JEE Main 2024 April 09, Shift 2 Question Paper with Solutions

The de-Broglie wavelength associated with a particle of mass m and energy E is $h/\sqrt{2mE}$. The dimensional formula for Planck's constant is :

Two cars are travelling towards each other at speed of 20 m $s^{-1}$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m $s^{-2}$. The distance between them when they come to rest is :

A 1 kg mass is suspended from the ceiling by a rope of length 4 m. A horizontal force ' F ' is applied at the mid point of the rope so that the rope makes an angle of $45^\circ$ with respect to the vertical axis as shown in figure. The magnitude of F is : (Assume that the system is in equilibrium and $g=10$ m/$s^2$ )

A satellite of $10^3$ kg mass is revolving in circular orbit of radius $2R$. If $\frac{10^4 R}{6}J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g=10$ m/$s^2$, $R=$ radius of earth)

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A spherical ball of radius $1\times10^{-4}$ m and density $10^5$ kg/$m^3$ falls freely under gravity through a distance h before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is $9.8\times10^{-6}$ N s/$m^2$ )

The temperature of a gas is $-78^\circ$C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K is :

Five charges $+q$, $+5q$, $-2q$, $+3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is :

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be

A proton and a deutron ( $q=+e$, $m=2.0$u) having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is:

A square loop of side 15 cm being moved towards right at a constant speed of 2 cm/s as shown in figure. The front edge enters the 50 cm wide magnetic field at $t=0$ . The value of induced emf in the loop at $t=10$ s will be :

The magnetic field in a plane electromagnetic wave is $B_y=\left(3.5\times10^{-7}\right)\sin\left(1.5\times10^3 x+0.5\times10^{11}t\right)$T. The corresponding electric field will be :

The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal length 10 cm and 15 cm respectively. The distance between $L_1$ & $L_2$ is :

UV light of 4.13eV is incident on a photosensitive metal surface having work function 3.13eV. The maximum kinetic energy of ejected photoelectrons will be:

A hydrogen atom in ground state is given an energy of 10.2eV. How many spectral lines will be emitted due to transition of electrons?

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2 : 1. After disintegration they will move :

The energy released in the fusion of 2 kg of hydrogen deep in the sun is $E_H$ and the energy released in the fission of 2 kg of $^{235}$U is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately: (Consider the fusion reaction as $4\mid H+2\mathrm{e}^-\rightarrow{}_2^4\mathrm{He}+2v+6\gamma+26.7\mathrm{MeV}$, energy released in the fission reaction of $^{235}$U is 200MeV per fission nucleus and $\mathrm{N_A}=6.023\times10^{23}$)

The $I-V$ characteristics of an electronic device shown in the figure. The device is:

In the truth table of the above circuit the value of X and Y are :

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is ______ $^\circ$.

A force $\left(3x^2+2x-5\right)$N displaces a body from $x=2$ m to $x=4$ m. Work done by this force is ______ J.

A circular disc reaches from top to bottom of an inclined plane of length l. When it slips down the plane, if takes t s. When it rolls down the plane then it takes $\left(\frac{\alpha}{2}\right)^{1/2}t$ s, where $\alpha$ is ______

At room temperature $\left(27^\circ\mathrm{C}\right)$, the resistance of a heating element is $50\Omega$. The temperature coefficient of the material is $2.4\times10^{-4}{}^\circ\mathrm{C}^{-1}$. The temperature of the element, when its resistance is $62\Omega$, is ______ $^\circ$C.

A particle of mass 0.50 kg executes simple harmonic motion under force $F=-50\left(\mathrm{Nm}^{-1}\right)x$. The time period of oscillation is $\frac{x}{35}$ s. The value of x is ______ (Given $\pi=\frac{22}{7}$ )

An electric field $\vec{E}=(2x\hat{i})NC^{-1}$ exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is ______ N$m^2$/C.

To determine the resistance (R) of a wire, a circuit is designed below. The $V-I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of R is ______ $\Omega$.

A straight magnetic strip has a magnetic moment of 44A$m^2$. If the strip is bent in a semicircular shape, its magnetic moment will be ______ A$m^2$. (given $\pi=\frac{22}{7}$ )

A capacitor of reactance $4\sqrt{3}\Omega$ and a resistor of resistance $4\Omega$ are connected in series with an ac source of peak value $8\sqrt{2}$ V. The power dissipation in the circuit is ______ W.

Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $=1.5$ ), the central maximum is shifted to a position previously occupied by the $4^{\mathrm{th}}$ bright fringe. The thickness of the glass-plate is ______ $\mu$m.

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency ' A ' $\times 10^{12}$ hertz and that has a radiant intensity in that direction of $\frac{1}{\text{'B'}}$ watt per steradian. 'A' and 'B' are respectively

The electronic configuration of Einsteinium is : (Given atomic number of Einsteinium $= 99$)

Match List I with List II

Match List I with List II

The correct increasing order for bond angles among $\text{BF}_3$, $\text{PF}_3$ and $\text{ClF}_3$ is :

The incorrect statement regarding ethyne is

For a sparingly soluble salt $\text{AB}_2$, the equilibrium concentrations of $\text{A}^{2+}$ ions and $\text{B}^-$ ions are $1.2 \times 10^{-4}$M and $0.24 \times 10^{-3}$M, respectively. The solubility product of $\text{AB}_2$ is :

The correct stability order of the following resonance structures of $\text{CH}_3 - \text{CH} = \text{CH} - \text{CHO}$ is

Total number of stereo isomers possible for the given structure :

Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for a weak electrolyte, if the symbols carry their usual meaning :

Match List I with List II

Give below are two statements: Statement I : The higher oxidation states are more stable down the group among transition elements unlike p-block elements. Statement II : Copper can not liberate hydrogen from weak acids. In the light of the above statements, choose the correct answer from the options given below :

Match List I with List II