JEE Main 2024 April 04, Shift 2 Question Paper with Solutions

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

A body of m kg slides from rest along the curve of vertical circle from point A to B in friction less path. velocity of the body at B is:
(given, $R=14$ m, $g=10$ m/$s^2$ and $\sqrt{2}=1.4$)

A 90 kg body placed at $2R$ distance from surface of earth experiences gravitational pull of : ( R $=$ Radius of earth, g $=10$ m $s^{-2}$ )

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 C$H_4$ molecule are:

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 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 A $m^2$. It is suspended in a uniform magnetic field of $8\times 10^{-2}$ T. The work done in rotating it from its most stable to most unstable position is:

Match List I with List II
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 $\mathbf{A}$ 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:

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

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

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.

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

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

A parallel plate capacitor of capacitance 12.5pF 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 ______ $10^{-12}$ J.

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 ______ $\Omega$.

A rod of length 60 cm rotates with a uniform angular velocity 20rad$s^{-1}$ 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.

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 $\sin 15^{\circ }=0.25$)

The disintegration energy Q for the nuclear fission of ${}^{235}$U $\to$ ${}^{140}$Ce $+$ ${}^{94}$Zr $+n$ is ______ MeV. Given atomic masses of ${}^{235}$U : 235.0439u; ${}^{140}$Ce : 139.9054u, ${}^{94}$Zr : 93.9063u; n : 1.0086u, Value of $c^2=931$MeV/u

Choose the Incorrect Statement about Dalton's Atomic Theory

The correct order of the first ionization enthalpy is

Given below are two statements : Statement I : The correct order of first ionization enthalpy values of $\text{Li},\text{Na},\text{F}$ and $\text{Cl}$ is $\text{Na}<\text{Li}<\text{Cl}<\text{F}$. Statement II : The correct order of negative electron gain enthalpy values of $\text{Li},\text{Na},\text{F}$ and $\text{Cl}$ is $\text{Na}<\text{Li}<\text{F}<\text{Cl}$ In the light of the above statements, choose the correct answer from the options given below :

The correct statement/s about Hydrogen bonding is/are A. Hydrogen bonding exists when $\text{H}$ is covalently bonded to the highly electro negative atom. B. Intermolecular $\text{H}$ bonding is present in o-nitro phenol C. Intramolecular $\text{H}$ bonding is present in HF. D. The magnitude of $\text{H}$ bonding depends on the physical state of the compound. E. H-bonding has powerful effect on the structure and properties of compounds Choose the correct answer from the options given below:

The number of species from the following that have pyramidal geometry around the central atom is ________.
${\text{S}}_2{\text{O}}_3^{2-},{\text{SO}}_4^{2-},{\text{SO}}_3^{2-},{\text{S}}_2{\text{O}}_7^{2-}$

The equilibrium constant for the reaction ${\text{SO}}_3(\text{g})\rightleftharpoons {\text{SO}}_2(\text{g})+\frac{1}{2}{\text{O}}_2(\text{g})$ is ${\text{K}}_{\text{c}}=4.9\times 10^{-2}$. The value of ${\text{K}}_{\text{c}}$ for the reaction given below is $2{\text{SO}}_2(\text{g})+{\text{O}}_2(\text{g})\rightleftharpoons 2{\text{SO}}_3(\text{g})$ is :

Correct order of stability of carbanion is -

Common name of Benzene - 1, 2 - diol is -

The adsorbent used in adsorption chromatography is/are - A. silica gel B. alumina C. quick lime D. magnesia Choose the most appropriate answer from the options given below :

Product P is

In the above chemical reaction sequence " A " and " B " respectively are

For a strong electrolyte, a plot of molar conductivity against (concentration${)}^{1/2}$ is a straight line, with a negative slope, the correct unit for the slope is

Fuel cell, using hydrogen and oxygen as fuels, A. has been used in spaceship B. has efficiency of 40% to produce electricity C. uses aluminum as catalysts D. is eco-friendry E. is actually a type of Galvanic cell only Choose the correct answer from the options given below :

When ${\text{MnO}}_2$ and ${\text{H}}_2{\text{SO}}_4$ is added to a salt (A), the greenish yellow gas liberated as salt (A) is :

A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of 3.86BM. The atomic number of the metal is

If an iron (III) complex with the formula $[{\text{Fe(NH}}_3{)}_x(\text{CN}{)}_y{]}^{-}$ has no electron in its $e_g$ orbital, then the value of $x+y$ is

The number of unpaired d-electrons in $[{\text{Co(H}}_2\text{O}{)}_6{]}^{3+}$ is

Find out the major product formed from the following reaction. [Me $:-{\text{CH}}_3$]

Match List I with List II

The maximum number of orbitals which can be identified with n = 4 and $m_l=0$ is _______

Number of compounds / species from the following with non-zero dipole moment is _______
BeC$l_2$, BC$l_3$, N$F_3$, Xe$F_4$, CC$l_4$, $H_2$O, $H_2$S, HBr, C$O_2$, $H_2$, HCl

Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using constant pressure of 5 atm. Heat exchange Q for the compression is - _______ Lit. atm.

The total number of 'sigma' and 'Pi' bonds in 2-oxohex-4-ynoic acid is _______

2.7 kg of each of water and acetic acid are mixed. The freezing point of the solution will be $-x^{\circ }$C. Consider the acetic acid does not dimerise in water, nor dissociates in water. $x=$ _______ (nearest integer) [Given: Molar mass of water $=18$ g mo$l^{-1}$, acetic acid $=60$ g mo$l^{-1}$ $K_f{H}_2$O $:1.86$ K kg mo$l^{-1}$ $K_f$ acetic acid: $3.90$ K kg mo$l^{-1}$ freezing point: $H_2$O $=273$ K, acetic acid $=290$ K]

Consider the following reaction, the rate expression of which is given below
$\text{A}+\text{B}\to \text{C}$
rate $=k[\text{A}{]}^{1/2}[\text{B}{]}^{1/2}$
The reaction is initiated by taking 1M concentration of A and B each. If the rate constant (k) is $4.6\times 10^{-2}$ $s^{-1}$, then the time taken for A to become 0.1M is _______ sec. (nearest integer)