JEE Main 2022 June 24, Shift 1 Question Paper with Solutions

Identify the pair of physical quantities which have different dimensions:

A projectile is projected with velocity of $25\ \text{m s}^{-1}$ at an angle $\theta$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $\theta$ will be : [use use $g = 10\ \text{m s}^{-2}$]

A boy ties a stone of mass $100\ \text{g}$ to the end of a $2\ \text{m}$ long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $80\ \text{N}$. If the maximum speed with which the stone can revolve is $\frac{K}{\pi}\ \text{rev.\ min}^{-1}$. The value of K is : (Assume the string is massless and un-stretchable)

A block of mass $10\ \text{kg}$ starts sliding on a surface with an initial velocity of $9.8\ \text{ms}^{-1}$. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is :[use $g = 9.8\ \text{m s}^{-2}$]

A particle experiences a variable force $\vec{F} = \left(4x\hat{i} + 3y^2\hat{j}\right)$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point $(1,2)$ to point $(2,3)$ in the $x - y$ plane, then Kinetic Energy changes by :

The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is : [Radius of earth $R = 6400\ \text{km}$ and $\sqrt{3} = 1.732$]

The bulk modulus of a liquid is $3 \times 10^{10}\ \text{Nm}^{-2}$. The pressure required to reduce the volume of liquid by $2\%$ is :

Two metallic blocks $M_1$ and $M_2$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_2$ is K then the thermal conductivity of $M_1$ will be : [Assume steady state heat conduction]

A Carnot engine whose heat sinks at $27^\circ C$, has an efficiency of $25\%$. By how many degrees should the temperature of the source be changed to increase the efficiency by $100\%$ of the original efficiency ?

The equations of two waves are given by : $y_1 = 5\sin 2\pi(x - vt)\ \text{cm}$ $y_2 = 3\sin 2\pi(x - vt + 1.5)\ \text{cm}$ These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

A vertical electric field of magnitude $4.9 \times 10^5\ \text{N C}^{-1}$ just prevents a water droplet of a mass $0.1\ \text{g}$ from falling. The value of charge on the droplet will be : (Given $g = 9.8\ \text{m s}^{-2}$)

A parallel plate capacitor is formed by two plates each of area $30\pi\ \text{cm}^2$ separated by $1\ \text{mm}$. A material of dielectric strength $3.6 \times 10^7\ \text{V m}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6}\ \text{C}$, the value of dielectric constant of the material is : [Use $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\ \text{N m}^2\,\text{C}^{-2}$]

Two identical cells each of emf $1.5\ \text{V}$ are connected in parallel across a parallel combination of two resistors each of resistance $20\ \Omega$. A voltmeter connected in the circuit measures $1.2\ \text{V}$. The internal resistance of each cell is :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R): Moving charged particle experiences magnetic force perpendicular to its direction of motion.

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre is :

A resistance of $40\ \Omega$ is connected to a source of alternating current rated $220\ \text{V},\ 50\ \text{Hz}$. Find the time taken by the current to change from its maximum value to the rms value :

A plane electromagnetic wave travels in a medium of relative permeability $1.61$ and relative permittivity $6.44$. If magnitude of magnetic intensity is $4.5 \times 10^{-2}\ \text{A m}^{-1}$ at a point, what will be the approximate magnitude of electric field intensity at that point ?
(Given : Permeability of free space $\mu_0 = 4\pi \times 10^{-7}\ \text{N A}^{-2}$, speed of light in vacuum $c = 3 \times 10^8\ \text{m s}^{-1}$)

Choose the correct option from the following options given below :

Nucleus A having mass number $220$ and its binding energy per nucleon is $5.6\ \text{MeV}$. It splits in two fragments B and C of mass numbers $105$ and $115$. The binding energy of nucleons in B and C is $6.4\ \text{MeV}$ per nucleon. The energy Q released per fission will be :

A baseband signal of $3.5\ \text{MHz}$ frequency is modulated with a carrier signal of $3.5\ \text{GHz}$ frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal ?

From the top of a tower, a ball is thrown vertically upward which reaches the ground in $6\ \text{s}$. A second ball thrown vertically downward from the same position with the same speed reaches the ground in $1.5\ \text{s}$. A third ball released, from the rest from the same location, will reach the ground in _____ s.

A ball of mass $100\ \text{g}$ is dropped from a height $h = 10\ \text{cm}$ on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is _____ $\text{N m}^{-1}$.
(Use $g = 10\ \text{m s}^{-2}$)

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass $10\ \text{g}$ are put one on the top of the other at the $10.0\ \text{cm}$ mark the scale is found to be balanced at $40.0\ \text{cm}$ mark. The mass of the metre scale is found to be $x \times 10^{-2}\ \text{kg}$. The value of x is _____ .

$0.056\ \text{kg}$ of Nitrogen is enclosed in a vessel at a temperature of $127^\circ\text{C}$. The amount of heat required to double the speed of its molecules is _____ kcal.
(Take $R = 2\ \text{cal mole}^{-1}\ \text{K}^{-1}$)

In a potentiometer arrangement, a cell gives a balancing point at $75\ \text{cm}$ length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is $3:2$, the difference in the balancing length of the potentiometer wire in above two cases will be _____ cm.

As shown in the figure an inductor of inductance $200\ \text{mH}$ is connected to an AC source of emf $220\ \text{V}$ and frequency $50\ \text{Hz}$. The instantaneous voltage of the source is $0\ \text{V}$ when the peak value of current is $\frac{\sqrt{a}}{\pi}\ \text{A}$. The value of a is _____ .

Two identical thin biconvex lenses of focal length $15\ \text{cm}$ and refractive index $1.5$ are in contact with each other. The space between the lenses is filled with a liquid of refractive index $1.25$. The focal length of the combination is _____ cm.

Sodium light of wavelengths $650\ \text{nm}$ and $655\ \text{nm}$ is used to study diffraction at a single slit of aperture $0.5\ \text{mm}$. The distance between the slit and the screen is $2.0\ \text{m}$. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _____ $\times 10^{-5}\ \text{m}$.

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is $v_1$. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes $v_2$. If $v_2 = xv_1$, the value of x will be _____ .

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of $10\ \text{mV}$ is added to the base-emitter voltage, the base current changes by $10\,\mu\text{A}$ and the collector current changes by $1.5\ \text{mA}$. The load resistance is $5\,\text{k}\Omega$. The voltage gain of the transistor will be _____ .

If a rocket runs on a fuel $(\text{C}_{15}\text{H}_{30})$ and liquid oxygen, the weight of oxygen required and $\text{CO}_2$ released for every litre of fuel respectively are : (Given : density of the fuel is $0.756\ \text{g/mL}$)

Consider the following pairs of electrons : (A) (a) $\text{n} = 3,\ l = 1,\ m_l = 1,\ m_s = +\frac{1}{2}$ (b) $\text{n} = 3,\ l = 2,\ m_l = 1,\ m_s = +\frac{1}{2}$ (B) (a) $\text{n} = 3,\ l = 2,\ m_l = -2,\ m_s = -\frac{1}{2}$ (b) $\text{n} = 3,\ l = 2,\ m_l = -1,\ m_s = -\frac{1}{2}$ (C) (a) $\text{n} = 4,\ l = 2,\ m_l = 2,\ m_s = +\frac{1}{2}$ (b) $\text{n} = 3,\ l = 2,\ m_l = 2,\ m_s = +\frac{1}{2}$ The pairs of electrons present in degenerate orbitals is/are :

For a reaction at equilibrium $\text{A}(g) \rightleftharpoons \frac{1}{2}\text{B}(g) + \frac{3}{2}\text{C}(g)$ the relation between dissociation constant (K), degree of dissociation $(\alpha)$ and equilibrium pressure (p) is given by :

The highest industrial consumption of molecular hydrogen is to produce compound of element :