JEE Main 2024 April 06, Shift 2 Question Paper with Solutions

Given below are two statements : Statement (I) : Dimensions of specific heat is $[\text{L}^2 \text{T}^{-2} \text{K}^{-1}]$. Statement (II) : Dimensions of gas constant is $[\text{ML}^2 \text{T}^{-1} \text{K}^{-1}]$. In the light of the above statements, choose the most appropriate answer from the options given below.

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_1$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_2$. Time required to reach the ground, if it is dropped from the top of the tower, is :

A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if $g = 10$ m/$s^2$) :

A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking $30^\circ$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely : $\left( g = 10 \text{ m/s}^2, \sqrt{3} = 1.73 \right)$

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at $R/4$ depth under surface of earth ?

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : R = Radius of bubble S = Surface tension of bubble)

A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^\circ$C. The work done by the gas is: Given, R = 8.3 J $K^{-1}$ mo$l^{-1}$.

Energy of 10 non rigid diatomic molecules at temperature $T$ is :

Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force 16 N. A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between P and S is :

The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is : ( Given $e = 1.6 \times 10^{-19}$C)

Match List-I with List-II :
Choose the correct answer from the options given below :

In a coil, the current changes from $-2$ A to $+2$ A in 0.2 s and induces an emf of 0.1 V. The self inductance of the coil is :

In the given electromagnetic wave $E_y = 600 \sin(\omega t - kx)Vm^{-1}$, intensity of the associated light beam is (in W/$m^2$ : (Given $\epsilon_0 = 9 \times 10^{-12}C^2$ $N^{-1}$ $m^{-2}$ )

In finding out refractive index of glass slab the following observations were made through travelling microscope: 50 vernier scale division = 49 MSD; 20 divisions on main scale in each cm. For mark on paper MSR = 8.45 cm, VC = 26. For mark on paper seen through slab MSR = 7.12 cm, VC = 41. For powder particle on the top surface of the glass slab MSR = 4.05 cm, VC = 1. (MSR = Main Scale Reading, VC = Vernier Coincidence). Refractive index of the glass slab is :

For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm. The refractive index of the material is :

When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13eV, electron emission takes place. The stopping potential is: (Given hc $= 1240$eVnm )

The longest wavelength associated with Paschen series is : (Given $R_H = 1.097 \times 10^7$SI unit)

The acceptor level of a p-type semiconductor is 6eV. The maximum wavelength of light which can create a hole would be : Given hc $= 1242$eVnm.

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\text{th}}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ?

A particle moves in a straight line so that its displacement x at any time t is given by $x^2 = 1 + t^2$. Its acceleration at any time t is $x^{-n}$ where n = ___________

Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m. The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be _______ kg$m^2$.

A wire of cross sectional area A, modulus of elasticity $2 \times 10^{11}Nm^{-2}$ and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle $\theta = \frac{1}{100}$ radian on the points of support. The value of A is _______ $\times 10^{-4}$ $m^2$ (consider $x << L$). (given : g $= 10$ m/$s^2$ )

Two open organ pipes of lengths 60 cm and 90 cm resonate at $6^{\text{th}}$ and $5^{\text{th}}$ harmonics respectively. The difference of frequencies for the given modes is _______ Hz. (Velocity of sound in air $= 333$ m/s )

A capacitor of $10\mu$F capacitance whose plates are separated by 10 mm through air and each plate has area 4 c$m^2$ is now filled equally with two dielectric media of $K_1 = 2$, $K_2 = 3$ respectively as shown in figure. If new force between the plates is 8 N. The supply voltage is _______ $\times 10^{-4}$ V.

In the given figure an ammeter A consists of a 240$\Omega$ coil connected in parallel to a 10$\Omega$ shunt. The reading of the ammeter is _______ mA.

A coil having 100 turns, area of $5 \times 10^{-3}$ $m^2$, carrying current of 1 mA is placed in uniform magnetic field of 0.20 T such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^\circ$ is _______ $\mu$J.

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 25nF. If resistance of 200$\Omega$ and 100mH inductor is being used in the given circuit. The frequency of ac source is _______ $\times 10^3$ Hz. (given $\pi^2 = 10$ )

Two coherent monochromatic light beams of intensities I and 4I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is xI. The value of x is _______.

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _______ nm. (Given hc $= 1245$eVnm, e $= 1.6 \times 10^{-19}$C ).

Molality ( m ) of 3M aqueous solution of NaCl is : (Given : Density of solution $= 1.25$ g m$L^{-1}$, Molar mass in gmo$l^{-1}$ : Na $- 23$, Cl $- 35.5$)

The ratio $\dfrac{K_P}{K_C}$ for the reaction : $\text{CO}_{(g)} + \frac{1}{2}\text{O}_{2(g)} \rightleftharpoons \text{CO}_{2(g)}$ is :

Match List - I with List - II.

The number of ions from the following that are expected to behave as oxidising agent is :
$\text{Sn}^{4+},\ \text{Sn}^{2+},\ \text{Pb}^{2+},\ \text{Tl}^{3+},\ \text{Pb}^{4+},\ \text{Tl}^{+}$

Evaluate the following statements related to group 14 elements for their correctness. (A) Covalent radius decreases down the group from C to Pb in a regular manner. (B) Electronegativity decreases from C to Pb down the group gradually. (C) Maximum covalence of C is 4 whereas other elements can expand their covalence due to presence of d orbitals. (D) Heavier elements do not form p$\pi - p\pi$ bonds. (E) Carbon can exhibit negative oxidation states. Choose the correct answer from the options given below :

The correct statement among the following, for a "chromatography" purification method is :

The incorrect statement regarding the geometrical isomers of 2-butene is :

How can an electrochemical cell be converted into an electrolytic cell?

Arrange the following elements in the increasing order of number of unpaired electrons in it. (A) Sc (B) Cr (C) V (D) Ti (E) Mn Choose the correct answer from the options given below :