Grass-G/jee-main-questions huggingface dataset:
Subject: Physics —  — 

Question: The angular frequency of oscillation of mass m connected
symmetrically to four spring each of force constant K, when it is
displaced very slightly along one of the springs is


Correct option: 2

Solution:
[IMAGE] TOPIC: Simple harmonic motion
SUB TOPIC: Angular frequency of oscillation
LEVEL:Moderate
Subject: Physics — Thermodynamics — First law of thermodynamics
Difficulty: Easy

Question: 110 J of heat are added to a gaseous system where change in
internal energy is 40 J, then the amount of external work done is

1) 40 J
2) 110J
3) 70 J
4) 150 J

Correct option: 3

Solution:
$\Delta W = \Delta u + \Delta W$
$\Rightarrow 110 = 40 + \Delta W$
$\Rightarrow \Delta W = 110 - 40 = 70J$
Subject: Physics — System of particles — Linear momentum of center of mass
Difficulty: Moderate

Question: A train of mass M is moving on a circular track of radius ' R
' with constant speed V. The length of thetrain is half of the
perimeter of the track. The linear momentum of the train will be

1) Zero
2) $\frac{2M\ V}{\pi}$
3) MVR
4) MV

Correct option: 2

Solution:
If we treat the train as a ring of mass then its COM will
be at a distance[IMAGE] from the centre of the circle. Velocity
of centre of mass is:
$V_{CM} = R_{CM} \cdot \omega$
= $\frac{2R}{\pi} \cdot \omega$ =
$\frac{2R}{\pi} \cdot \left( \frac{v}{R} \right)$
$\left( \because\omega = \frac{v}{R} \right)$
$\Rightarrow$ $V_{CM} = \frac{2V}{\pi}$ $\Rightarrow$
${MV}_{CM} = \frac{2MV}{\pi}$
As the linear momentum of any system = MV_CM
[IMAGE] The linear momentum of the train $= \frac{2MV}{\pi}$
Subject: Physics —  — 

Question: A solid cylinder of mass m is placed over the trolley as shown
in the figure. The trolley starts to move forward with constant
horizontal acceleration a. The frictional force acting on the solid
cylinder will be (Assume no slipping)

2) ma

Correct option: 3

Solution:
From the reference frame of trolley, the forces acting on the
cylinder is as shown.
and [IMAGE] (ii) From (i) and (ii),
Subject: Physics — Mechanical Properties of Fluids — Terminal velocity
Difficulty: Moderate

Question: A container filled with viscous liquid is moving vertically
downwards with constant speed
[IMAGE]. At the instant shown, a sphere of radius
r is moving vertically downwards (in liquid) has speed
The coefficient of viscosity is η. There is no relative motion between
the liquid and the container. Then at the shown instant, the magnitude
of viscous force acting on sphere is $2x\pi\eta\text{r}\text{v}_{0}$.
Find x


Answer: 6

Solution:
Relative to liquid, the velocity of sphere is
${\text{2}\text{v}}_{0}$ upwar Viscous force on sphere
$= 6\pi\eta\text{r}\text{v}_{0}$ downward
$= 12\pi\eta\text{r}\text{v}_{0}$ downward
Subject: Physics — Electronic devices — 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
 izFke Hkkx OR 
Second part of figure shown is NOT gate
rFkk Hkkx NOT 
So vr Y_p = OR + NOT = NOR gate
Subject: Physics — Centre of Mass — Center of mass of system at rest
Difficulty: Moderate

Question: A penguin of mass m stands at the right edge of a sled of mass 3m
and legnth [IMAGE]. The sled lies onfrictionless ice. The
penguin starts moving towards left, reaches the left end and jumps with
a velocity uat an angle[IMAGE] with horizontal relative to
ground. (Neglect the height of the sled)

1) Till the penguin reaches the left end, the sled is displaced
2) Till the penguin reaches the left end, the sled is displaced
3) After jumping, it will fall on the ground at a
distance[IMAGE] from the left end of the sled.
4) After jumping, it will fall on the ground at a distance
[IMAGE] from the left end of the sled.

Correct option: 3

Solution:
$S_{CM} = \frac{m_{1}S_{1} + m_{2}S_{2}}{m_{1} + m_{2}}$
$0 = \frac{(3m)( - x) + (m)(\mathcal{l -}x)}{3m + m}\ $
$x = \frac{\mathcal{l}}{4}$
Displacement of sled in this time
$= \left( \frac{{ucos}\theta}{3} \right)\left( \frac{2{usin}\theta}{g} \right) = \frac{1}{3}\left( \frac{u^{2}\sin{2\theta}}{g} \right)$
Total distance between penguin and left end of
sled$= \frac{4}{3}\left( \frac{u^{2}sin2\theta}{g} \right)$
Subject: Physics — Wave on a string — Sonometer
Difficulty: Moderate

Question: Two forks A and B when sounded together produce 4 beats/s. The
fork A is in unison with 30cm length of a sonometer wire and B is in
unison with 25cm length of the same wire at the same tension. What can
be frequency of forks.


Correct option: 1

Solution:
Subject: Physics —  — 
Difficulty: Moderate

Question: A block of mass 2 kg is given a push horizontally and then the
block starts sliding over a horizontal plane. The graph shows the
velocity time graph of the motion. The co-efficient of friction between
the plane and the block is

1) 0.02
2) 0.2
3) 0.04
4) 0.4
2 kg 
 ≤

Correct option: 2

Solution:
a = slope of v-t graph = - 2 m/s2
∴ Ft = μmg = m × 2
⇒μ × 2 × 10 = 2 × 2 ⇒ μ = 0.2
TOPIC: NLM
SUB TOPIC: FRICTION
Subject: Physics —  — 

Question: As soon as the valve is opened, the mercury level at B in the
tube

1) Remains same
2) Oscillates
3) Goes down
4) Goes up

Correct option: 4

Solution:
In narrow passage velocity is greater.
Hence static pressure will be less at B. So the level moves up.
Subject: Physics —  — 

Question: In a common-base configuration of transistor, α = 0.98, I_B =
0.02mA, R_L = 5 kΩ. Output voltage across load is

1) 3.2 V (B) 4.9 V
3) 5.2
4) 6.2 V

Correct option: 2

Solution:
[IMAGE] I_E 0.98 = I_C
I_E = I_B + I_C
I_E = 1 mA
I_C = 0.98 mA
V_0 = R_L × I_C
Subject: Physics — EMI — Faraday's law
Difficulty: Moderate/ Tough

Question: A uniform magnetic field B in positive z direction exists in a
circular region of radius R = 5 m. A loop of radius R = 5 m lying x-y
plane encloses the magnetic field at t = 0 and then pulled at uniform
velocity$\ \overset{\rightarrow}{v} = 4\overset{\hat{}}{i}m/s$. The emf
induced (in volts) is the loop at t = 2 sec is 6 V. Then magnitude of 45
B is


Answer: 11.25

Solution:
$\varepsilon = |(\overset{\rightarrow}{v} \times \overset{\rightarrow}{B}) \cdot \overset{\rightarrow}{\mathcal{l}}|$
$= VB2\sqrt{R^{2} - {(\frac{vt}{2})}^{2}} = VB\sqrt{4R^{2} - V^{2}t^{2}}$
$6V = 4 \times B\sqrt{4 \times 25 - 16 \times 4}$
Subject: Physics — Mechanical Properties of Fluids — Hydrostatic pressure
Difficulty: Moderate

Question: A container of a large uniform cross-sectional area A resting on
a horizontal surface holds two immiscible, non-viscous and
incompressible liquids of densities and each of height
(1/2)H as shown. The smaller density liquid is open to atmosphere. A
homogeneous solid cylinder of length $\left( L < \frac{1}{2}h \right)$
cross-sectional area (1/5) A is immersed such that it floats with its
axis vertical to the liquid-liquid interface with length (1/4) L in
denser liquid. If D is the density of the solid cylinder then

1) $D = \frac{3d}{2}$
2) $D = \frac{d}{2}$
3) $D = \frac{2d}{3}$
4) $D = \frac{5d}{4}$

Correct option: 4

Solution:
$D \times L \times Ag = 2d \times \frac{L}{4} \times Ag + d \times \frac{3L}{4} \times Ag$
$D = \frac{5d}{4}$
Subject: Physics —  — 
Difficulty: Easy

Question: 20 m ehukj,d dadM+ 10 izkjfEHkd osx Qsa o gksxh (g = 10 m/s2)
20 m 10 m/s, (g=10 m/s^2)

3) 20

Correct option: 2

Solution:
vy2 - uy2 = 2 × g × s
[IMAGE] vy2 = 0 + 2 × 10 × 10 = 10
TOPIC:KINEMATIC
SUB TOPIC: 2 D
Subject: Physics — Thermodynamics — Isobaric process
Difficulty: tough

Question: Figure shows the variation of internal energy "U" with the
density "$\rho$ " of one mole of ideal diatomic gas. Process BA is a
part of rectangular hyperbola. If the work done by gas in the process BA
is 7n joules. Find n ?


Answer: 2

Solution:
For rectangular hyperbola
XY = constant
$U\rho =$ constant
$nC_{V}T\rho =$ constant
$n\frac{5}{2}RT\frac{M}{V} =$constant
$\frac{5}{2}P\frac{VM}{V} =$constant $\Rightarrow$ P = constant
(isobaric process)
$\Delta U_{B \rightarrow A} = 37 - 2 = 35J = \frac{5}{2}nR\Delta T$
$14J = nR\Delta T$
$\therefore$ $W = 14J$
Subject: Physics — Elasticity — Potential stored in elongated rod
Difficulty: Tough

Question: Two steel wires having same length are suspended from a ceiling
under the same load. If the ratio oftheir energy stored per unit volume
is 1: 4, the ratio of their diameters is:
leky yEckbZ ds nks LVhy ds rkjksa ij leku Hkkj cka/kdj bUg a NRk ls
vuqikr 1: 4

1) 1: 2
3) 2: 1

Correct option: 4

Solution:
Subject: Physics —  — 
Difficulty: Moderate

Question: The potential energy of a particle moving along x axis, starting
from x = 0 at rest is given by
U = (ax - b) x
 b are positive constant]

4) [IMAGE] x = 0 x-. U =
(ax-b)x: (a, b 
)

Correct option: 4

Solution:
Kmax ⇒ Umin
⇒[IMAGE] = 0
⇒ 2ax - b = 0
x =[IMAGE] Ki + Ui = Kf + Uf
0 + 0 = Kf +[IMAGE] ⇒ Kf = [IMAGE] TOPIC: WPE
SUB TOPIC: ENERGY CONSERVATION
Subject: Physics —  — 

Question: A car is initially at rest, 330 m away from a stationary
observer. It begins to move towards the observer with an acceleration of
[IMAGE], sounding its horn continuously. 20 second
later, the driver stops sound the horn. The velocity of sound in air is
330 m/s. The observer will hear the sound of the horn for a duration of
[IMAGE] sec. Find n.


Answer: 3

Solution:
[IMAGE] In 20 seconds, distance travelled by the Source is:
[IMAGE] Let, t = 0 be the starting time.
The sound wave started at t = 0 from reaches the observer at
'B' after [IMAGE] ie. observer started hearing the
sound at t = 1 sec. At t = 20 sec. the source reaches at 220 m
The last sound wave starting from reaches Hence, the observer do not hear the sound for whole 20 sec.
but for: [IMAGE] TOPIC: Sound wave
SUB TOPIC: Doppler effect
LEVEL: Moderate
Subject: Physics — Newton's Laws of Motion — String constraint
Difficulty: Moderate

Question: Block A is given an acceleration $12{ms}^{- 2}$ towards left as
shown in Figure. Assume block B always remains horizontal, find the
acceleration $\left( \text{ in }{ms}^{- 2} \right)$ of B.


Correct option: 1

Solution:
$\mathcal{l}_{1} + \mathcal{l}_{2} = C \Rightarrow \mathcal{l}_{1}^{''} + \mathcal{l}_{2}^{''} = 0$
Subject: Physics — Wave on a string — speed of wave
Difficulty: Moderate

Question: A perfectly elastic uniform string is suspended vertically with
its upper end fixed to the ceiling and the lower end loaded with the
weight. If a transverse wave is imparted to the lower end of the string,
the pulse will

1) not travel along the length of the string
2) travel upwards with increasing speed
3) travel upwards with decreasing speed
4) travelled upwards with variable acceleration

Correct option: 2

Solution:
Subject: Physics — Centre of Mass — Torque
Difficulty: Moderate

Question: A uniform triangular plate ABC of moment of inertia I (about an
axis passing through A and perpendicular to plane of the plate) can
rotate freely in the vertical plane about point as shown in
figure. The plate is released from the position shown in the figure.
Line AB is horizontal. The acceleration of centre of mass just after the
release of plate is

1) $\frac{mg}{\sqrt{3}}a^{2}$
2) $\frac{{\ mga\ }^{2}}{4\sqrt{3}\ I\ }$
3) $\frac{mga^{2}}{2\sqrt{3}i}$
4) $\frac{mg\ a^{2}}{3\ \ I}$

Correct option: 3

Solution:
Torque about A:
$\Rightarrow$ $\alpha = \frac{mga}{2I}$
$\Rightarrow$ Acceleration
$= \frac{a}{\sqrt{3}}\alpha = \frac{m\ g{\ a}^{2}}{2\sqrt{3}\ I}$
Subject: Physics — Gravitation — Escape velocity
Difficulty: Moderate

Question: Planet A has mass M and radius R. Planet B has half the mass and
half the radius of Planet A. If the escape velocities from the Planets A
and B are [IMAGE] and [IMAGE],
respectively, then [IMAGE] The value of n is


Answer: 4

Solution:
Subject: Physics —  — 

Question: In a corner on a smooth horizontal surfaces we kept two masses
[IMAGE] and [IMAGE] attached to a spring
in natural length as shown. The spring has a spring constant 150 N/m.
Now [IMAGE] is suddenly given a velocity towards the
left at t = 0. After this spring attains natural length first at time
[IMAGE] sec and then next at time
[IMAGE]. If mass of [IMAGE] (in kg) is K
then K is


Answer: 1

Solution:
Solving (i) and (ii), [IMAGE] TOPIC: Simple harmonic motion
SUB TOPIC: Block and spring system
LEVEL: Moderate
Subject: Physics —  — 

Question: A mass of material exists in its solid form at its melting
temperature 10°C. The following processes then occur to the material:
Process-1: An amount of thermal energy Q is added to the material
and [IMAGE] of the material melts.
Process-2: An identical additional amount of thermal energy Q is
added to the material and the material is now a liquid at 50°C.
What is the ratio of the latent heat of fusion to the specific heat of
the liquid for this material?


Answer: 80

Solution:
[IMAGE] mL = Q
Q = [IMAGE] + mS × 40
[IMAGE] = 4mS
[IMAGE] = 80
Subject: Physics — Motion in 1D — Velocity-time and acceleration-time graph
Difficulty: Moderate

Question: The variation of velocity with time of a toy car moving along a
straight line is as shown below. Which of the following graphs correctly
represents the variation of acceleration with time for the toy car?


Correct option: 4

Solution:
for 0 to 1 seconds velocity increases linearly
$a = \frac{4 - 2}{1 - 0} = 2m/s^{2}$
$\Rightarrow$a vs t graph is st. line parallel to x-axis (+ve
acceleration)
for 1 to 1.5 sec.$v = constant \Rightarrow a = 0$
for $t > 1.5\ sec.\ $a is negative
Subject: Physics — Kinetic Theory of Gases — Ideal Gas
Difficulty: Moderate

Question: 70 calories of heat is required to raise the temperature of 2
moles of an ideal gas at constant pressure from 30°C to 35°C (R= 2 cal
/mol-°C) The gas may be:
ls] bl gks tkrk gs
rks xSl gks ldrh

2) He

Correct option: 1

Solution:
[IMAGE] So gas is