datavorous/entrance-exam-dataset huggingface dataset:
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: A metallic surface is irradiated by a monochromatic light of frequency $v>v_0$ (the threshold frequency). If the incident frequency is now doubled, the photocurrent and the maximum kinetic energy are also doubled.
Statement 2: The maximum kinetic energy of photoelectrons emitted from a surface is linearly dependent on the frequency of the incident light. The photocurrent depends only on the intensity of the incident light.

Options:
A
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

B
Statement 1 is false, Statement 2 is true.

C
Statement 1 is true, Statement 2 is false.

D
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

The correct answer is:
Statement 1 is false, Statement 2 is true.

Solution:
The maximum kinetic energy of photoelectrons depends upon frequency on incident light and photo current depends upon intensity of incident light.

Topic: Physics, Dual Nature of Matter, JEE Main, JEE Main 2012 (19 May Online)
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: A pure semiconductor has negative temperature coefficient of resistance.
Statement 2: On raising the temperature, more charge carriers are released into the conduction band.

Options:
A
Statement 1 is false, Statement 2 is true.

B
Statement 1 is true, Statement 2 is false.

C
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

D
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Solution:
Temperature coefficient of resistance is negative for pure semiconductor. And no. of charge carriers in conduction band increases with increase in temperature.

Topic: Physics, Semiconductors, JEE Main, JEE Main 2012 (12 May Online)
This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals.
Statement-2 : The state of ionosphere varies from hour to hour, day to day and season to season.

Options:
A
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

B
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

C
Statement- 1 is false, Statement- 2 is true.

D
Statement-1 is true, Statement-2 is false.

The correct answer is:
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

Solution:
Since ionospheric properties change with time, these signals are in general less stable than ground wave signals.

Topic: Physics, Communication System, JEE Main, JEE Main 2011
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: An inventor claims to have constructed an engine that has an efficiency of $30 \%$ when operated between the boiling and freezing points of water. This is not possible.
Statement 2: The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.

Options:
A
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

B
Statement 1 is true, Statement 2 is false.

C
Statement 1 is false, Statement 2 is true.

D
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Solution:
According to Carnot's theorem - no heat engine working between two given temperatures of source and sink can be more efficient than a perfectly reversible engine i.e. Carnot engine working between the same two temperatures.
Efficiency of Carnot's engine, $n=1-\frac{T_2}{T_1}$ where, $T_1=$ temperature of source $T_2=$ temperature of sink

Topic: Physics, Thermodynamics, JEE Main, JEE Main 2012 (19 May Online)
This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: Bats emitting ultrasonic waves can detect the location of a prey by hearing the waves reflected from it.
Statement 2: When the source and the detector are moving, the frequency of reflected waves is changed.

Options:
A
Statement 1 is false, Statement 2 is true.

B
Statement 1 is true, Statement 2 is false.

C
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

D
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

Solution:
Bats catch the prey by hearing reflected ultrasonic waves.
When the source and the detector (observer) are moving, frequency of reflected waves change. This is according to Doppler's effect.

Topic: Physics, Waves and Sound, JEE Main, JEE Main 2012 (12 May Online)
This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${ }^9 \mathrm{C}_3$
Statement-2: The number of ways of choosing any 3 places from 9 different places is ${ }^9 \mathrm{C}_3$.

Options:
A
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$

B
Statement $-1$ is true, Statement $-2$ is false.

C
Statement $-1$ is false, Statement- 2 is true.

D
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$

The correct answer is:
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$

Solution:
$$
{ }^{(n-1)} C_{(r-1)}={ }^{(10-1)} C_{(4-1)}={ }^9 C_3
$$
Statement 1 is correct
Statement 2 is also correct
From 9 we can select 3 in ${ }^9 \mathrm{C}_3$ ways. It is correct explanation.

Topic: Mathematics, Permutation Combination, JEE Main, JEE Main 2011
This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : A metallic surface is irradiated by a monochromatic light of frequency $v>v_0$ (the threshold frequency). The maximum kinetic energy and the stopping potential are $\mathrm{K}_{\max }$ and $\mathrm{V}_0$ respectively. If the frequency incident on the surface doubled, both the $\mathrm{K}_{\max }$ and $\mathrm{V}_0$ are also doubled.
Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

Options:
A
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

B
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

C
Statement-1 is false, Statement-2 is true.

D
Statement-1 is true, Statement-2 is false.

The correct answer is:
Statement-1 is false, Statement-2 is true.

Solution:
$$
\begin{aligned}
& \mathrm{KE}_{\max }=\mathrm{hu}-\mathrm{hu}_0 \\
& \mathrm{hu}-\mathrm{hu}=\mathrm{e} \times \Delta \mathrm{v} \\
& \mathrm{V}_0=\frac{\mathrm{hu}}{\mathrm{e}}-\frac{\mathrm{hv_{0 }}}{\mathrm{e}}
\end{aligned}
$$
' $v$ ' is doubled
$$
\begin{aligned}
& \mathrm{KE}_{\max }=2 \mathrm{hu}-\mathrm{hu}_0 \\
& \mathrm{~V}_0^{\prime}=(\Delta \mathrm{V})^{\prime}=\frac{2 \mathrm{hu}}{\mathrm{e}}-\frac{h \mathrm{u}_0}{\mathrm{e}}
\end{aligned}
$$
$\frac{\mathrm{KE}_{\max }}{\mathrm{KE}_{\max }}$ may not be equal to 2
$\Rightarrow \frac{\mathrm{V}_0^{\prime}}{\mathrm{V}_0}$ may not equal to 2
$\mathrm{KE} \max =\mathrm{hu}-\mathrm{hv}_0$
$$
\mathrm{V}=\frac{h \mathrm{v}}{\mathrm{e}}-\frac{h \mathrm{~h}_0}{\mathrm{e}}
$$

Topic: Physics, Dual Nature of Matter, JEE Main, JEE Main 2011
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: When moment of inertia $I$ of a body rotating about an axis with angular speed $\omega$ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if there is no torque applied on it.
Statement 2: $L=I \omega$, kinetic energy of rotation $=\frac{1}{2} I \omega^2$

Options:
A
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

B
Statement 1 is false, Statement 2 is true.

C
Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation of the Statement 1.

D
Statement 1 is true, Statement 2 is false.

The correct answer is:
Statement 1 is false, Statement 2 is true.

Solution:
As $L=I \omega$ so $L$ increases with increase in $\omega$. Kinetic energy $_{\text {(rotational) }}$ depends on an angular velocity ' $\omega$ ' and moment of inertia of the body $I$.
i.e., $K \cdot E \cdot\left(\right.$ rotational $=\frac{1}{2} I \omega^2$

Topic: Physics, Rotational Motion, JEE Main, JEE Main 2012 (12 May Online)
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: Self inductance of a long solenoid of length $L$, total number of turns $\mathrm{N}$ and radius $\mathrm{r}$ is less than $\frac{\pi \mu_0 N^2 r^2}{L}$.
Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current $I$ is $\frac{\mu_0 N I}{L}$ in the middle of the solenoid but becomes less as we move towards its ends.

Options:
A
Statement 1 is true, Statement 2 is false.

B
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

C
Statement 1 is false, Statement 2 is true.

D
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Solution:
Self inductance of a long solenoid is given by
$$
L=\frac{\mu_0 N^2 A}{l}
$$
Magnetic field at the centre of solenoid
$$
B=\frac{\mu_0 N I}{l}
$$
So both the statements are correct and statement 2 is correct explanation of statement 1

Topic: Physics, Electromagnetic Induction, JEE Main, JEE Main 2012 (19 May Online)
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: The possibility of an electric bulb fusing is higher at the time of switching $\mathrm{ON}$.
Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.

Options:
A
Statement 1 is true, Statement 2 is false

B
Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

C
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

D
Statement 1 is false, Statement 2 is true.

The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

Solution:
No Solution Available

Topic: Physics, Current Electricity, JEE Main, JEE Main 2012 (07 May Online)
This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: It is not possible to make a sphere of capacity 1 farad using a conducting material.
Statement 2: It is possible for earth as its radius is $6.4 \times 10^6 \mathrm{~m}$.

Options:
A
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

B
Statement 1 is false, Statement 2 is true.

C
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

D
Statement 1 is true, Statement 2 is false.

The correct answer is:
Statement 1 is true, Statement 2 is false.

Solution:
Capacitance of sphere is given by:
$C=4 \pi \epsilon_0 r$
If, $C=1 \mathrm{~F}$ then radius of sphere needed:
$r=\frac{C}{4 \pi \epsilon_0}=\frac{1}{4 \pi \times 8.85 \times 10^{-12}}$
or, $r=\frac{10^{12}}{4 \pi \times 8.85}=9 \times 10^9 \mathrm{~m}$
$9 \times 10^9 \mathrm{~m}$ is very large, it is not possible to obtain such a large sphere. Infact earth has radius $6.4 \times 10^6 \mathrm{~m}$ only and capacitance of earth is $711 \mu \mathrm{F}$.

Topic: Physics, Capacitance, JEE Main, JEE Main 2012 (26 May Online)
This question has statement $1$ and statement $2$. Of the four choices given after the statements, choose the one that best describes the two statements
Statement 1 : Davisson - germer experiment established the wave nature of electrons.
Statement 2 : If electrons have wave nature, they can interfere and show diffraction.

Options:
A
Statement $1$ is false, Statement $2$ is true

B
Statement $1$ is true, Statement $2$ is false

C
Statement $1$ is true, Statement $2$ is the correct explanation for statement $1$

D
Statement $1$ is true, Statement $2$ is true, Statement $2$ is not the correct explanation for statement $1$.

The correct answer is:
Statement $1$ is true, Statement $2$ is the correct explanation for statement $1$

Solution:
Davisson - Germer experiment showed that electron beams can undergo diffraction when passed through atomic crystals. This shows the wave nature of electrons as waves can exhibit interference and diffraction.

Topic: Physics, Dual Nature of Matter, JEE Main, JEE Main 2012 (Offline)
This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: If you push on a cart being pulled by a horse so that it does not move, the cart pushes you back with an equal and opposite force.
Statement 2: The cart does not move because the force described in statement 1 cancel each other.

Options:
A
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

B
Statement 1 is false, Statement 2 is true.

C
Statement 1 is true, Statement 2 is false.

D
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Solution:
According to newton third law of motion i.e. every action is associated with equal and opposite reaction.

Topic: Physics, Laws of Motion, JEE Main, JEE Main 2012 (26 May Online)
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: A charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged.
Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field.

Options:
A
Statement 1 is false, Statement 2 is true.

B
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

C
Statement 1 is true, Statement 2 is false.

D
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Solution:
When a charged particle enters the magnetic field in perpendicular direction then it experience a force in perpendicular direction.
i.e. $F=B q v \sin \theta$
Due to which it moves in a circular path.

Topic: Physics, Magnetic Effects of Current, JEE Main, JEE Main 2012 (26 May Online)
This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : The point $A(1,0,7)$ is the mirror image of the point $B(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$.
Statement-2 : The line: $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ bisects the line segment joining $A(1,0,7)$ and $B(1,6,3)$.

Options:
A
Statement $-1$ is true, Statement-2 is true; Statement $-2$ is not a correct explanation for Statement $-1$

B
Statement $-1$ is true, Statement $-2$ is false.

C
Statement $-1$ is false, Statement $-2$ is true.

D
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$

The correct answer is:
Statement $-1$ is true, Statement-2 is true; Statement $-2$ is not a correct explanation for Statement $-1$

Solution:
Statement $-1: A B$ is perpendicular to given line and mid point of $A B$ lies on line Statement $-2$ is true but it is not correct explanation as it is bisector only. If it is perpendicular bisector then only statement $-2$ is correct explanation.

Topic: Mathematics, Three Dimensional Geometry, JEE Main, JEE Main 2011
This question has Statement 1and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: In the resonance tube experiment, if the tuning fork is replaced by another identical turning fork but with its arm having been filled, the length of the air column should be increased to obtain resonance again.
Statement 2: On filling the arms, the frequency of a tuning fork increases.

Options:
A
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

B
Statement 1 is true, Statement 2 is false.

C
Statement 1 is false, Statement 2 is true.

D
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

The correct answer is:
Statement 1 is false, Statement 2 is true.

Solution:
On loading frequency of a tuning fork decreases and on filing frequency increases.
If a tuning fork filled length $x$, then new frequency produced by the tuning fork $n^{\prime}=n+x$

Topic: Physics, Waves and Sound, JEE Main, JEE Main 2012 (07 May Online)
This question has Statement - I and Statement - II of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I: A point particle of mass m moving with speed ν collides with stationary point particle of mass M. If the maximum energy loss possible is given as
f12mν2 then f=mM+m.
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Options:
A Statement-I is true, Statement-II is false.
B Statement- I is false, Statement- II is true.
C Statement- I is true, Statement- II is true, Statement- II is a correct explanation of Statement- I .
D Statement- I is true, Statement- II is true, Statement- II is not a correct explanation of Statement- I .

The correct answer is:
Statement- I is false, Statement- II is true.

Solution:
Maximum energy loss will take place in perfectly inelastic collision, and is given by, ∆K=P22m-P22m+M
⇒∆K=P22m1-mm+M
⇒∆K=P22mMm+M
⇒∆K=12mv2Mm+M
On comparing with the given form of equation, we have, f=Mm+M
Hence Statement- I is false, Statement- II is true. ( As it is perfect Inelastic collision)

Topic: Physics, Center of Mass Momentum and Collision, JEE Main, JEE Main 2013 (07 Apr)
This question has Statement - I and Statement - II of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I: A point particle of mass m moving with speed ν collides with stationary point particle of mass M. If the maximum energy loss possible is given as
f12mν2 then f=mM+m.
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Options:
A Statement-I is true, Statement-II is false.
B Statement- I is false, Statement- II is true.
C Statement- I is true, Statement- II is true, Statement- II is a correct explanation of Statement- I .
D Statement- I is true, Statement- II is true, Statement- II is not a correct explanation of Statement- I .

The correct answer is:
Statement- I is false, Statement- II is true.

Solution:
Maximum energy loss will take place in perfectly inelastic collision, and is given by, ∆K=P22m-P22m+M
⇒∆K=P22m1-mm+M
⇒∆K=P22mMm+M
⇒∆K=12mv2Mm+M
On comparing with the given form of equation, we have, f=Mm+M
Hence Statement- I is false, Statement- II is true. ( As it is perfect Inelastic collision)

Topic: Physics, Center of Mass Momentum and Collision, JEE Main
This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I : Higher the range, greater is the resistance of ammeter.
Statement - II : To increase the range of ammeter, additional shunt needs to be used across it.

Options:
A Statement-I is true, Statement-II is false.
B Statement- I is false, Statement- II is true.
C Statement- I is true, Statement- II is true, Statement- II is the correct explanation of Statement- I .
D Statement- I is true, Statement- II is true, Statement- II is not the correct explanation of Statement- I .

The correct answer is:
Statement- I is false, Statement- II is true.

Solution:
For higher range resistance should be less,so statement I is false.
To increase the range by n-times additional shunt should be placed S=Gn-1 where 'G' resistance of galvanometer

Topic: Physics, Current Electricity, JEE Main, JEE Main 2013 (07 Apr)
This question has Statement-1 and Statement- 2 . Of the four choices given after the Statements, choose the one that best describes the two Statetnents.
Statement-1: A capillary is dipped in a liquid and liquid rises to a height $h$ in it. As the temperature of the liquid is raised, the height $h$ increases (if the density of the liquid and the angle of contact remain the same).
Statement-2: Surface tension of a liquid decreases with the rise in its temperature.

Options:
A
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1.

B
Statement-1 is false, Statement- 2 is true.

C
Statement-1 is true, Statement- 2 is false.

D
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1.

The correct answer is:
Statement-1 is false, Statement- 2 is true.

Solution:
Surface tension of a liquid decreases with the rise in temperture. At the boiling point of liquid, surface tension is zero.
Capillary rise $h=\frac{2 \mathrm{~T} \cos \theta}{\mathrm{rdg}}$
As surface tension $\mathrm{T}$ decreases with rise in temperature hence capillary rise also decreases.

Topic: Physics, Mechanical Properties of Fluids, JEE Main, JEE Main 2013 (09 Apr Online)
This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: Short wave transmission is achieved due to the total internal reflection of the e-m wave from an appropriate height in the ionosphere.
Statement-2: Refractive index of a plasma is independent of the frequency of e-m waves.

Options:
A
Statement-1 is true, Statement- 2 is false.

B
Statement-1 is false, Statement- 2 is true.

C
Statement-1 is true, Statement- 2 is true but Statement $-2$ is not the correct explanation of statement-1.

D
Statement-1 is true, Statement-2 is true and Statement $-2$ is the correct explanation of Statement-1.

The correct answer is:
Statement-1 is true, Statement- 2 is false.

Solution:
Effective refractive index of the ionosphere
$$
\mathrm{n}_{\mathrm{eff}}=\mathrm{n}_0\left[1-\frac{80.5 \mathrm{~N}}{\mathrm{f}^2}\right]^{1 / 2}
$$
where $\mathrm{f}$ is the frequency of em waves

Topic: Physics, Ray Optics, JEE Main, JEE Main 2013 (22 Apr Online)