JEE Main 2022 · 28 Jul 2022 · Shift 2

Q1.Consider the efficiency of Carnot's engine is given by $\eta =\frac{\alpha \beta }{\sin \theta }{\log }_{\mathrm{e}}\frac{\beta \mathrm{x}}{\mathrm{kT}}$, where $\alpha$ and $\beta$ are constants. If T is temperature, k is Boltzman constant, $\theta$ is angular displacement …

Q2.At time $\mathrm{t}=0$ a particle starts travelling from a height $7\hat{\mathrm{z}}\mathrm{cm}$ in a plane keeping z coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3t$ and $5t^3$ respectively. At …

Q3.A pressure-pump has a horizontal tube of cross-sectional area $10{\mathrm{cm}}^2$ for the outflow of water at a speed of $20\mathrm{m}/\mathrm{s}$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, i …

Q4.A uniform metal chain of mass m and length ' L ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' $l$ ' is hanging on one side and rest of its length ' $\mathrm{L}-l$ ' is hanging on the other side of the pulley. At a certai …

Q5.A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is

Q6.Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4 s and 6 s respectively. Then the value of h is (consider radius of …

Q7.Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of $5\times 10^5\mathrm{N}$ is applied an the top surfac …

Q8.A vessel contains 14 g of nitrogen gas at a temperature of $27^{\circ }\mathrm{C}$. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take $\mathrm{R}=8.32\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{k}}^{-1}$ )

Q9.A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4}\mathrm{d}$, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be …

Q10.A uniform electric field $\mathrm{E}=(8\mathrm{m}/\mathrm{e})\mathrm{V}/\mathrm{m}$ is created between two parallel plates of length 1 m as shown in figure, (where $\mathrm{m}=$ mass of electron and $\mathrm{e}=$ charge of electron). An electron enters the field symm …

Q11.Given below are two statements :

Statement I : A uniform wire of resistance $80\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5\Omega$.

Statement II : Two resistance 2 R and 3 R are co …

Q12.A triangular shaped wire carrying 10A current is placed in a uniform magnetic field of 0.5 T , as shown in figure. The magnetic force on segment CD is (Given $\mathrm{BC}=\mathrm{CD}=\mathrm{BD}=5\mathrm{cm}$ ).

Q13.The magnetic field at the center of current carrying circular loop is ${\mathrm{B}}_1$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is ${\mathrm{B}}_2$. The value of ${\mathrm{B}}_1/{\mathrm{B}}_2$ will be

Q14.A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

Q15.Sun light falls normally on a surface of area $36{\mathrm{cm}}^2$ and exerts an average force of $7.2\times 10^{-9}\mathrm{N}$ within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is

Q16.The power of a lens (biconvex) is $1.25{\mathrm{m}}^{-1}$ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding medium :

Q17.Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be

Q18.A radioactive sample decays to $\frac{1}{8}$th of its original quantity in 15 minutes. The half-life of the sample is

Q19.An n.p.n transistor with current gain $\beta =100$ in common emitter configuration is shown in figure. The output voltage of the amplifier will be

Q20.A FM Broad cast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth required for transmission is :

Q21.A ball is thrown vertically upwards with a velocity of $19.6{\mathrm{ms}}^{-1}$ from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be $\left(\frac{\mathrm{k}}{5}\right)\mathrm{m}$. The value of k is ..... …

Q22.The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $\rho ={\rho }_0\left(1-\frac{x^2}{L^2}\right)\mathrm{kg}/\mathrm{m}$ and length $L$ (in meter) is $\frac{3\mathrm{L}}{\alpha }\mathrm{m}$. The value of $\alpha$ is ........... (whe …

Q23.A string of area of cross-section $4{\mathrm{mm}}^2$ and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of $5\mathrm{m}/\mathrm{s}$ at the bottom of the circular path. Strain …

Q24.At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.

Q25.The potential energy of a particle of mass 4 kg in motion along the x-axis is given by $U=4(1-\cos 4x)$ J. The time period of the particle for small oscillation $(\sin \theta \simeq \theta )$ is $\left(\frac{\pi }{K}\right)$ s. The value of $K$ is ____

Q26.An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about ____ W.

Q27.For the given circuit the current through battery of 6 V just after closing the switch 'S' will be ____ A.

Q28.An object 'O' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10 s will be at ____ cm.

Q29.In an experiment with a convex lens, the plot of the image distance ($v^{\prime }$) against the object distance ($u^{\prime }$) measured from the focus gives a curve $v^{\prime }{u}^{\prime }=225$. If all the distances are measured in cm, the magnitude of the focal length of the lens is ____ cm.

Q30.In an experiment to find acceleration due to gravity $(g)$ using simple pendulum, time period of 0.5 s is measured from time of 100 oscillations with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, the accuracy in the determination of $g$ i …

Q1.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Zero orbital overlap is an out of phase overlap.

Reason : It results due to different orientation/ direction of approach of orbitals.

In the light of the above st …

Q2.The correct decreasing order for metallic character is

Q3.Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R

Assertion A : The reduction of a metal oxide is easier if the metal formed is in liquid state than solid state.

Reason R : The value of $\Delta {\mathrm{G}}^{\Theta }$ becomes mor …

Q4.The products obtained during treatment of hard water using Clark's method are:

Q5.Statement I: An alloy of lithium and magnesium is used to make aircraft plates.

Statement II : The magnesium ions are important for cell-membrane integrity.

In the light the above statements, choose the correct answer from the options given below

Q6.White phosphorus reacts with thionyl chloride to give

Q7.Concentrated ${\mathrm{HNO}}_3$ reacts with Iodine to give

Q8.Which of the following pair is not isoelectronic species?
(At. no. Sm, 62; Er, 68: Yb, 70: Lu, 71; Eu, 63: Tb, 65; Tm, 69)

Q9.Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Permanganate titrations are not performed in presence of hydrochloric acid.

Reason R: Chlorine is formed as a consequence of oxidation of hydrochloric acid.

In t …

Q10.Dinitrogen and dioxygen. the main constituents of air do not react with each other in atmosphere to form oxides of nitrogen because

Q11.The major product in the given reaction is

Q12.Arrange the following in increasing order of reactivity towards nitration
A. p-xylene
B. bromobenzene
C. mesitylene
D. nitrobenzene
E. benzene

Choose the correct answer from the options given below

Q13.Compound I is heated with Conc. HI to give a hydroxy compound A which is further heated with Zn dust to give compound B. Identify A and B.

Q14.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Aniline on nitration yields ortho, meta & para nitro derivatives of aniline.

Reason R: Nitrating mixture is a strong acidic mixture.

In the light of the above stat …

Q15.Two statements in respect of drug-enzyme interaction are given below
Statement I: Action of an enzyme can be blocked only when an inhibitor blocks the active site of the enzyme.
Statement II: An inhibitor can form a strong covalent bond with the enzyme.
In the light of the above …

Q16.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Thin layer chromatography is an adsorption chromatography.
Reason R: A thin layer of silica gel is spread over a glass plate of suitable size in thin layer chromatog …

Q17.The formulas of A and B for the following reaction sequence are

Q18.Find out the major product for the above reaction.

Q19.2 L of 0.2 M H₂SO₄ is reacted with 2 L of 0.1 M NaOH solution, the molarity of the resulting product Na₂SO₄ in the solution is _____ millimolar. (Nearest integer).

Q20.Metal M crystallizes into a FCC lattice with the edge length of 4.0 × 10⁻⁸ cm. The atomic mass of the metal is _____ g/mol. (Nearest integer).
(Use: Nₐ = 6.02 × 10²³ mol⁻¹, density of metal, M = 9.03 g cm⁻³)

Q21.If the wavelength for an electron emitted from H atom is 3.3 × 10⁻¹⁰ m, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is _____ times. (Nearest integer).
[Given: h = 6.626 × 10⁻³⁴ Js, Mass of electron = 9 …

Q22.A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapour phase and 0.2 in the liquid phase. The vapour pressure of pure liquid A is _____ atm. (Nearest int …

Q23.At 600 K, 2 mol of NO are mixed with 1 mol of O₂.
2NO₍ₘ₎ + O₂₍ₘ₎ ⇌ 2NO₂₍ₘ₎
The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reacti …

Q24.A sample of 0.125 g of an organic compound when analysed by Duma's method yields 22.78 mL of nitrogen gas collected over KOH solution at 280 K and 759 mm Hg . The percentage of nitrogen in the given organic compound is ____. (Nearest integer).
(a) The vapour pressure of water at …

Q25.On reaction with stronger oxidizing agent like ${\mathrm{KIO}}_4$, hydrogen peroxide oxidizes with the evolution of ${\mathrm{O}}_2$. The oxidation number of I in ${\mathrm{KIO}}_4$ changes to ____.

Q26.For a reaction, given below is the graph of $\ln \mathrm{k}$ vs $\frac{1}{\mathrm{T}}$. The activation energy for the reaction is equal to ____ cal mol${}^{-1}$. (Nearest integer).
(Given : $\mathrm{R}=2\mathrm{cal}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$)

Q27.Among the following the number of curves not in accordance with Freundlich adsorption isotherm is ____.

Q28.Among the following the number of state variable is ____.
Internal energy (U)
Volume (V)
Heat (q)
Enthalpy (H)

Q1.Let $S=\left\{x\in [-6,3]-\{-2,2\}:\frac{|x+3|-1}{|x|-2}\ge 0\right\}$ and $T=\left\{x\in Z:x^2-7|x|+9\le 0\right\}$. Then the number of elements in $\mathrm{S}\cap \mathrm{T}$ is

Q2.Let $\alpha ,\beta$ be the roots of the equation $x^2-\sqrt{2}x+\sqrt{6}=0$ and $\frac{1}{{\alpha }^2}+1,\frac{1}{{\beta }^2}+1$ be the roots of the equation $x^2+ax+b=0$. Then the roots of the equation …

Q3.Let A and B be any two $3\times 3$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

Q4.Let $\mathrm{f}(\mathrm{x})={\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$ be such that $\mathrm{f}(1)=3,\mathrm{f}(-2)=\lambda$ and $\mathrm{f}(3)=4$. If $\mathrm{f}(0)+\mathrm{f}(1)+\mathrm{f}(-2)+\mathrm{f}(3)=14$, then $\lambda$ is equal to

Q5.The function $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ defined by
$f(x)={\lim }_{n\to \infty }\frac{\cos (2\pi x)-x^{2n}\sin (x-1)}{1+x^{2n+1}-x^{2n}}$ is
continuous for all x in

Q6.The function $\mathrm{f}(\mathrm{x})={\mathrm{xe}}^{\mathrm{x}(1-\mathrm{x})},\mathrm{x}\in \mathrm{R}$, is

Q7.The sum of the absolute maximum and absolute minimum values of the function $f(x)={\tan }^{-1}(\sin x-\cos x)$ in the interval $[0,\pi ]$ is

Q8.Let $x(t)=2\sqrt{2}\cos t\sqrt{\sin 2t}$ and
$y(t)=2\sqrt{2}\sin t\sqrt{\sin 2t},t\in \left(0,\frac{\pi }{2}\right)$. Then $\frac{1+{\left(\frac{dy}{dx}\right)}^2}{\frac{d^{2}y}{d{x}^2}}$ at $t=\frac{\pi }{4}$ is equal to

Q9.Let ${\mathrm{I}}_{\mathrm{n}}(\mathrm{x})={\int }_0^{\mathrm{x}}\frac{1}{{\left({\mathrm{t}}^2+5\right)}^{\mathrm{n}}}\mathrm{dt},\mathrm{n}=1,2,3,\dots$. Then

Q10.The area enclosed by the curves $y={\log }_e\left(x+e^2\right)$, $x={\log }_e\left(\frac{2}{y}\right)$ and $x={\log }_{e}2$, above the line $y=1$ is

Q11.Let $y=y(x)$ be the solution curve of the differential equation $\frac{dy}{dx}+\frac{1}{x^2-1}y={\left(\frac{x-1}{x+1}\right)}^{\frac{1}{2}}$, $x>1$ passing through the point $\left(2,\sqrt{\frac{1}{3}}\right)$. Then $\sqrt{7}y(8)$ is equal to

Q12.The differential equation of the family of circles passing through the points $(0,2)$ and $(0,-2)$ is

Q13.Let the tangents at two points A and B on the circle $x^2+y^2-4x+3=0$ meet at origin $\mathrm{O}(0,0)$. Then the area of the triangle of OAB is

Q14.Let the hyperbola $\mathrm{H}:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ pass through the point $(2\sqrt{2},-2\sqrt{2})$. A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola …

Q15.Let the lines $\frac{x-1}{\lambda }=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{\mathrm{x}+26}{-2}=\frac{\mathrm{y}+18}{3}=\frac{\mathrm{z}+28}{\lambda }$ be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lies on P?

Q16.A plane P is parallel to two lines whose direction ratios are $-2,1,-3$, and $-1,2,-2$ and it contains the point $(2,2,-2)$. Let P intersect the co-ordinate axes at the points $\mathrm{A},\mathrm{B},\mathrm{C}$ making the intercepts $\alpha ,\beta ,\gamma$. If V is th …

Q17.Let S be the set of all $\mathrm{a}\in \mathrm{R}$ for which the angle between the vectors $\overrightarrow{\mathrm{u}}=\mathrm{a}\left({\log }_{\mathrm{e}}\mathrm{b}\right)\hat{\mathrm{i}}-6\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and …

Q18.A horizontal park is in the shape of a triangle OAB with $\mathrm{AB}=16$. A vertical lamp post OP is erected at the point O such that $\angle \mathrm{PAO}=\angle \mathrm{PBO}=15^{\circ }$ and $\angle \mathrm{PCO}=45^{\circ }$, where C is the midpoint of AB. Then …

Q19.Let A and B be two events such that $\mathrm{P}(\mathrm{B}\mid \mathrm{A})=\frac{2}{5}$, $\mathrm{P}(\mathrm{A}\mid \mathrm{B})=\frac{1}{7}$ and $\mathrm{P}(\mathrm{A}\cap \mathrm{B})=\frac{1}{9}$. Consider
(S1) …

Q20.Let
$\mathbf{p}$ : Ramesh listens to music.
q: Ramesh is out of his village
r : It is Sunday
s : It is Saturday
Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as

Q21.Let the coefficients of the middle terms in the expansion of ${\left(\frac{1}{\sqrt{6}}+\beta x\right)}^4,(1-3\beta x{)}^2$ and ${\left(1-\frac{\beta }{2}x\right)}^6,\beta >0$, respectively form the first three terms of an A.P. If d is the common difference of this A.P., the …

Q22.A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then $\mathrm{b}+3\mathrm{g}$ is equal to

Q23.Let the tangents at the points P and Q on the ellipse $\frac{{\mathrm{x}}^2}{2}+\frac{{\mathrm{y}}^2}{4}=1$ meet at the point $\mathrm{R}(\sqrt{2},2\sqrt{2}-2)$. If S is the focus of the ellipse on its negative major axis, then ${\mathrm{SP}}^2+{\mathrm{SQ}}^2$ is equal t …

Q24.If $1+\left(2+{}^{49}{\mathrm{C}}_1+{}^{49}{\mathrm{C}}_2+\dots ..+{}^{49}{\mathrm{C}}_{49}\right)\left({}^{50}{\mathrm{C}}_2+{}^{50}{\mathrm{C}}_4+\dots ..+{}^{50}{\mathrm{C}}_{50}\right)$ is equal to $2^{\mathrm{n}}.\mathrm{m}$, where m is odd, then n +m is eq …

Q25.Two tangent lines $l_1$ and $l_2$ are drawn from the point $(2,0)$ to the parabola $2y^2=-x$. If the lines $l_1$ and $l_2$ are also tangent to the circle $(x-5{)}^2+y^2=r$, then 17 r is equal to

Q26.If $\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+\dots ..+\frac{10240}{3}=2^n\cdot m$, where m is odd, then $\mathrm{m}.\mathrm{n}$ is equal to

Q27.Let $\mathrm{S}=\left[-\pi ,\frac{\pi }{2}\right)-\left\{-\frac{\pi }{2},-\frac{\pi }{4},-\frac{3\pi }{4},\frac{\pi }{4}\right\}$. Then the number of elements in the set
$A=\{\theta \in S:\tan \theta (1+\sqrt{5}\tan (2\theta ))=\sqrt{5}-\tan (2\theta )\}$ is

Q28.Let $z=a+ib,b\ne 0$ be complex numbers satisfying $z^2=\bar{z}\cdot 2^{1-|z|}$. Then the least value of $n\in \mathrm{N}$, such that ${\mathrm{z}}^{\mathrm{n}}=(\mathrm{z}+1{)}^{\mathrm{n}}$, is equal to

Q29.A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If ${\sigma }^2$ is the variance of X , then $100{\sigma }^2$ is equal to

Q30.The value of the integral ${\int }_0^{\frac{\pi }{2}}60\frac{\sin (6x)}{\sin x}dx$ is equal to