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 $\frac{1}{4\pi {\epsilon }_0}=9\times 10^9{\text{N m}}^2{\text{C}}^{-2}$]

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 $v_2=x{v}_1$, 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 :

Which of the following statements are correct ? (A) Both $\text{LiCl}$ and ${\text{MgCl}}_2$ are soluble in ethanol. (B) The oxides ${\text{Li}}_2\text{O}$ and $\text{MgO}$ combine with excess of oxygen to give superoxide. (C) $\text{LiF}$ is less soluble in water than other alkali metal fluorides. (D) ${\text{Li}}_2\text{O}$ is more soluble in water than other alkali metal oxides. Choose the most appropriate answer from the options given below :

Identify the correct statement for ${\text{B}}_2{\text{H}}_6$ from those given below. (A) In ${\text{B}}_2{\text{H}}_6$, all $\text{B}-\text{H}$ bonds are equivalent. (B) In ${\text{B}}_2{\text{H}}_6$, there are four 3-centre- 2-electron bonds. (C) ${\text{B}}_2{\text{H}}_6$ is a Lewis acid. (D) ${\text{B}}_2{\text{H}}_6$ can be synthesized from both ${\text{BF}}_3$ and ${\text{NaBH}}_4$. (E) ${\text{B}}_2{\text{H}}_6$ is a planar molecule. Choose the most appropriate answer from the options given below :

Which of the following is an example of conjugated diketone?

In the given reaction sequence, the major product 'C' is : ${\text{C}}_8{\text{H}}_{10}\underset{{\text{H}}_2{\text{SO}}_4}{\overset{{\text{HNO}}_3}{\to }}\text{A}\underset{\Delta }{\overset{{\text{Br}}_2}{\to }}\text{B}\underset{\text{KOH}}{\overset{\text{alcoholic}}{\to }}\text{C}$

Given below are two statements :
Statement I : Emulsions of oil in water are unstable and sometimes they separate into two layers on standing.
Statement II : For stabilisation of an emulsion, excess of electrolyte is added.
In the light of the above statements, choose the most appropriate answer from the options given below :

Match List - I with List - II :

Given below are the oxides : ${\text{Na}}_2\text{O},{\text{As}}_2{\text{O}}_3,{\text{N}}_2\text{O},\text{NO and }{\text{Cl}}_2{\text{O}}_7$ Number of amphoteric oxides is :

The most stable trihalide of nitrogen is :

Which one of the following elemental forms is not present in the enamel of the teeth?

Match List - I with List - II :