JEE Main 2022 (Online) 28th July Evening Shift

Paper was held on
Thu, Jul 28, 2022 9:30 AM

## Chemistry

Given below are two statements: One is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathb

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The correct decreasing order for metallic character is

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Given below are two statements: One is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathb

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

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Statement I : An alloy of lithium and magnesium is used to make aircraft plates.
Statement II : The magnesium ions are i

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White phosphorus reacts with thionyl chloride to give

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Concentrated $$\mathrm{HNO}_{3}$$ reacts with Iodine to give

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Which of the following pair is not isoelectronic species?
(At. no. Sm, 62; Er, 68; Yb, 70; Lu, 71; Eu, 63; Tb, 65; Tm, 6

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

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Match List I with List II
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Dinitrogen and dioxygen, the main constituents of air do not react with each other in atmosphere to form oxides of nitr

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The major product in the given reaction is

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

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

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Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathb

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Match List I with List II
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.tg td{border-color:black;border-style:soli

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Two statements in respect of drug-enzyme interaction are given below
Statement I : Action of an enzyme can be blocked on

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

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

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Find out the major product for the above reaction.

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2L of 0.2M H2SO4 is reacted with 2L of 0.1M NaOH solution, the molarity of the resulting product Na2SO4 in the solution

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Metal $$\mathrm{M}$$ crystallizes into a fcc lattice with the edge length of $$4.0 \times 10^{-8} \mathrm{~cm}$$. The at

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If the wavelength for an electron emitted from $$\mathrm{H}$$-atom is $$3.3 \times 10^{-10} \mathrm{~m}$$, then energy a

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A gaseous mixture of two substances A and B, under a total pressure of $$0.8$$ atm is in equilibrium with an ideal liqui

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At $$600 \mathrm{~K}, 2 \mathrm{~mol}$$ of $$\mathrm{NO}$$ are mixed with $$1 \mathrm{~mol}$$ of $$\mathrm{O}_{2}$$.
$$2

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A sample of $$0.125 \mathrm{~g}$$ of an organic compound when analyzed by Duma's method yields $$22.78 \mathrm{~mL}$$ of

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On reaction with stronger oxidizing agent like $$\mathrm{KIO}_{4}$$, hydrogen peroxide oxidizes with the evolution of $

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For a reaction, given below is the graph of $$\ln k$$ vs $${1 \over T}$$. The activation energy for the reaction is equa

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Among the following the number of curves not in accordance with Freundlich adsorption isotherm is ________.
(a)
(b)
(c

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Among the following the number of state variables is __________.
Internal energy (U)
Volume (V)
Heat (q)
Enthalpy (H)

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## Mathematics

$$
\text { Let } S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\} \text { and } $$$$T=\left\{x \in \m

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Let $$\alpha$$, $$\beta$$ be the roots of the equation $$x^{2}-\sqrt{2} x+\sqrt{6}=0$$ and $$\frac{1}{\alpha^{2}}+1, \fr

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Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be any two $$3 \times 3$$ symmetric and skew symmetric matrices respectively. Then

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$$
\text { Let } f(x)=a x^{2}+b x+c \text { be such that } f(1)=3, f(-2)=\lambda \text { and } $$ $$f(3)=4$$. If $$f(0)+

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The function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$f(x)=\lim\limits_{n \rightarrow \infty} \frac{\cos (2

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The function $$f(x)=x \mathrm{e}^{x(1-x)}, x \in \mathbb{R}$$, is :

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The sum of the absolute maximum and absolute minimum values of the function $$f(x)=\tan ^{-1}(\sin x-\cos x)$$ in the in

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Let $$x(t)=2 \sqrt{2} \cos t \sqrt{\sin 2 t}$$ and $$y(t)=2 \sqrt{2} \sin t \sqrt{\sin 2 t}, t \in\left(0, \frac{\pi}{2}

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Let $$I_{n}(x)=\int_{0}^{x} \frac{1}{\left(t^{2}+5\right)^{n}} d t, n=1,2,3, \ldots .$$ Then :

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The area enclosed by the curves $$y=\log _{e}\left(x+\mathrm{e}^{2}\right), x=\log _{e}\left(\frac{2}{y}\right)$$ and $$

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Let $$y=y(x)$$ be the solution curve of the differential equation $$
\frac{d y}{d x}+\frac{1}{x^{2}-1} y=\left(\frac{x-1

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

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Let the tangents at two points $$\mathrm{A}$$ and $$\mathrm{B}$$ on the circle $$x^{2}+\mathrm{y}^{2}-4 x+3=0$$ meet at

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Let the hyperbola $$H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$$ pass through the point $$(2 \sqrt{2},-2 \sqrt{2})$$.

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Let the lines $$\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$$ and $$\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lamb

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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

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Let S be the set of all a $$\in R$$ for which the angle between the vectors $$
\vec{u}=a\left(\log _{e} b\right) \hat{i}

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A horizontal park is in the shape of a triangle $$\mathrm{OAB}$$ with $$\mathrm{AB}=16$$. A vertical lamp post $$\mathrm

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Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be two events such that $$P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$$ and $

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Let
$$\mathrm{p}$$ : Ramesh listens to music.
$$\mathrm{q}$$ : Ramesh is out of his village.
$$\mathrm{r}$$ : It is Sund

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Let the coefficients of the middle terms in the expansion of $$\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4},(1-3 \beta x)

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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

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Let the tangents at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the ellipse $$\frac{x^{2}}{2}+\frac{y^{2}}{4}=1$$ me

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If $$1 + (2 + {}^{49}{C_1} + {}^{49}{C_2} + \,\,...\,\, + \,\,{}^{49}{C_{49}})({}^{50}{C_2} + {}^{50}{C_4} + \,\,...\,\,

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Two tangent lines $$l_{1}$$ and $$l_{2}$$ are drawn from the point $$(2,0)$$ to the parabola $$2 \mathrm{y}^{2}=-x$$. If

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$${6 \over {{3^{12}}}} + {{10} \over {{3^{11}}}} + {{20} \over {{3^{10}}}} + {{40} \over {{3^9}}} + \,\,...\,\, + \,\,{{

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Let $$S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$$.

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Let $$\mathrm{z}=a+i b, b \neq 0$$ be complex numbers satisfying $$z^{2}=\bar{z} \cdot 2^{1-z}$$. Then the least value

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A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $$\mathrm{X}$$ be the number

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The value of the integral $$\int\limits_{0}^{\frac{\pi}{2}} 60 \frac{\sin (6 x)}{\sin x} d x$$ is equal to _________.

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## Physics

Consider the efficiency of carnot's engine is given by $$\eta=\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T

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At time $$t=0$$ a particle starts travelling from a height $$7 \hat{z} \mathrm{~cm}$$ in a plane keeping z coordinate co

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A pressure-pump has a horizontal tube of cross sectional area $$10 \mathrm{~cm}^{2}$$ for the outflow of water at a spee

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A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest

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A bullet of mass $$200 \mathrm{~g}$$ having initial kinetic energy $$90 \mathrm{~J}$$ is shot inside a long swimming poo

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Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a spa

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Consider a cylindrical tank of radius $$1 \mathrm{~m}$$ is filled with water. The top surface of water is at $$15 \mathr

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A vessel contains $$14 \mathrm{~g}$$ of nitrogen gas at a temperature of $$27^{\circ} \mathrm{C}$$. The amount of heat t

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A slab of dielectric constant $$\mathrm{K}$$ has the same cross-sectional area as the plates of a parallel plate capacit

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A uniform electric field $$\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}$$ is created between two pa

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Given below are two statements :
Statement I : A uniform wire of resistance $$80 \,\Omega$$ is cut into four equal parts

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A triangular shaped wire carrying $$10 \mathrm{~A}$$ current is placed in a uniform magnetic field of $$0.5 \mathrm{~T}$

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The magnetic field at the center of current carrying circular loop is $$B_{1}$$. The magnetic field at a distance of $$\

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A transformer operating at primary voltage $$8 \,\mathrm{kV}$$ and secondary voltage $$160 \mathrm{~V}$$ serves a load o

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Sun light falls normally on a surface of area $$36 \mathrm{~cm}^{2}$$ and exerts an average force of $$7.2 \times 10^{-9

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The power of a lens (biconvex) is $$1.25 \mathrm{~m}^{-1}$$ in particular medium. Refractive index of the lens is 1.5 an

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Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the m

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A radioactive sample decays $$\frac{7}{8}$$ times its original quantity in 15 minutes. The half-life of the sample is

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An n.p.n transistor with current gain $$\beta=100$$ in common emitter configuration is shown in figure. The output volta

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A FM Broadcast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth requi

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A ball is thrown vertically upwards with a velocity of $$19.6 \mathrm{~ms}^{-1}$$ from the top of a tower. The ball stri

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The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $$\rho=\rho_{0}\left(1-\frac

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A string of area of cross-section $$4 \mathrm{~mm}^{2}$$ and length $$0.5 \mathrm{~m}$$ is connected with a rigid body o

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At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expan

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The potential energy of a particle of mass $$4 \mathrm{~kg}$$ in motion along the x-axis is given by $$\mathrm{U}=4(1-\c

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An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across

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

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An object 'O' is placed at a distance of $$100 \mathrm{~cm}$$ in front of a concave mirror of radius of curvature $$200

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In an experiment with a convex lens, The plot of the image distance $$\left(v^{\prime}\right)$$ against the object dista

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In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of $$0.5 \mathrm{~s}$$ is me

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