PHYSICS - PH
PH 6/36
Q.8 Consider a two-dimensional force field
๐น
โโโ (๐ฅ, ๐ฆ) = (5๐ฅ2
+ ๐๐ฆ2
+ ๐๐ฅ๐ฆ) ๐ฅ
ฬ + (4๐ฅ2
+ 4๐ฅ๐ฆ + ๐ฆ2) ๐ฆ.
ฬ
If the force field is conservative, then the values of ๐ and ๐ are
(A) ๐ = 2 and ๐ = 4
(B) ๐ = 2 and ๐ = 8
(C) ๐ = 4 and ๐ = 2
(D) ๐ = 8 and ๐ = 2
Q.9 Consider an electrostatic field ๐ธ
โ in a region of space. Identify the INCORRECT
statement.
(A) The work done in moving a charge in a closed path inside the region is zero
(B) The curl of ๐ธ
โ is zero
(C) The field can be expressed as the gradient of a scalar potential
(D) The potential difference between any two points in the region is always zero
6. JAM 2022 PHYSICS - PH
PH 7/36
Q.10 Which one of the following figures correctly depicts the intensity distribution for
Fraunhofer diffraction due to a single slit? Here, ๐ denotes the distance from the
centre of the central fringe and ๐ฐ denotes the intensity.
(A)
(B)
(C)
(D)
7. JAM 2022 PHYSICS - PH
PH 8/36
Section A: Q.11 โ Q.30 Carry TWO marks each.
Q.11 The function ๐(๐ฅ) = ๐sin ๐ฅ
is expanded as a Taylor series in ๐ฅ, around ๐ฅ = 0,
in the form ๐(๐ฅ) = โ ๐๐๐ฅ๐
โ
๐=0 . The value of ๐0 + ๐1 + ๐2 is
(A) 0
(B) 3
2
(C) 5
2
(D) 5
Q.12 Consider a unit circle ๐ถ in the ๐ฅ๐ฆ plane, centered at the origin. The value of the
integral โฎ[(sin ๐ฅ โ ๐ฆ)๐๐ฅ โ (sin ๐ฆ โ ๐ฅ)๐๐ฆ] over the circle ๐ถ, traversed
anticlockwise, is
(A) 0
(B) 2๐
(C) 3๐
(D) 4๐
8. JAM 2022 PHYSICS - PH
PH 9/36
Q.13 The current through a series ๐ ๐ฟ circuit, subjected to a constant emf โฐ, obeys
๐ฟ
๐๐
๐๐ก
+ ๐๐ = โฐ. Let ๐ฟ = 1 ๐๐ป, ๐ = 1 ๐โฆ and โ = 1 ๐. The initial condition
is ๐(0) = 0. At ๐ก = 1 ยต๐ , the current in mA is
(A) 1 โ 2๐โ2
(B) 1 โ 2๐โ1
(C) 1 โ ๐โ1
(D) 2 โ 2๐โ1
Q.14 An ideal gas in equilibrium at temperature ๐ expands isothermally to twice its
initial volume. If ฮ๐, ฮ๐ and ฮ๐น denote the changes in its entropy, internal energy
and Helmholtz free energy respectively, then
(A) ฮ๐ < 0, ฮ๐ > 0, ฮ๐น < 0
(B) ฮ๐ > 0, ฮ๐ = 0, ฮ๐น < 0
(C) ฮ๐ < 0, ฮ๐ = 0, ฮ๐น > 0
(D) ฮ๐ > 0, ฮ๐ > 0, ฮ๐น = 0
9. JAM 2022 PHYSICS - PH
PH 10/36
Q.15 In a dilute gas, the number of molecules with free path length โฅ ๐ฅ is given by
๐(๐ฅ) = ๐0๐โ๐ฅ/๐
, where ๐0 is the total number of molecules and ๐ is the mean
free path. The fraction of molecules with free path lengths between ๐ and 2๐ is
(A) 1
๐
(B) ๐
๐ โ 1
(C) ๐2
๐ โ 1
(D) ๐ โ 1
๐2
10. JAM 2022 PHYSICS - PH
PH 11/36
Q.16 Consider a quantum particle trapped in a one-dimensional potential well in the
region [โ๐ฟ/2 < ๐ฅ < ๐ฟ/2], with infinitely high barriers at ๐ฅ = โ๐ฟ/2 and
๐ฅ = ๐ฟ/2. The stationary wave function for the ground state is ๐(๐ฅ) =
โ
2
๐ฟ
cos (
๐๐ฅ
๐ฟ
). The uncertainties in momentum and position satisfy
(A) ฮ๐ =
๐โ
๐ฟ
and ฮ๐ฅ = 0
(B) ฮ๐ =
2๐โ
๐ฟ
and 0 < ฮ๐ฅ <
๐ฟ
2โ3
(C) ฮ๐ =
๐โ
๐ฟ
and ฮ๐ฅ >
๐ฟ
2โ3
(D) ฮ๐ = 0 and ฮ๐ฅ =
๐ฟ
2
Q.17 Consider a particle of mass ๐ moving in a plane with a constant radial speed ๐ฬ
and a constant angular speed ๐ฬ. The acceleration of the particle in (๐, ๐)
coordinates is
(A) 2๐๐ฬ2
๐ฬ โ ๐ฬ๐ฬ๐
ฬ
(B) โ ๐๐ฬ2
๐ฬ + 2๐ฬ๐ฬ๐
ฬ
(C) ๐ฬ๐ฬ + ๐๐ฬ๐
ฬ
(D) ๐ฬ๐๐ฬ + ๐๐ฬ๐
ฬ
11. JAM 2022 PHYSICS - PH
PH 12/36
Q.18 A planet of mass ๐ moves in an elliptical orbit. Its maximum and minimum
distances from the Sun are ๐ and ๐, respectively. Let ๐บ denote the universal
gravitational constant, and ๐ the mass of the Sun. Assuming ๐ >> ๐, the
angular momentum of the planet with respect to the center of the Sun is
(A)
๐โ
2๐บ๐๐ ๐
(๐ + ๐)
(B)
๐โ
๐บ๐๐ ๐
2(๐ + ๐)
(C)
๐โ
๐บ๐๐ ๐
(๐ + ๐)
(D)
2๐โ
2๐บ๐๐ ๐
(๐ + ๐)
12. JAM 2022 PHYSICS - PH
PH 13/36
Q.19 Consider a conical region of height โ and base radius ๐ with its vertex at the
origin. Let the outward normal to its base be along the positive ๐ง-axis, as shown
in the figure. A uniform magnetic field, ๐ต
โ = ๐ต0๐งฬ exists everywhere. Then the
magnetic flux through the base (ฮฆ๐) and that through the curved surface of the
cone (ฮฆ๐) are
(A) ฮฆ๐ = ๐ต0๐๐ 2
; ฮฆ๐ = 0
(B) ฮฆ๐ = โ
1
2
๐ต0๐๐ 2
; ฮฆ๐ =
1
2
๐ต0๐๐ 2
(C) ฮฆ๐ = 0 ; ฮฆ๐ = โ ๐ต0๐๐ 2
(D) ฮฆ๐ = ๐ต0๐๐ 2
; ฮฆ๐ = โ๐ต0๐๐ 2
13. JAM 2022 PHYSICS - PH
PH 14/36
Q.20 Consider a thin annular sheet, lying on the ๐ฅ๐ฆ-plane, with ๐ 1 and ๐ 2 as its inner
and outer radii, respectively. If the sheet carries a uniform surface-charge density
๐ and spins about the origin ๐ with a constant angular velocity
๐
โ
โ = ๐0๐งฬ then, the total current flow on the sheet is
(A) 2๐๐๐0(๐ 2
3
โ ๐ 1
3
)
3
(B) ๐๐0(๐ 2
3
โ ๐ 1
3
)
(C) ๐๐๐0(๐ 2
3
โ ๐ 1
3
)
3
(D) 2๐๐๐0(๐ 2 โ ๐ 1)3
3
14. JAM 2022 PHYSICS - PH
PH 15/36
Q.21 A radioactive nucleus has a decay constant ๐ and its radioactive daughter nucleus
has a decay constant 10๐. At time ๐ก = 0, ๐0 is the number of parent nuclei and
there are no daughter nuclei present. ๐1(๐ก) and ๐2(๐ก) are the number of parent
and daughter nuclei present at time ๐ก, respectively.
The ratio ๐2(๐ก)/๐1(๐ก) is
(A) 1
9
[1 โ ๐โ9๐๐ก
]
(B) 1
10
[1 โ ๐โ10๐๐ก
]
(C) [1 โ ๐โ10๐๐ก
]
(D) [1 โ ๐โ9๐๐ก
]
15. JAM 2022 PHYSICS - PH
PH 16/36
Q.22 A uniform magnetic field ๐ต
โ = ๐ต0๐ง,
ฬ where ๐ต0 > 0 exists as shown in the figure.
A charged particle of mass m and charge q (q > 0) is released at the origin, in the
yz-plane, with a velocity ๐ฃ
โโโ directed at an angle ๐ = 45โ
with respect to the
positive ๐ง-axis. Ignoring gravity, which one of the following is TRUE.
(A) The initial acceleration ๐ =
๐๐ฃ๐ต0
โ2 ๐
๐ฅ
ฬ
(B) The initial acceleration ๐ =
๐๐ฃ๐ต0
โ2 ๐
๐ฆ
ฬ
(C) The particle moves in a circular path
(D) The particle continues in a straight line with constant speed
16. JAM 2022 PHYSICS - PH
PH 17/36
Q.23 For an ideal intrinsic semiconductor, the Fermi energy at 0 ๐พ
(A) lies at the top of the valence band
(B) lies at the bottom of the conduction band
(C) lies at the center of the bandgap
(D) lies midway between center of the bandgap and bottom of the conduction band
17. JAM 2022 PHYSICS - PH
PH 18/36
Q.24 A circular loop of wire with radius ๐ is centered at the origin of the ๐ฅ๐ฆ-plane.
The magnetic field at a point within the loop is, ๐ต
โ (๐, ๐, ๐ง, ๐ก) = ๐๐3
๐ก3
๐งฬ, where ๐
is a positive constant of appropriate dimensions. Neglecting the effects of any
current induced in the loop, the magnitude of the induced emf in the loop at time
๐ก is
(A) 6๐๐๐ก2
๐ 5
5
(B) 5๐๐๐ก2
๐ 5
6
(C) 3๐๐๐ก2
๐ 5
2
(D) ๐๐๐ก2
๐ 5
2
18. JAM 2022 PHYSICS - PH
PH 19/36
Q.25 For the given circuit, ๐ = 125 โฆ, ๐ ๐ฟ = 470 โฆ, ๐
๐ง = 9 ๐, and ๐ผ๐ง
๐๐๐ฅ
= 65 mA.
The minimum and maximum values of the input voltage (๐๐
๐๐๐
and ๐๐
๐๐๐ฅ
) for
which the Zener diode will be in the โONโ state are
(A) ๐๐
๐๐๐
= 9.0 ๐ and ๐๐
๐๐๐ฅ
= 11.4 ๐
(B) ๐๐
๐๐๐
= 9.0 ๐ and ๐๐
๐๐๐ฅ
= 19.5 ๐
(C) ๐๐
๐๐๐
= 11.4 ๐ and ๐๐
๐๐๐ฅ
= 15.5 ๐
(D) ๐๐
๐๐๐
= 11.4 ๐ and ๐๐
๐๐๐ฅ
= 19.5 ๐
19. JAM 2022 PHYSICS - PH
PH 20/36
Q.26 A square laminar sheet with side ๐ and mass ๐, has mass per unit area given by
๐(๐ฅ) = ๐0 [1 โ
๐ฅ
๐
], (see figure). Moment of inertia of the sheet about ๐ฆ-axis is
(A) ๐๐2
2
(B) ๐๐2
4
(C) ๐๐2
6
(D) ๐๐2
12
20. JAM 2022 PHYSICS - PH
PH 21/36
Q.27 A particle is subjected to two simple harmonic motions along the ๐ฅ and ๐ฆ axes,
described by ๐ฅ(๐ก) = ๐ sin(2๐๐ก + ๐) and ๐ฆ(๐ก) = 2๐ sin(๐๐ก). The resultant
motion is given by
(A) ๐ฅ2
๐2
+
๐ฆ2
4๐2
= 1
(B) ๐ฅ2
+ ๐ฆ2
= 1
(C)
๐ฆ2
= ๐ฅ2
(1 โ
๐ฅ2
4๐2
)
(D)
๐ฅ2
= ๐ฆ2
(1 โ
๐ฆ2
4๐2
)
Q.28 For a certain thermodynamic system, the internal energy ๐ = ๐๐ and ๐ is
proportional to ๐2
. The entropy of the system is proportional to
(A) ๐๐
(B)
โ
๐
๐
(C)
โ
๐
๐
(D) โ๐๐
21. JAM 2022 PHYSICS - PH
PH 22/36
Q.29 The dispersion relation for certain type of waves is given by ๐ = โ๐2 + ๐2 ,
where ๐ is the wave vector and ๐ is a constant. Which one of the following
sketches represents ๐ฃ๐, the group velocity?
(A)
(B)
(C)
(D)
22. JAM 2022 PHYSICS - PH
PH 23/36
Q.30 Consider a binary number with ๐ digits, where ๐ is an even number. This binary
number has alternating 1โs and 0โs, with digit 1 in the highest place value. The
decimal equivalent of this binary number is
(A) 2๐
โ 1
(B) (2๐
โ 1)
3
(C) (2๐+1
โ 1)
3
(D) 2
3
(2๐
โ 1)
23. JAM 2022 PHYSICS - PH
PH 24/36
Section B: Q.31 โ Q.40 Carry TWO marks each.
Q.31 Consider the 2 ร 2 matrix ๐ = (
0 ๐
๐ ๐
), where ๐, ๐ > 0. Then,
(A) ๐ is a real symmetric matrix
(B) One of the eigenvalues of ๐ is greater than ๐
(C) One of the eigenvalues of ๐ is negative
(D) Product of eigenvalues of ๐ is ๐
Q.32 In the Compton scattering of electrons, by photons incident with wavelength ฮป,
(A) โ๐
๐
is independent of ฮป
(B) โ๐
๐
increases with decreasing ฮป
(C) there is no change in photonโs wavelength for all angles of deflection of the
photon
(D) โ๐
๐
increases with increasing angle of deflection of the photon
24. JAM 2022 PHYSICS - PH
PH 25/36
Q.33 The figure shows a section of the phase boundary separating the vapour (1) and
liquid (2) states of water in the P โ ๐ plane. Here, ๐ถ is the critical point. ๐1, ๐ฃ1
and ๐ 1 are the chemical potential, specific volume and specific entropy of the
vapour phase respectively, while ๐2, ๐ฃ2 and ๐ 2 respectively denote the same for
the liquid phase. Then
(A) ๐1 = ๐2 along AB
(B) ๐ฃ1 = ๐ฃ2 along AB
(C) ๐ 1 = ๐ 2 along AB
(D) ๐ฃ1 = ๐ฃ2 at the point C
25. JAM 2022 PHYSICS - PH
PH 26/36
Q.34 A particle is executing simple harmonic motion with time period ๐. Let ๐ฅ, ๐ฃ and
๐ denote the displacement, velocity and acceleration of the particle, respectively,
at time t. Then,
(A) ๐๐
๐ฅ
does not change with time
(B) (๐๐ + 2๐๐ฃ) does not change with time
(C) ๐ฅ and ๐ฃ are related by an equation of a straight line
(D) ๐ฃ and ๐ are related by an equation of an ellipse
Q.35 A linearly polarized light beam travels from origin to point A (1,0,0). At the point
A, the light is reflected by a mirror towards point B (1, โ1, 0). A second mirror
located at point B then reflects the light towards point C (1, โ1, 1). Let
๐
ฬ(๐ฅ, ๐ฆ, ๐ง) represent the direction of polarization of light at (๐ฅ, ๐ฆ, ๐ง).
(A) If ๐
ฬ(0, 0, 0) = ๐ฆ
ฬ, then ๐
ฬ(1, โ1, 1) = ๐ฅ
ฬ
(B) If ๐
ฬ(0, 0, 0) = ๐งฬ, then ๐
ฬ(1, โ1, 1) = ๐ฆ
ฬ
(C) If ๐
ฬ(0, 0, 0) = ๐ฆ
ฬ, then ๐
ฬ(1, โ1, 1) = ๐ฆ
ฬ
(D) If ๐
ฬ(0, 0, 0) = ๐งฬ, then ๐
ฬ(1, โ1, 1) = ๐ฅ
ฬ
26. JAM 2022 PHYSICS - PH
PH 27/36
Q.36 Let (๐, ๐) denote the polar coordinates of a particle moving in a plane. If ๐ฬ and ๐
ฬ
represent the corresponding unit vectors, then
(A) ๐๐ฬ
๐๐
= ๐
ฬ
(B) ๐๐ฬ
๐๐
= โ๐
ฬ
(C) ๐๐
ฬ
๐๐
= โ๐ฬ
(D) ๐๐
ฬ
๐๐
= ๐ฬ
Q.37 The electric field associated with an electromagnetic radiation is given by
๐ธ = ๐(1 + ๐๐๐ ๐1๐ก)๐๐๐ ๐2๐ก. Which of the following frequencies are present in
the field?
(A) ๐1
(B) ๐1 + ๐2
(C) |๐1 โ ๐2|
(D) ๐2
27. JAM 2022 PHYSICS - PH
PH 28/36
Q.38 A string of length ๐ฟ is stretched between two points ๐ฅ = 0 and ๐ฅ = ๐ฟ and the
endpoints are rigidly clamped. Which of the following can represent the
displacement of the string from the equilibrium position?
(A) ๐ฅ cos (
๐๐ฅ
๐ฟ
)
(B) ๐ฅ sin (
๐๐ฅ
๐ฟ
)
(C) ๐ฅ (
๐ฅ
๐ฟ
โ 1)
(D)
๐ฅ (
๐ฅ
๐ฟ
โ 1)
2
Q.39 The Boolean expression ๐ = ๐๐
ฬ ฬ ฬ ฬ R+ Q๐
ฬ + ๐
ฬ ๐๐ + ๐๐๐ simplifies to
(A) ๐
ฬ ๐ + ๐
(B) ๐๐ + ๐
ฬ
(C) ๐ + ๐
(D) ๐ + ๐
28. JAM 2022 PHYSICS - PH
PH 29/36
Q.40 For an ๐-type silicon, an extrinsic semiconductor, the natural logarithm of
normalized conductivity (๐) is plotted as a function of inverse temperature.
Temperature interval-I corresponds to the intrinsic regime, interval-II
corresponds to saturation regime and interval-III corresponds to the freeze-out
regime, respectively. Then
(A) the magnitude of the slope of the curve in the temperature interval-I is
proportional to the bandgap, ๐ธ๐
(B) the magnitude of the slope of the curve in the temperature interval-III is
proportional to the ionization energy of the donor, ๐ธ๐
(C) in the temperature interval-II, the carrier density in the conduction band is equal
to the density of donors
(D) in the temperature interval-III, all the donor levels are ionized
29. JAM 2022 PHYSICS - PH
PH 30/36
Section C: Q.41 โ Q.50 Carry ONE mark each.
Q.41 The integral โฌ(๐ฅ2
+ ๐ฆ2)๐๐ฅ๐๐ฆ over the area of a disk of radius 2 in the ๐ฅ๐ฆ
plane is ___๐.
Q.42 For the given operational amplifier circuit ๐ 1 = 120 โฆ, ๐ 2 = 1.5 kโฆ and
๐
๐ = 0.6 V, then the output current ๐ผ0 is ___________ mA.
30. JAM 2022 PHYSICS - PH
PH 31/36
Q.43 For an ideal gas, AB and CD are two isothermals at temperatures ๐1 and ๐2 (๐1 >
๐2), respectively. AD and BC represent two adiabatic paths as shown in figure.
Let ๐๐ด, ๐๐ต , ๐๐ถ and ๐๐ท be the volumes of the gas at A, B, C and D respectively. If
๐๐ถ
๐๐ต
= 2 , then
๐๐ท
๐๐ด
= __________.
Q.44 A satellite is revolving around the Earth in a closed orbit. The height of the
satellite above Earthโs surface at perigee and apogee are 2500 km and 4500 km,
respectively. Consider the radius of the Earth to be 6500 km. The eccentricity of
the satelliteโs orbit is ____ (Round off to 1 decimal place).
Q.45 Three masses ๐1 = 1, ๐2 = 2 and ๐3 = 3 are located on the ๐ฅ-axis such that
their center of mass is at ๐ฅ = 1 . Another mass ๐4 = 4 is placed at ๐ฅ0 and the
new center of mass is at ๐ฅ = 3. The value of ๐ฅ0 is _____.
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Q.46 A normal human eye can distinguish two objects separated by 0.35 ๐ when
viewed from a distance of 1.0 ๐๐. The angular resolution of eye is
________seconds (Round off to the nearest integer).
Q.47 A rod with a proper length of 3 m moves along ๐ฅ-axis, making an angle of 300
with respect to the ๐ฅ-axis. If its speed is
๐
2
m/s, where c is the speed of light, the
change in length due to Lorentz contraction is ____m (Round off to 2 decimal
places).
[Use ๐ = 3 ร 108
๐/๐ ]
Q.48 Consider the Bohr model of hydrogen atom. The speed of an electron in the
second orbit (๐ = 2) is ______ร 106
๐/๐ (Round off to 2 decimal places).
[Use โ = 6.63 ร 10โ34
๐ฝ๐ , ๐ = 1.6 ร 10โ19
๐ถ, ๐0 = 8.85 ร 10โ12
๐ถ2
๐2
/๐]
Q.49 Consider a unit circle ๐ถ in the ๐ฅ๐ฆ plane with center at the origin. The line integral
of the vector field, ๐น(๐ฅ, ๐ฆ, ๐ง) = โ2๐ฆ๐ฅ
ฬ โ 3๐ง๐ฆ
ฬ + ๐ฅ๐งฬ, taken anticlockwise over ๐ถ
is _____ ๐.
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Q.50 Consider a p-n junction at ๐ = 300 ๐พ. The saturation current density at reverse
bias is โ20 ๐๐ด/๐๐2
. For this device, a current density of magnitude
10 ๐๐ด/๐๐2
is realized with a forward bias voltage, ๐๐น. The same magnitude of
current density can also be realized with a reverse bias voltage, ๐๐ . The value of
|๐๐น/๐๐ | is _______ (Round off to 2 decimal places).
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Section C: Q.51 โ Q.60 Carry TWO marks each.
Q.51 Consider the second order ordinary differential equation, ๐ฆโฒโฒ
+ 4๐ฆโฒ
+ 5๐ฆ = 0. If
๐ฆ(0) = 0 and ๐ฆโฒ(0) = 1, then the value of ๐ฆ(๐/2) is __________ (Round off
to 3 decimal places).
Q.52 A box contains a mixture of two different ideal monoatomic gases, 1 and 2, in
equilibrium at temperature ๐. Both gases are present in equal proportions. The
atomic mass for gas 1 is ๐, while the same for gas 2 is 2๐ . If the rms speed of
a gas molecule selected at random is ๐ฃ๐๐๐ = ๐ฅโ
๐๐ต๐
๐
, then ๐ฅ is __________
(Round off to 2 decimal places).
Q.53 A hot body with constant heat capacity 800 ๐ฝ/๐พ at temperature 925 ๐พ is dropped
gently into a vessel containing 1 ๐๐ of water at temperature 300 ๐พ and the
combined system is allowed to reach equilibrium. The change in the total entropy
ฮ๐ is _________ ๐ฝ/๐พ (Round off to 1 decimal place).
[Take the specific heat capacity of water to be 4200 ๐ฝ/๐๐ ๐พ. Neglect any loss of
heat to the vessel and air and change in the volume of water.]
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Q.54 Consider an electron with mass ๐ and energy ๐ธ moving along the ๐ฅ-axis towards
a finite step potential of height ๐0 as shown in the figure. In region ๐ (๐ฅ < 0), the
momentum of the electron is ๐1 = โ2๐๐ธ. The reflection coefficient at the barrier
is given by ๐ = (
๐1โ๐2
๐1+๐2
)
2
, where ๐2 is the momentum in region ๐. If, in the limit
๐ธ โซ ๐0, ๐ โ
๐0
2
๐๐ธ2
, then the integer ๐ is ___.
Q.55 A current density for a fluid flow is given by,
๐ฝ (๐ฅ, ๐ฆ, ๐ง, ๐ก) =
8๐๐ก
(1+๐ฅ2+๐ฆ2+๐ง2)
๐ฅ
ฬ .
At time ๐ก = 0, the mass density ๐(๐ฅ, ๐ฆ, ๐ง, 0) = 1.
Using the equation of continuity, ๐(1,1,1,1) is found to be _______ (Round off
to 2 decimal places).
Q.56 The work done in moving a โ5 ๐๐ถ charge in an electric field
๐ธ
โ = (8๐ sin ๐ ๐ฬ + 4๐ cos ๐ ๐
ฬ) ๐/๐, from a point ๐ด(๐, ๐) = (10,
๐
6
) to a point
๐ต(๐, ๐) = (10,
๐
2
), is ______ m๐ฝ.
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Q.57 A pipe of 1 ๐ length is closed at one end. The air column in the pipe resonates at
its fundamental frequency of 400 ๐ป๐ง. The number of nodes in the sound wave
formed in the pipe is _____.
[Speed of sound = 320 ๐/๐ ]
Q.58 The critical angle of a crystal is 30โ
. Its Brewster angle is ______ degrees (Round
off to the nearest integer).
Q.59 In an LCR series circuit, a non-inductive resistor of 150 โฆ, a coil of 0.2 ๐ป
inductance and negligible resistance, and a 30 ยต๐น capacitor are connected across
an ac power source of 220 ๐, 50 Hz. The power loss across the resistor is ____W
(Round off to 2 decimal places).
Q.60 A charge q is uniformly distributed over the volume of a dielectric sphere of
radius a. If the dielectric constant ๐๐ = 2, then the ratio of the electrostatic energy
stored inside the sphere to that stored outside is_______ (Round off to 1 decimal
place).
END OF THE QUESTION PAPER