JEE Main 2024 Apr 4 Shift 2 — Physics

Which of the diode circuit shows correct biasing used for the measurement of dynamic resistance of p-n junction diode :

Applying the principle of homogeneity of dimensions, determine which one is correct,

where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

A cyclist starts from the point $P$ of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is:

a circle with centre O; point P at the top, Q at the right, R at the bottom, S at the left; arrows along the circumference show travel from P through Q and R to S

A 2 kg brick begins to slide over a surface which is inclined at an angle of $45°$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of :

($\mathrm{R}$ = Radius of earth, $\mathrm{g} = 10~\mathrm{m\,s^{-2}}$)

A body of $m$ kg slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is:

a vertical circle with centre marked; point A on the upper right of the circle at $45°$ above the horizontal radius, point B at the bottom of the circle; the vertical diameter is shown dashed

(given, $R = 14~m$, $g = 10~m/s^2$ and $\sqrt{2} = 1.4$ )

Correct formula for height of a satellite from earths surface is:

Given below are two statements :

Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.

In the light of the above statements, choose the correct answer from the options given below :

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma = 3/2$. The work done by the gas in the process is:

($\mu = 1$ mole)

The translational degrees of freedom ($f_t$) and rotational degrees of freedom ($f_r$) of $CH_4$ molecule are:

A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:

An electric bulb rated $50~W$ - $200~V$ is connected across a $100~V$ supply. The power dissipation of the bulb is:

The magnetic moment of a bar magnet is $0.5~\mathrm{Am^2}$. It is suspended in a uniform magnetic field of $8\times 10^{-2}~\mathrm{T}$. The work done in rotating it from its most stable to most unstable position is:

Match List I with List II

	LIST I		LIST II
A.	Purely capacitive circuit	I.	[Phasor diagram: current $I$ along the vertical axis, voltage $V$ along the horizontal axis, with a $90°$ angle between them ($I$ leads $V$ by $90°$)]
B.	Purely inductive circuit	II.	[Phasor diagram: $V$ and $I$ both along the same horizontal direction (in phase)]
C.	LCR series at resonance	III.	[Phasor diagram: $V$ at an angle $\theta$ above the horizontal $I$ axis ($V$ leads $I$ by $\theta$)]
D.	LCR series circuit	IV.	[Phasor diagram: voltage $V$ along the vertical axis, current $I$ along the horizontal axis, with a $90°$ angle between them ($V$ leads $I$ by $90°$)]

Choose the correct answer from the options given below:

Arrange the following in the ascending order of wavelength:

A. Gamma rays ($\lambda_1$) B. x - rays ($\lambda_2$) C. Infrared waves ($\lambda_3$) D. Microwaves ($\lambda_4$)

Choose the most appropriate answer from the options given below

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Number of photons increases with increase in frequency of light.

Reason R: Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.

In the light of the above statements, choose the most appropriate answer from the options given below:

According to Bohr's theory, the moment of momentum of an electron revolving in $4^{th}$ orbit of hydrogen atom is:

Identify the logic gate given in the circuit:

inputs A and B each pass through a NOT gate (inverter); the two inverted outputs feed a two-input OR-shaped gate whose output carries a bubble (inversion), giving output Y

In simple harmonic motion, the total mechanical energy of given system is $E$. If mass of oscillating particle $P$ is doubled then the new energy of the system for same amplitude is:

a spring of stiffness $k$ hanging from a ceiling with a block of mass $m$ (particle $P$) attached at its lower end

The disintegration energy $Q$ for the nuclear fission of $^{235}U \rightarrow\ ^{140}Ce +\ ^{94}Zr + n$ is ______ MeV.

Given atomic masses of $^{235}U$: $235.0439\,u$; $^{140}Ce$ : $139.9054\,u$,

$^{94}Zr$ : $93.9063\,u$ ; $n$ : $1.0086\,u$,

Value of $c^2 = 931~MeV/u$.

A light ray is incident on a glass slab of thickness $4\sqrt{3}$ cm and refractive index $\sqrt{2}$. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ______ cm.

(Given $\sin 15° = 0.25$)

A rod of length 60 $cm$ rotates with a uniform angular velocity 20 rad $s^{-1}$ about its perpendicular bisector, in a uniform magnetic filed $0.5T$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is ______ V.

Two parallel long current carrying wire separated by a distance $2r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is ______.

two vertical parallel wires carrying currents $I$ (left wire) and $2I$ (right wire), separated by distance $2r$ with midpoint $O$; point $A$ lies at distance $r$ to the left of the left wire, and point $C$ lies at distance $r$ to the right of the right wire

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0~mm$ and wire $B$ has radius of $4.0~mm$. The resistance of wire $B$ is $2\Omega$. The resistance of wire $A$ is ______ $\Omega$.

The displacement of a particle executing SHM is given by $x = 10\sin\left(wt + \frac{\pi}{3}\right) m$. The time period of motion is 3.14 s. The velocity of the particle at $t = 0$ is ______ $m/s$.

Mercury is filled in a tube of radius 2 $cm$ up to a height of 30 $cm$. The force exerted by mercury on the bottom of the tube is ______ N.

(Given, atmospheric pressure $= 10^5~Nm^{-2}$, density of mercury $= 1.36 \times 10^4~kg\,m^{-3}$, $g = 10~m\,s^{-2}$, $\pi = \frac{22}{7}$)

In a system two particles of masses $m_1 = 3~kg$ and $m_2 = 2~kg$ are placed at certain distance from each other. The particle of mass $m_1$ is moved towards the center of mass of the system through a distance 2 cm. In order to keep the center of mass of the system at the original position, the particle of mass $m_2$ should move towards the center of mass by the distance ______ $cm$.

A bus moving along a straight highway with speed of $72~km/h$ is brought to halt within 4 $s$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ______ $m$.

A parallel plate capacitor of capacitance $12.5~pF$ is charged by a battery connected between its plates to potential difference of 12.0 V. The battery is now disconnected and a dielectric slab ($\epsilon_r = 6$) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ______ $\times 10^{-12}$ J.