Grass-G/jee-main-questions huggingface dataset:
Subject: Physics — Gravitation — Energy of satellite
Difficulty: Moderate

Question: A Comet is observed as it passes our solar system. Its closest
approach to the sun is r = 6.67 × 10^10 m,at that time it has velocity
v = 2 × 10^6 m/s. If G = 6.67 × 10^-11 N m^-2 kg^-2 and mass of the
sun is 2 × 10^30kg. Then which of the following is true in respect with
this comet?

1) The comet will return after 20 years
2) The comet will never return to the solar system
3) The comets
path is circular
4) The comets total energy is negative

Correct option: 2

Solution:
Total energy of the comet = U+K
$= \frac{- GM_{s}m}{r} + \frac{1}{2}m\left( 2 \times 10^{6} \right)^{2}$ where m mass
of the Comet 
$= m\left\lbrack \left( - 2 \times 10^{9} \right) + \left( 2 \times 10^{12} \right) \right\rbrack$
= 1998 m 10^9 = +ve
[IMAGE] Comets will never returns to the solar system
because total energy is +ve.
Subject: Physics —  — 

Question: A small block of mass m is released from position A, inside the
frictionless circular groove of radius 2 m on a fixed inclined plane as
shown in figure. The contact force between the block and inclined plane
at point B is[IMAGE]. Find x


Answer: 7

Solution:
[IMAGE] TOPIC: Newton's law of motion
SUB TOPIC: Circular motion
LEVEL: Moderate
Subject: Physics — Rigid Body Dynamics — Conservation of mechanical energy
Difficulty: Moderate

Question: In the below figure, a bob a mass m is tied by a massless string
whose other end portion is wound on a fly wheel (disc) of radius r and
mass m. When released from rest the bob starts falling vertically. When
it has covered a distance of h, the angular speed of the wheel will be


Correct option: 4

Solution:
[IMAGE] (no slipping)
Subject: Physics —  — 
Difficulty: Moderate

Question: A hinged construction consists of three rhombus with the ratio
of sides (5: 3: 2). Vertex A3 moves in the horizontal direction with
velocity V. Velocity of A2 will be

1) 2.5 V
2) 1.5V
4) 0.8V

Correct option: 4

Solution:
$u = \frac{dy}{dt} = - 16\sin\theta\frac{d\theta}{dt}$
$\Rightarrow u = \frac{4}{5}v = 0.8v$
TOPIC: Newton's first law
SUB TOPIC: Constraint motion
Subject: Physics — Wave Optics — Superposition of waves
Difficulty: Easy

Question: Three harmonic waves having equal frequency v and same intensity
$I_{0}$, have phase angles 0, $\frac{\pi}{4}$ and$- \frac{\pi}{4}$
respectively. When they are superimposed the intensity of the resultant
wave is close to

1) $5.8\ I_{0}$
2) ${3\ I}_{0}$
3) $I_{0}$
4) $0.2\ I_{0}$

Correct option: 1

Solution:
$I_{res} = (\sqrt{2} + 1)^{2}I_{0}$
$= (3 + 2\sqrt{2})I_{0} = 5.8I_{0}$
Subject: Physics — Newton's Laws of Motion — Relative motion between blocks
Difficulty: Moderate

Question: If acceleration of block B w.r.t. A is $2m/s^{2}$just after the
system is released from rest, then mass(in kg) of block C will be 5m.
Find m. [pulley and string both are massless, take


Answer: 9

Solution:
[IMAGE] Given Condition is possible if$a_{B} - a_{A} = 2m/s^{2}$
And $a_{A} = \frac{30}{5} = 6m/s^{2} \Rightarrow a_{a} = 8m/s^{2}$B & C
will move with same acc.$a_{B}$
$\Rightarrow mg - 50 = (m + 5)a_{B}$
$10m - 50 = 8m + 40$
$\Rightarrow m = 45kg$
Subject: Physics — Electrostatics — Electric field by uniformly charged sphere
Difficulty: Tough

Question: Consider a sphere of radius R which carries a uniform charge
density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it,
as shown, the
ratio$\left| \frac{{\overset{\rightarrow}{E}}_{A}}{{\overset{\rightarrow}{E}}_{B}} \right|$
of magnitude of electric field of magnitude of electric field
${\overset{\rightarrow}{E}}_{A}$and ${\overset{\rightarrow}{E}}_{B}$,
respectively, atpoints A and B due to the remaining portion is:,d R f= xksys esa leku /uRo $\rho$ forfjr gSA;fn bl
xksys $\frac{R}{2}$ f= xksykdkVDj fp=kuqlkj fudky rks
cps gq, Hkkx j.k fcUnqvksa A rFkk B ijfo|qr {ks=k ¼Ø ½

1) $\frac{18}{34}$
2) $\frac{21}{34}$
3) $\frac{17}{54}$
4) $\frac{18}{54}$

Correct option: 1

Solution:
For a solid sphere Bksl xksys ds fy, e
$E = \frac{\rho r}{3\varepsilon_{0}}$
$E_{A} = \frac{- \rho R}{2\left( 3\varepsilon_{0} \right)}$
$\left| E_{A} \right| = \frac{\rho R}{6\varepsilon_{0}}$
Electric field at point ¼fcUnq B ijkfo|qr {ks=k dh rhozrk½ B = E_B =
E_1A + E_2A
E_1A= Electric Field Due to solid sphere of radius R at
point $B = \frac{\rho R}{3\varepsilon_{0}}$
E_1A= R f= Bkslxksys j.k fcUnqBijfo|qr {ks=k dh
rhozrk$= \frac{\rho R}{3\varepsilon_{0}}$
E_2A = Electric Field Due to solid sphere of radius R/2 (which having
charge density -$\rho$)
E_2A = R/2 f= Bksl xksys ¼ftl ?kuRo- $\rho$ gS½
Subject: Physics — Wave — Superposition of waves
Difficulty: Moderate

Question: Three simple harmonic motions in the same direction, having the
same amplitude A and same time period, are superimposed. If each differs
in phase from the next by 45^0, then

1) the resultant amplitude is 2[IMAGE]
2) the phase of the resultant motion relative to the first is 90^o
3) the energy associated with the resulting motion is
[IMAGE] times the energy associated with any single
motion
4) the resulting motion is not simple harmonic.

Correct option: 3

Solution:
Subject: Physics — Magnetism — Hysteresis loop
Difficulty: Moderate

Question: The figure gives experimentally measured B vs. H variation in a
ferromagnetic material. The retentivity, coercivity and saturation,
respectively, of the material are

1) 1.0 T, 50 A/m and 1.5 T
2) 150 A/m, 1.0 T and 1.5 T
3) 1.5 T, 50 A/m and 1.0 T
4) 1.5T, 50 A/m and 1.0 T

Correct option: 1

Solution:
[IMAGE] x = retentivity
y = coercivity
z = saturation magnetization
Subject: Physics — Sound wave — Organ pipe
Difficulty: Moderate

Question: The second overtone of an open organ pipe A and that of a closed
pipe B have the same frequency at a given temperature. It follows that
the ratio of the

1) length of A and B is 4: 3
2) fundamental frequencies of A and B is 5: 6
3) length of B to length of A is 5: 6
4) frequencies of first overtone of A and B is 10: 9

Correct option: 4

Solution:
Subject: Physics —  — 
Difficulty: Tough

Question: Block M slide down on frictionless inclined plane as shown. Find
frictional force acting on block m while it is at rest with respect to
the block M. (m = 2kg, M = 5kg, g = 10 m/sec2)

1) 8.5 N
2) 9.6 N
3) 12.8 N
4) 16.5 N
 M m 
 M (m = 2kg, M =
5kg, g = 10 m/sec2)

Correct option: 2

Solution:
a = g sin 37°
f = m × a × cos 37°
TOPIC: NLM
SUB TOPIC: NEWTON'S SECOND LAW
Subject: Physics — Rigid Body Dynamics — Torque
Difficulty: Moderate

Question: A thin uniform rod of mass is hinged at
one end. This rod is maintained in horizontal position by colliding very
tiny balls each of mass m/10 completely elastically 10 times per sec
striking at the opposite end as shown in figure. Find the speed of the


Correct option: 2

Solution:
[IMAGE] Taking torque about hinge
Subject: Physics — Ray Optics — Apparent depth
Difficulty: Moderate

Question: A concave mirror of radius of curvature 40 cm is filled with
water (n=4/3) upto a height of 12 cm. A point object O is kept on the
principal axis of the mirror at height 13.5 cm from the water surface.
The final image formed after refraction at water surface, reflection at
mirror and again refraction at water surface in succession is situated
at.

1) 36 cm above the water surface
2) 24 cm above the water surface
3) 20 cm above the water surface
4) 12 cm above the water surface

Correct option: 1

Solution:
Refraction -1: Apparent depth from water surface
$d^{'} = 13.5 \times \frac{4}{3} = 18cm$
Reflection from concave mirror.
$\frac{1}{v} + \frac{1}{( - 30)} = \frac{1}{- 20}$
$v = - 60cm$
Image is formed 48 cm above water surface
Refraction-2: $d^{''} = \frac{48}{4/3} = 36cm$ above water surface
Subject: Physics — Magnetic effect of current — Magnetic field due to current carrying conductor
Difficulty: Moderate

Question: The magnitude of magnetic field at O (centre of the circular
part) of the current carrying coil as shownis

1) $\frac{\mu_{0}i}{4\pi}\left( \frac{3\pi}{a} + \frac{\sqrt{2}}{b} \right)$
2) $\frac{\mu_{0}i}{2\pi}\left( \frac{3\pi}{2a} + \frac{\sqrt{2}}{b} \right)$
3) $\frac{\mu_{0}i}{2\pi}\left( \frac{\pi}{3a} + \frac{3}{\sqrt{2}b} \right)$
4) $\frac{\mu_{0}i}{4\pi}\left( \frac{3\pi}{2a} + \frac{\sqrt{2}}{b} \right)$

Correct option: 4

Solution:
Magnetic field due to circular
segment$= \frac{3}{4} \cdot \frac{\mu_{0}i}{2a}$
 Due to one straight wire
segment $= \frac{\mu_{0}i}{4\pi b}\left( sin45^{\circ} + sin0^{\circ} \right) = \frac{\mu_{0}i}{4\sqrt{2}\pi b}$
Net field
$= \frac{3\mu_{0}i}{8a} + 2 \times \frac{\mu_{0}i}{4\sqrt{2}\pi b} = \frac{\mu_{0}i}{4\pi}\left( \frac{3\pi}{2a} + \frac{\sqrt{2}}{b} \right)$.
Subject: Physics — Dual Nature of Matter — Einstein's photoelectric equation
Difficulty: Moderate

Question: When photon of energy
[IMAGE] strikes the surface of a metal A, the ejected photoelectrons have
maximum kinetic energy Ta eV and de-Broglie
wavelength[IMAGE]. The maximum kinetic energy of photoelectrons liberated
from another metal B by photon of energy
[IMAGE] is [IMAGE] If the de-Broglie wavelength of these
photoelectrons[IMAGE], then the work function of metal B is

1) 2 eV
2) 3 eV
3) 1.5 eV
4) 4 eV

Correct option: 4

Solution:
Relation between De-Broglie wavelength and K. E. is
Subject: Physics — Wave on a string — variable linear mass density
Difficulty: Moderate

Question: A non−uniform string of mass 45 kg and length 1.5 m has a
variable linear mass density given by μ = kx, where x is the distance
from one end of the string and k is a constant. Tension in the string is
15 N which is uniform. If the time (in second) required for a pulse
generated at one end of the string to travel to the other end is x, then
find the value of 2x.


Answer: 4

Solution:
Subject: Physics —  — 
Difficulty: Moderate

Question: t = 0 
-10 m

1) 1s
3) 5s
4) 2s

Correct option: 3

Solution:
a = - 3t + 5
[IMAGE] ∆x = [IMAGE] + [IMAGE] ∆x = 0
⇒[IMAGE] t = 0s & t = 5s
TOPIC:KINEMATIC
SUB TOPIC: ACCERATION
Subject: Physics — EMI — Induced emf
Difficulty: Moderate

Question: At time t = 0 magnetic field of 1000 Gauss is passing
perpendicularly through the area defined by theclosed loop shown in the
figure. If the magnetic field reduces linearly to 500 Gauss, in the next
5 s, theninduced EMF in $\mu V$in the loop is 8n. Find n



Solution:
$\varepsilon = \left| - \frac{d\varphi}{dt} \right| = \left| - \frac{AdB}{dt} \right|$
$=.(16 \times 4 - 4 \times 2)\frac{(1000 - 500)}{5} \times 10^{- 4} \times 10^{- 4}$
$= 56 \times \frac{500}{5} \times 10^{- 8} = 56 \times 10^{- 6}V$
Subject: Physics — Sound — Doppler effect
Difficulty: Moderate

Question: A train is moving with a constant speed 15 m/s along a circular
track. The length of the train makes an angle 90º at the centre. A siren
in its engine is emitting a sound of frequency 1.5kHz. Find the apparent
frequency of sound as heard by a passenger at the rear end of the train.

1) 2.5kHz
2) 1.5kHz
3) 3.5kHz
4) 4.5kHz

Correct option: 2

Solution:
Subject: Physics — Current Electricity — KVL
Difficulty: Easy

Question: The current I_1 (in A) flowing through 1$\Omega$ resistor in
the following circuit is

1) 0.2
2) 0.4
3) 0.5
4) 0.25

Correct option: 1

Solution:
$i = \frac{I}{2} = 0.2A$
Subject: Physics — Thermodynamics — P-V diagram
Difficulty: Moderate

Question: One mole of an ideal gas at pressure P_0, volume V_0 and
temperature T_0 is expanded isothermally to twice its volume and then
compressed at constant pressure to (V_0/2) and the gas is brought back
to original state by a process in which P ∝ V (Pressure is directly
proportional to volume). The correct representation of process is
[IMAGE] rFkk rkieku nqxqus:i ls çlkfjr dh tkrh gSrFkk fQj lenkoh çØe rd laihfMr dh tkrh gS rFkk xSl dks okil çkjfEHkd
voLFkk esa,sls çØe lsykrs gS ftl ¼ lekuqikrh gksrk gS½ gS rks mijksä çØe


Correct option: 3

Solution:
Process AB is isothermal expansion BC is isobaric compression
and in process CA
izfØ;k AB lerkih izlkj gS rFkk BC lenkch laihMu
Subject: Physics — Rigid Body Dynamics — Conservation of angular momentum

Question: In the figure (i) a disc of mass M(kg) and radius R(m) is
rotating smoothly about a fixed vertical axis AB with angular speed 26
rad/s. A rod CD of length [IMAGE] and mass M(kg) is
hinged at one end at point on the disc. The rod remains in vertical
position and rotates along with the disc about axis AB. At some moment
the rod CD gets a very small impulse at point due to air due to
which the rod falls on the disc along one radius and sticks to the disc
as shown in figure (ii). Now find the angular velocity of the disc in

1) $\frac{11}{13}\omega$
2) $\frac{15}{13}\omega$
3) $\frac{17}{13}\omega$
4) $\frac{18}{13}\omega$

Correct option: 4

Solution:
MI of the system when rod is vertical
[IMAGE] MI of system when rod is horizontal
[IMAGE] From conservation of angular momentum of system about axis AB is
Subject: Physics — Work Power & Energy — Conservation of mechanical energy
Difficulty: Moderate

Question: Two children are playing a game in which they try to hit a small
box using a spring-loaded marble gun, which is fixed rigidly to a table
is a height h above the top of the box. The spring has a spring constant
k and the edge of the box is some unknown horizontal distance
$\mathcal{l}$ away from the table. The first child compresses the spring
a distance x and finds that the marble falls short of its target by a
horizontal distance y. The second child compresses the spring by an
extra amount $\Delta x$ so that marble lands in the box. The value of
$\Delta x$is $y\sqrt{\frac{mg}{Nhk}}$ (Where N is integer) then find the
value of N.

1) 5
2) 3
3) 2
4) 4

Correct option: 3

Solution:
time taken or time of flight is same for both projectiles.
i.e. $t = \sqrt{\frac{2h}{g}}$
using energy conservation:
$\Rightarrow \frac{1}{2}{kx}^{2} = \frac{1}{2}{mv}^{2}$.......(1)
$\Rightarrow \frac{1}{2}k(x + \Delta x)^{2} = \frac{1}{2}mv^{'2}$.......(2)
$\mathcal{l -}y = vt$.......(3)
$\mathcal{l =}v't$.......(4)
On solving we get
$\Delta x = y\sqrt{\frac{mg}{2hk}}$
N = 2
Subject: Physics — Ray Optics — Magnification and position of object graph
Difficulty: Easy

Question: An object is gradually moving away from the focal point of a
concave mirror along the axis of the mirror. The graphical
representation of the magnitude of linear magnification (m) versus
distance of the object from the mirror (x) is correctly qiven by (Graphs
are drawn schematically and are not to scale)


Correct option: 1

Solution:
At focus, magnification is $\infty$
Subject: Physics — Rigid Body Dynamics — Moment of inertia
Difficulty: Moderate

Question: Find momentum of inertia about an axis passing through COM of
system and it is perpendicular to theplane of 3 rods.

1) ${mL}^{2}\left( \frac{7}{3} \right)$
2) ${mL}^{2}\left( \frac{2}{3} \right)$
3) ${mL}^{2}\left( \frac{5}{2} \right)$
4) ${mL}^{2}\left( \frac{1}{2} \right)$

Correct option: 1

Solution:
$\because I_{2} = I_{3}$
$= \frac{(2m)(2L)^{2}}{12} + 2\left\lbrack \frac{{ML}^{2}}{12} + {Md}^{2} \right\rbrack$
$= {mL}^{2}\left( \frac{2 \times 2 \times 2}{12} \right) + 2\left( \frac{1}{12} + \frac{3}{4} \right){mL}^{2}$
${mL}^{2}\left( \frac{2}{3} \right) + 2\left( \frac{1 + 9}{12} \right){mL}^{2}$
${mL}^{2}\left( \frac{2}{3} \right) + 2\left( \frac{1 + 9}{12} \right){mL}^{2}$
$= {mL}^{2}\lbrack\left( \frac{2}{3} \right) + \frac{20}{12}\rbrack$
$I_{net\ } = {mL}^{2}\left( \frac{7}{3} \right)$
Subject: Physics —  — 
Difficulty: Moderate

Question: A man and car both starts moving from rest simultaneously along
the same straight line in such a way that acceleration of A and B are
given by
A will catch B in time T. Then T is


Answer: 6

Solution:
Let study the motion of A with respect to B
[IMAGE] a = t
[IMAGE] TOPIC:Rectilinear motion
SUB TOPIC:Non-Uniform acceleration
Subject: Physics — Work Power & Energy — Work done by variable force
Difficulty: Tough

Question: A force F= 4t acts on a particle of mass 1kg. If the particle
starts from rest the work done by the force during the first 2 second
will be 8n J, find n.

1) 4
2) 6
3) 5
4) 3

Correct option: 1

Solution:
$\frac{dv}{dt} = 4t$ $\int_{0}^{v}{dv} = 4\int_{0}^{t}{t\ dt}$
$V = 2t^{2}$
$ds = 2t^{2}dt$
$W = \int_{}^{}{Fds\ cos0^{\circ}}$
$= \int_{0}^{2}\mspace{2mu} 4t \cdot 2t^{2}dt$
$= 8\left\lbrack \frac{t^{4}}{4} \right\rbrack_{0}^{2}$
Subject: Physics — Rigid Body Dynamics — Angular momentum in pure rotation
Difficulty: Easy

Question: A particle performs uniform circular motion with an angular
momentum L. If thefrequency of particle's motion is doubled and its
kinetic energy is halved, the angularmomentum becomes

1) 2L
2) 4L

Correct option: 4

Solution:
$L = I\omega$
$\omega^{'} = 2\omega$
$\frac{1}{2}\left( \frac{1}{2}I\omega^{2} \right) = \frac{1}{2}I^{'}\omega^{'2}$
$\frac{I\omega^{2}}{2} = I^{'}4\omega^{2}$
$I^{'} = \left( \frac{I}{8} \right) \Rightarrow L^{'} = I^{'}\omega^{'} = \frac{I}{8}2\omega = \frac{I\omega}{4} = (L/4)$
Subject: Physics —  — 
Difficulty: Moderate

Question: A river is flowing with velocity 5 km/hr relative to the ground
as shown in the figure. A boat starts from A and reaches the other bank
by covering shortest possible distance. Velocity of boat in still water
is 3 km/hr. The distance (in m) boat covers is s. The value


Answer: 1

Solution:
For drift to be minimum
[IMAGE] time taken by boat to cross the river = t
 So, distance covered[IMAGE] TOPIC:Motion in a plane
SUB TOPIC:Relative motion
Subject: Physics — Thermodynamics — Adiabatic process
Difficulty: Moderate

Question: A monoatomic ideal gas follows the process:
The molar specific heat for this process is: ( R = gas constant)
bl çØe ds fy, eksyj

4) R

Correct option: 2

Solution:
[IMAGE] For polytropic process, cgqijek.koh; izØe
Subject: Physics —  — 
Difficulty: Easy

Question: The net power P of all the forces acting on a particle versus time
curve is shown. Work done upon the particle from A to B

1) Increases
2) Decreases
3) First increases then decreases
4) First decreases then increases
 (P) A B

Correct option: 1

Solution:
Area under the graph || [IMAGE] Area under graph increases, hence work done upon the particle from A to
B increases.
TOPIC: WPE
SUB TOPIC: POWER
Subject: Physics — Mechanical properties of liquid — Surface tension
Difficulty: Moderate

Question: If two soap bubbles of different radii are connected by a tube:;fn fofHkUu f= nks lkcqu ds cqycqyksa

1) air flows from the bigger bubble to the smaller bubble till the
sizes become
2) air flows from bigger bubble to the smaller bubble till the sizes
are intercha
3) air flows from the smaller bubble to the bigger bubble
4) there is no flow of air

Correct option: 3

Solution:
The excess pressure inside the soap bubble in inversely
proportional to radius of soap bubble i.e. $P \propto 1/r$, r being the
radius of bubble. It follows that pressure inside a smaller bubble is
greater than that inside a bigger bubble. Thus, if these two bubbles are
connected by a tube, air will flow from smaller bubble to bigger bubble
and the bigger bubble grows at the expense of the smaller one.
cqycqys cqycqys dh f= Øekuqikrh gksrk gSA
$P \propto 1/r$] tgk¡ rcqycqys dh f= SA vr NksVs cqycqys esa cM+s
cqycqys dh rqyuk gskxk;fn nksuksa cqycqyksa dks
ufy tksM+k rks gok NksVs cqycqys
Subject: Physics — Rigid Body Dynamics — Moment of inertia
Difficulty: Moderate

Question: A thin walled hollow cylinder is closed from both the ends. The
mass of the curved part is m and the mass of each circular part is also
m. The radius of the cylinder is R and its length is 2R. What will be
the moment of inertia of this hollow cylinder about the axis,
perpendicular to its length and passing through its centre of mass?


Correct option: 1

Solution:
First find I of the hollow tube
[IMAGE] Where [IMAGE] So [IMAGE] Now moment of inertias of each circular plate about that axis.
Subject: Physics — Thermodynamics — 
Difficulty: Moderate

Question: Figure below shows two paths that may be taken by a gas to go
from a state A to a state C.
[IMAGE] In process AB, 400J of heat is added to the system and in process BC,
100 J of heat is added to the system. The heat absorbed by the system
in the process AC (in J) is 230n. Find n.;gk¡ nks iFk ftu 
A ls voLFkk B rd ys tk;k tk ldrk gSA
 s AB] çØe esa 400 J rFkk çØe BC esa 100 J nh tkrh gSA
rks] çØe AC (in J) 230 n gSA rks n
Kkr dhft,A


Answer: 2

Solution:
For a complete cycle
iw.kZ pfØ; çØe ds fy,
Q_cycle = W_cycle
$+ 400 + 100 + Q_{C \rightarrow A} = \frac{1}{2}\left( 2 \times 10^{- 3} \right)\left( 4 \times 10^{4} \right)$
⇒ Q~C→ A~ = - 460 J
⇒ Q_A→C = + 460 J
Subject: Physics — Sound wave — Doppler effect
Difficulty: Moderate

Question: An observer moves towards a stationary source of sound with speed
one - fifth of speed of sound, then

1) apparant wavelength increases
2) apparant wavelength decreases
3) apparant frequency increases by 20
4) apparant frequency decreases by 25

Correct option: 3

Solution:
Subject: Physics — Atomic Physics — Radiation emitted by electron
Difficulty: Moderate

Question: The energy required to ionize a hydrogen like ion in its ground
state is 9Rydbergs. What is the wavelength of the radiation emitted when
the electron in this ion jumps from the second excited state to the
ground state

1) 24.2 nm
2) 6.8 nm
3) 35.8 nm
4) 11.4 nm

Correct option: 4

Solution:
Subject: Physics — Dual Nature of Matter — De brogle wavelength
Difficulty: Moderate

Question: An electron (of mass m) and a photon have the same energy E in
the range of a few[IMAGE]. The ratio of the de-Broglie
wavelength associated with the electron and the wavelength of the photon
is (c = speed of light in vacuum)


Correct option: 4

Solution:
Subject: Physics — Rigid Body Dynamics — Rotation about a fixed axis
Difficulty: Easy

Question: A mass supported by a massless string wound around a
uniform hollow cylinder of mass m and radius R. If the string does not
slip on the cylinder, with what acceleration will the mass fall on
release?

1) $\frac{3g}{3}$
2) $\frac{g}{2}$
3) $\frac{5g}{6}$
4) g

Correct option: 2

Solution:
[IMAGE] mg - T = ma....(1)
T.R = mR^2$\frac{a}{R}$....(2)
$\frac{g}{2} = a$
Subject: Physics — Electronic device — Boolean relation
Difficulty: Moderate

Question: Boolean relation at the output stage-Y for the following circuit
is


Correct option: 2

Solution:
First part of figure shown is OR gate and
Second part of figure shown is NOT gate
Subject: Physics — Mechanical properties of matter — Elongation in wire
Difficulty: Moderate

Question: The following four wires are made of the same material. Which of
these will have the largest extension when the same tension is applied?
fuEu pkj rkj leku inkFkZ ds cus
vf/kdre gksxk tc leku ruko vkjksfir A

1) Length 50 cm and diameter 0.5 mm
2) Length 100 cm and diameter 1 mm
3) Length 200 cm and diameter 2 mm
4) Length 300 cm and diameter 3 mm

Correct option: 1

Solution:
$Y = \frac{FL}{\pi r^{2}\mathcal{l}}$
$\therefore\mathcal{l =}\frac{FL}{\pi r^{2}Y} \Rightarrow \mathcal{l \propto}\frac{L}{r^{2}}$
$\therefore\frac{L}{r^{2}}$is greatest for option A. fodYi A
Subject: Physics — Wave Optics — Diffraction
Difficulty: Moderate

Question: The aperture diameter of a telescope is 5 m. The separation
between the moon and the earth is $4 \times 10^{5}$km. With light of
wavelength of 5893 A, the minimum separation between objects on the
surface ofmoon, so that they are just resolved, is close to

1) 600 m
2) 20 m
3) 200 m
4) 58 m

Correct option: 4

Solution:
$\theta = 1.22\frac{\lambda}{a}$
[IMAGE] Distance $= O_{1}O_{2} = d\theta = 1.22\frac{\lambda}{a}d$
Distance
$= O_{1}O_{2} = \frac{1.22 \times 5893 \times 10^{- 10} \times 4 \times 10^{8}}{5} \approx 57.5m$
answer from options = 58 m
(minimum distance)
Subject: Physics — Kinetic Theory of Gases — Heat capacity
Difficulty: Moderate

Question: Two moles of an ideal gas with [IMAGE] are mixed
with 3 moles of another ideal gas with [IMAGE] Thevalue
of [IMAGE] for the mixture is (10+n)/12. Find n.
eksy=


Answer: 7

Solution:
[IMAGE] On rearranging we getiqu ij
Subject: Physics — Thermodynamics — Adiabatic process
Difficulty: Moderate

Question: Under an adiabatic process, the volume of an ideal gas gets
doubled. Consequently the mean collisiontime between the gas molecules
changes from. If
[IMAGE] for this gas then a good estimate
for[IMAGE] is given by [IMAGE]:,d 
bl j.k mlds v.kqvksa esa gksus okyh VDdjksa


Answer: 1

Solution: