JEE Main 2022 · 25 Jun 2022 · Shift 2

Q1.Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R . If A and B reached the maximum height …

Q2.Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $X_P(t)=\alpha t+\beta t^2$ and ${\mathrm{X}}_{\mathrm{Q}}(\mathrm{t})=\mathrm{ft}-{\mathrm{t}}^2$. At what time, both the buses have same velocity?

Q3.A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and th …

Q4.A solid metallic cube having total surface area 24 ${\mathrm{m}}^2$ is uniformly heated. If its temperature is increased by $10^{\circ }\mathrm{C}$, calculate the increase in volume of the cube (Given : $\alpha =5.0\times 10^{-4}{}^{\circ }{\mathrm{C}}^{-1}$ )

Q5.A copper block of mass 5.0 kg is heated to a temperature of $500^{\circ }\mathrm{C}$ and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper: $0.39{\mathrm{Jg}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$ and latent heat of fusion of …

Q6.The ratio of specific heats $\left(\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}\right)$ in terms of degree of freedom (f) is given by:

Q7.For a particle in uniform circular motion, the acceleration $\overrightarrow{\mathrm{a}}$ at any point $\mathrm{P}(\mathrm{R},\theta )$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive x -axis and v is uniform speed) :

Q8.Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacita …

Q9.Two cells of same emf but different internal resistances $r_1$ and $r_2$ are connected in series with a resistance $R$. The value of resistance $R$, for which the potential difference across second cell is zero, is

Q10.Given below are two statements:

Statement-I: Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature.
Statement - II: Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic …

Q11.A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

Q12.A sinusoidal voltage $\mathrm{V}(\mathrm{t})=210\sin 3000\mathrm{t}$ volt is applied to a series LCR circuit in which L $=10\mathrm{mH},\mathrm{C}=25\mu \mathrm{F}$ and $\mathrm{R}=100\Omega$. The phase difference $(\Phi )$ between the applied voltage and resultant …

Q13.The electromagnetic waves travel in a medium at a speed of $2.0\times 10^8\mathrm{m}/\mathrm{s}$. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:

Q14.The interference pattern is obtained with two coherent light sources of intensity ratio $4:1$. And the ratio $\frac{I_{\text{max }}+I_{\text{min }}}{I_{\text{max }}-I_{\text{min }}}$ is $\frac{5}{x}$. Then, the value of $x$ will be equal to:

Q15.A light whose electric field vectors are completely removed by using a good Polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

Q16.A proton, a neutron, an electron and an $\alpha$-particle have same energy. If ${\lambda }_{\mathrm{p}},{\lambda }_{\mathrm{n}},{\lambda }_{\mathrm{e}}$ and ${\lambda }_{\alpha }$ are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose t …

Q17.Which of the following figure represents the variation of $\ln \left(\frac{\mathrm{R}}{{\mathrm{R}}_0}\right)$ with $\ln \mathrm{A}$ (If $\mathrm{R}=$ radius of a nucleus and $\mathrm{A}=$ its mass number)

Q18.Match List I with List II

Choose the correct answer from the following options:

Q19.If n represents the actual number of deflections in a converted galvanometer of resistance G and shunt resistance S. Then the total current I when its figure of merit is K will be:

Q20.For $z=a^2{x}^3{y}^{\frac{1}{2}}$, where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are $4\%$ and $12\%$, respectively, then the percentage error for 'z' will be ____%.

Q21.A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be $30\mathrm{m}/\mathrm{s}$ without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maxi …

Q22.A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force $\mathrm{F}=\sqrt{\mathrm{x}}\mathrm{N}$ as shown in figure. The value of $x=$ _____.

Q23.Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius '$2\mathrm{R}$' are as follows:
${\mathrm{I}}_1=$ M.I. of solid sphere about its diameter
${\mathrm{I}}_2=$ M.I. of solid cylinder about its axis
${\mathrm{I}}_3=$ M.I. of solid circular disc about its diame …

Q24.Two satellites $S_1$ and $S_2$ are revolving in circular orbits around a planet with radius $R_1=3200\mathrm{km}$ and $R_2=800\mathrm{km}$ respectively. The ratio of speed of satellite $S_1$ to the speed of satellite $S_2$ in their respective orbits would be …

Q25.When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ }\mathrm{C}$, its pressure increase by $0.4\%$. The initial temperature of the gas is $\_\_\_\_$ K.

Q26.27 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be $\_\_\_\_$ V.

Q27.The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be $\_\_\_\_$ %.

Q28.In a series LCR circuit, the inductance, capacitance and resistance are $L=100\mathrm{mH}$, $C=100\mu \mathrm{F}$ and $R=10\Omega$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be …

Q29.In an experiment of CE configuration of n-p-n transistor, the transfer characteristics are observed as given in figure.

If the input resistance is $200\Omega$ and output resistance is $60\Omega$ the voltage gain in this experiment will be $\_\_\_\_$

Q1.The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is:
[Given: The threshold frequency of platinum is $1.3\times 10^{15}{\mathrm{s}}^{-1}$ and $\mathrm{h}=6.6\times 10^{-34}\mathrm{J}\mathrm{s}$.]

Q2.At $25^{\circ }\mathrm{C}$ and 1 atm pressure, the enthalpy of combustion of benzene (l) and acetylene (g) are $-3268\mathrm{kJ}{\mathrm{mol}}^{-1}$ and $-1300\mathrm{kJ}{\mathrm{mol}}^{-1}$, respectively. The change in enthalpy for the reaction …

Q3.Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 g of water, it depresses the freezing point by $0.2^{\circ }\mathrm{C}$. The percentage association of solute A in water, is
[Given : Molar mass of $\mathrm{A}=93\mathrm{g}{\mathrm{mol}}^{-1}$. Molal depr …

Q4.The ${\mathrm{K}}_{\mathrm{sp}}$ for bismuth sulphide $({\mathrm{Bi}}_2{\mathrm{S}}_3)$ is $1.08\times 10^{-73}$. The solubility of ${\mathrm{Bi}}_2{\mathrm{S}}_3$ in $\mathrm{mol}{\mathrm{L}}^{-1}$ at 298 K is

Q5.Match List I with List II.

List I
A. Zymase
B. Diastase
C. Urease
D. Pepsin

List II
I. Stomach
II. Yeast
III. Malt
IV. Soyabean

Choose the correct answer from the options given below:

Q6.The correct order of electron gain enthalpies of Cl, $\mathrm{F}$, $\mathrm{Te}$ and Po is

Q7.Given below are two statements.

Statement I: During electrolytic refining, blister copper deposits precious metals

Statement II: In the process of obtaining pure copper by electrolysis method, copper blister is used to make the anode.

In the light of the above statements, choo …

Q8.Given below are two statements one is labelled as Assertion A and the other is labelled as Reason R:

Assertion A : The amphoteric nature of water is explained by using Lewis acid/base concept.
Reason R: Water acts as an acid with ${\mathrm{NH}}_3$ and as a base with …

Q9.The correct order of reduction potentials of the following pairs is
A. ${\mathrm{Cl}}_2/{\mathrm{Cl}}^{-}$
B. ${\mathrm{I}}_2/{\mathrm{I}}^{-}$
C. ${\mathrm{Ag}}^{+}/\mathrm{Ag}$
D. ${\mathrm{Na}}^{+}/\mathrm{Na}$
E. ${\mathrm{Li}}^{+}/\mathrm{Li}$

Choose the correct answer from …

Q10.The number of bridged oxygen atoms present in compound B formed from the following reactions is
$\mathrm{Pb}({\mathrm{NO}}_3{)}_2\stackrel{673\mathrm{K}}{\to }\mathrm{A}+\mathrm{PbO}+{\mathrm{O}}_2$
$\mathrm{A}\stackrel{\text{ Dimerise }}{\to }\mathrm{B}$

Q11.The metal ion (in gaseous state) with lowest spin-only magnetic moment value is

Q12.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Polluted water may have a value of BOD of the order of 17 ppm.

Reason R: BOD is a measure of oxygen required to oxidise both the biodegradable and non-biodegradable …

Q13.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: A mixture contains benzoic acid and napthalene. The pure benzoic acid can be separated out by the use of benzene.
Reason R: Benzoic acid is soluble in hot water.
In …

Q14.During halogen test, sodium fusion extract is boiled with concentrated ${\mathrm{HNO}}_3$ to

Q15.Amongst the following, the major product of the given chemical reaction is

Q16.In the given reaction 'A' can be

Q17.Which of the following conditions or reaction sequence will NOT give acetophenone as the major product?
(A) (a) (see structure)
(b) ${\mathrm{Na}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7,{\mathrm{H}}^{+}$
(B) (see structure)
(b) PCC, DCM
(C) (see structure)
(D) (see structure) …

Q18.Which of the following ketone will NOT give enamine on treatment with secondary amines? [where t-Bu is $-\mathrm{C}{\left({\mathrm{CH}}_3\right)}_3$]

Q19.An antiseptic dettol is a mixture of two compounds 'A' and 'B' where A has $6\pi$ electrons and B has $2\pi$ electrons. What is 'B'?

Q20.A protein 'A' contains $0.30\%$ of glycine (molecular weight 75). The minimum molar mass of the protein 'A' is $\_\_\_\_$ $\times 10^3\mathrm{g}{\mathrm{mol}}^{-1}$ [nearest integer]

Q21.A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is $27^{\circ }\mathrm{C}$. At 03:00 pm, when the temperature is $45^{\circ }\mathrm{C}$, the pressure in the tank will be $\_\_\_\_$ atm. [nearest integer]

Q22.Amongst ${\mathrm{BeF}}_2,{\mathrm{BF}}_3,{\mathrm{H}}_2\mathrm{O},{\mathrm{NH}}_3,{\mathrm{CCl}}_4$ and HCl, the number of molecules with non-zero net dipole moment is $\_\_\_\_$.

Q23.At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is $\_\_\_\_$. [integer answer]

Q24.A solution of ${\mathrm{Fe}}_2({\mathrm{SO}}_4{)}_3$ is electrolyzed for 'x' min with a current of 1.5 A to deposit 0.3482 g of Fe.

The value of $x$ is ______. [nearest integer]
Given: $1\mathrm{F}=96500\mathrm{C}{\mathrm{mol}}^{-1}$
Atomic mass of …

Q25.Consider the following reactions:
${\mathrm{PCl}}_3+{\mathrm{H}}_2\mathrm{O}⟶\mathrm{A}+\mathrm{HCl}$
$\mathrm{A}+{\mathrm{H}}_2\mathrm{O}⟶\mathrm{B}+\mathrm{HCl}$
number of ionisable protons present in the product B ______.

Q26.Amongst ${\mathrm{FeCl}}_3.3{\mathrm{H}}_2\mathrm{O}$, ${\mathrm{K}}_3[\mathrm{Fe}(\mathrm{CN}{)}_6]$ and $[\mathrm{Co}({\mathrm{NH}}_3{)}_6]{\mathrm{Cl}}_3$, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is ______ B.M. …

Q27.The Novolac polymer has mass of 963 g. The number of monomer units present in it are ______.

Q28.How many of the given compounds will give a positive Biuret test ______?
Glycine, Glycylalanine, Tripeptide, Biuret

Q29.The neutralization occurs when 10 mL of 0.1 M acid 'A' is allowed to react with 30 mL of 0.05 M base $\mathrm{M}(\mathrm{OH}{)}_2$. The basicity of the acid 'A' is ______. [M is a metal]

Q1.Let $A=\{x\in R:|x+1|<2\}$ and
$B=\{x\in R:|x-1|\ge 2\}$. Then which one of the following statements is NOT true ?

Q2.Let $\mathrm{a},\mathrm{b}\in \mathrm{R}$ be such that the equation ${\mathrm{ax}}^2-2\mathrm{bx}+15=0$ has a repeated root $\alpha$. If $\alpha$ and $\beta$ are the roots of the equation $x^2-2bx+21=0$, then ${\alpha }^2+{\beta }^2$ is equal to:

Q3.Let ${\mathrm{z}}_1$ and ${\mathrm{z}}_2$ be two complex numbers such that ${\overline{\mathrm{z}}}_1=\mathrm{i}{\overline{\mathrm{z}}}_2$ and $\arg \left(\frac{{\mathrm{z}}_1}{{\overline{\mathrm{z}}}_2}\right)=\pi$. Then

Q4.The system of equations
$-kx+3y-14z=25$
$-15x+4y-kz=3$
$-4x+y+3z=4$
is consistent for all k in the set

Q5.${\lim }_{\mathrm{x}\to \frac{\pi }{2}}\left({\tan }^2\mathrm{x}\left({\left(2{\sin }^2\mathrm{x}+3\sin \mathrm{x}+4\right)}^{\frac{1}{2}}-{\left({\sin }^2\mathrm{x}+6\sin \mathrm{x}+2\right)}^{\frac{1}{2}}\right)\right)$ is equal to

Q6.The area of the region enclosed between the parabolas ${\mathrm{y}}^2=2\mathrm{x}-1$ and ${\mathrm{y}}^2=4\mathrm{x}-3$ is

Q7.The coefficient of $x^{101}$ in the expression $(5+x{)}^{500}+x(5+x{)}^{499}+x^2(5+x{)}^{498}+\dots ..x^{500}$, $\mathrm{x}>0$, is

Q8.The sum $1+2\cdot 3+3\cdot 3^2+\dots ..+10\cdot 3^9$ is equal to

Q9.Let P be the plane passing through the intersection of the planes
$\vec{r}\cdot (\hat{i}+3\hat{j}-\hat{k})=5$ and $\vec{r}\cdot (2\hat{i}-\hat{j}+\hat{k})=3$, and the point $(2,1,-2)$. Let the position vectors of the points $X$ and $Y$ be $\hat{i}-2\hat{j}+4\hat{k}$ and …

Q10.A circle touches both the y -axis and the line $x+y=0$. Then the locus of its center is

Q11.Water is being filled at the rate of $1{\mathrm{cm}}^3/\sec$ in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm . When the height of the water level is 10 cm , the rate ( $\mathrm{in}{\mathrm{cm}}^2/\sec$ ) at which the …

Q12.If $b_n={\int }_0^{\frac{\pi }{2}}\frac{{\cos }^{2}nx}{\sin x}dx,n\in N$, then

Q13.If $y=y(x)$ is the solution of the differential equation $2x^2\frac{dy}{dx}-2xy+3y^2=0$ such that $y(e)=\frac{e}{3}$, then $y(1)$ is equal to

Q14.If the angle made by the tangent at the point $(x_0,y_0)$ on the curve $x=12(t+\sin t\cos t)$, $y=12(1+\sin t{)}^2$, $0<t<\frac{\pi }{2}$, with the positive $x$-axis is $\frac{\pi }{3}$, then $y_0$ is equal to

Q15.The value of $2\sin (12^{\circ })-\sin (72^{\circ })$ is :

Q16.A biased die is marked with numbers $2,4,8,16$, 32, 32 on its faces and the probability of getting a face with mark $n$ is $\frac{1}{n}$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 , is

Q17.The negation of the Boolean expression $((\sim q)\wedge p)\Rightarrow ((\sim p)\vee q)$ is logically equivalent to

Q18.If the line $y=4+kx,k>0$, is the tangent to the parabola $y=x-x^2$ at the point P and V is the vertex of the parabola, then the slope of the line through P and V is :

Q19.The value of ${\tan }^{-1}\left(\frac{\cos \left(\frac{15\pi }{4}\right)-1}{\sin \left(\frac{\pi }{4}\right)}\right)$ is equal to

Q20.The line $y=x+1$ meets the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$ at two points P and Q . If r is the radius of the circle with PQ as diameter then $(3r{)}^2$ is equal to

Q21.Let $A=\left(\begin{array}{ll}2& -2\\ 1& -1\end{array}\right)$ and $B=\left(\begin{array}{ll}-1& 2\\ -1& 2\end{array}\right)$. Then the number of elements in the set
$\{(n,m):n,m\in \{1,2,\dots ,10\}$ and $n{A}^n+m{B}^m=I\}$
is

Q22.Let $f(x)=[2x^2+1]$ and $g(x)=\{\begin{array}{ll}2x-3,& x<0\\ 2x+3,& x\ge 0\end{array}$, where $[t]$ is the greatest integer $\le t$. Then, in the open interval $(-1,1)$, the number of points where fog is discontinuous is equal to

Q23.The value of $b>3$ for which
$12{\int }_3^b\frac{1}{(x^2-1)(x^2-4)}dx={\log }_e\left(\frac{49}{40}\right)$, is equal to

Q24.If the sum of the coefficients of all the positive even powers of x in the binomial expansion of ${\left(2x^3+\frac{3}{x}\right)}^{10}$ is $5^{10}-\beta \cdot 3^9$, then $\beta$ is equal to

Q25.If the mean deviation about the mean of the numbers $1,2,3,\dots ,n$, where $n$ is odd, is $\frac{5(n+1)}{n}$, then n is equal to

Q26.Let $\vec{b}=\hat{i}+\hat{j}+\lambda \hat{k},\lambda \in R$. If $\vec{a}$ is a vector such that $\vec{a}\times \vec{b}=13\hat{i}-\hat{j}-4\hat{k}$ and $\vec{a}\cdot \vec{b}+21=0$, then $(\vec{b}-\vec{a})\cdot (\hat{k}-\hat{j})+(\vec{b}+\vec{a})\cdot (\hat{i}-\hat{k})$ is equ …

Q27.The total number of three-digit numbers, with one digit repeated exactly two times, is

Q28.Let $f(x)=\left|(x-1)\left(x^2-2x-3\right)\right|+x-3,x\in R$. If $m$ and $M$ are respectively the number of points of local minimum and local maximum of $f$ in the interval $(0,4)$, then $m+M$ is equal to

Q29.Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\frac{5}{4}$. If the equation of the normal at the point $\left(\frac{8}{\sqrt{5}},\frac{12}{5}\right)$ on the hyperbola is $8\sqrt{5}x+\beta y=\lambda$, then $\lambda -\beta$ is equal to

Q30.Let $l_1$ be the line in xy-plane with x and y intercepts $\frac{1}{8}$ and $\frac{1}{4\sqrt{2}}$ respectively, and $l_2$ be the line in zx-plane with x and z intercepts $-\frac{1}{8}$ and $-\frac{1}{6\sqrt{3}}$ respectively. If d is the shortest distance between the line …