JEE Main 2022 (Online) 29th July Morning Shift

Paper was held on
Fri, Jul 29, 2022 3:30 AM

## Chemistry

Which of the following pair of molecules contain odd electron molecule and an expanded octet molecule?

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$$
\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{NH}_{3(\mathrm{~g})}
$$
$$20 \

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$$100 \mathrm{~mL}$$ of $$5 \%\,(\mathrm{w} / \mathrm{v})$$ solution of $$\mathrm{NaCl}$$ in water was prepared in $$250

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The first ionization enthalpy of Na, Mg and Si, respectively, are : 496, 737 and $$786 \mathrm{~kJ} \mathrm{~mol}^{-1}$$

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In metallurgy the term "gangue" is used for :

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The reaction of zinc with excess of aqueous alkali, evolves hydrogen gas and gives :

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Lithium nitrate and sodium nitrate, when heated separately, respectively, give :

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Number of lone pairs of electrons in the central atom of $$\mathrm{SCl}_{2}, \mathrm{O}_{3}, \mathrm{ClF}_{3}$$ and $$\m

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In following pairs, the one in which both transition metal ions are colourless is :

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In neutral or faintly alkaline medium, $$\mathrm{KMnO}_{4}$$ being a powerful oxidant can oxidize, thiosulphate almost q

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Which among the following pairs has only herbicides?

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Which among the following is the strongest Bronsted base?

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Which among the following pairs of the structures will give different products on ozonolysis? (Consider the double bonds

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Considering the above reactions, the compound 'A' and compound 'B' respectively are :

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Consider the above reaction sequence, the Product 'C' is :

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Consider the above reaction, the compound 'A' is :

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Which among the following represent reagent 'A'?

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Consider the following reaction sequence:
The product 'B' is :

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Which of the following compounds is an example of hypnotic drug?

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A compound 'X' is acidic and it is soluble in NaOH solution, but insoluble in NaHCO3 solution. Compound 'X' also gives v

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Resistance of a conductivity cell (cell constant $$129 \mathrm{~m}^{-1}$$) filled with $$74.5 \,\mathrm{ppm}$$ solution

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Ionic radii of cation $$\mathrm{A}^{+}$$ and anion $$\mathrm{B}^{-}$$ are 102 and $$181 \,\mathrm{pm}$$ respectively. Th

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The minimum uncertainty in the speed of an electron in an one dimensional region of length $$2 \mathrm{a}_{\mathrm{o}}$$

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When 600 mL of 0.2 M HNO3 is mixed with $$400 \mathrm{~mL}$$ of 0.1 M NaOH solution in a flask, the rise in temperature

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If $$\mathrm{O}_{2}$$ gas is bubbled through water at $$303 \mathrm{~K}$$, the number of millimoles of $$\mathrm{O}_{2}$

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If the solubility product of PbS is 8 $$\times$$ 10$$-$$28, then the solubility of PbS in pure water at 298 K is x $$\ti

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The reaction between X and Y is first order with respect to X and zero order with respect to Y.
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In a linear tetrapeptide (Constituted with different amino acids), (number of amino acids) $$-$$ (number of peptide bond

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In bromination of Propyne, with Bromine, 1, 1, 2, 2-tetrabromopropane is obtained in 27% yield. The amount of 1, 1, 2, 2

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$$\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$$ should be an inner orbital complex. Ignoring the pairing energy, the

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## Mathematics

Let R be a relation from the set $$\{1,2,3, \ldots, 60\}$$ to itself such that $$R=\{(a, b): b=p q$$, where $$p, q \geqs

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If $$z=2+3 i$$, then $$z^{5}+(\bar{z})^{5}$$ is equal to :

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Let A and B be two $$3 \times 3$$ non-zero real matrices such that AB is a zero matrix. Then

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If $$\frac{1}{(20-a)(40-a)}+\frac{1}{(40-a)(60-a)}+\ldots+\frac{1}{(180-a)(200-a)}=\frac{1}{256}$$, then the maximum val

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If $$\lim\limits_{x \rightarrow 0} \frac{\alpha \mathrm{e}^{x}+\beta \mathrm{e}^{-x}+\gamma \sin x}{x \sin ^{2} x}=\frac

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The integral $$\int\limits_{0}^{\frac{\pi}{2}} \frac{1}{3+2 \sin x+\cos x} \mathrm{~d} x$$ is equal to :

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

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Let a line L pass through the point of intersection of the lines $$b x+10 y-8=0$$ and $$2 x-3 y=0, \mathrm{~b} \in \math

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If the foot of the perpendicular from the point $$\mathrm{A}(-1,4,3)$$ on the plane $$\mathrm{P}: 2 x+\mathrm{m} y+\math

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Let $$\overrightarrow{\mathrm{a}}=3 \hat{i}+\hat{j}$$ and $$\overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}+\hat{k}$$. Let

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The angle of elevation of the top of a tower from a point A due north of it is $$\alpha$$ and from a point B at a distan

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The statement $$(p \wedge q) \Rightarrow(p \wedge r)$$ is equivalent to :

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Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersec

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Let $$\hat{a}$$ and $$\hat{b}$$ be two unit vectors such that the angle between them is $$\frac{\pi}{4}$$. If $$\theta$$

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If $$f(\alpha)=\int\limits_{1}^{\alpha} \frac{\log _{10} \mathrm{t}}{1+\mathrm{t}} \mathrm{dt}, \alpha>0$$, then $$f\lef

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The area of the region
$$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$$ is equal to :

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Let the focal chord of the parabola $$\mathrm{P}: y^{2}=4 x$$ along the line $$\mathrm{L}: y=\mathrm{m} x+\mathrm{c}, \m

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The number of points, where the function $$f: \mathbf{R} \rightarrow \mathbf{R}$$,
$$f(x)=|x-1| \cos |x-2| \sin |x-1|+(x

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Let $$S=\{1,2,3, \ldots, 2022\}$$. Then the probability, that a randomly chosen number n from the set S such that $$\mat

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Let $$f(x)=3^{\left(x^{2}-2\right)^{3}+4}, x \in \mathrm{R}$$. Then which of the following statements are true?
$$\mathr

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Let $$S=\left\{\theta \in(0,2 \pi): 7 \cos ^{2} \theta-3 \sin ^{2} \theta-2 \cos ^{2} 2 \theta=2\right\}$$. Then, the su

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Let the mean and the variance of 20 observations $$x_{1}, x_{2}, \ldots, x_{20}$$ be 15 and 9 , respectively. For $$\alp

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Let a line with direction ratios $$a,-4 a,-7$$ be perpendicular to the lines with direction ratios $$3,-1,2 b$$ and $$b,

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Let $$a_{1}, a_{2}, a_{3}, \ldots$$ be an A.P. If $$\sum\limits_{r=1}^{\infty} \frac{a_{r}}{2^{r}}=4$$, then $$4 a_{2}$$

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Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of $$\left(\

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The number of matrices of order $$3 \times 3$$, whose entries are either 0 or 1 and the sum of all the entries is a prim

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Let p and p + 2 be prime numbers and let
$$
\Delta=\left|\begin{array}{ccc}
\mathrm{p} ! & (\mathrm{p}+1) ! & (\mathrm{p

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If $$\frac{1}{2 \times 3 \times 4}+\frac{1}{3 \times 4 \times 5}+\frac{1}{4 \times 5 \times 6}+\ldots+\frac{1}{100 \time

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Let $$S=\{4,6,9\}$$ and $$T=\{9,10,11, \ldots, 1000\}$$. If $$A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in \mathbf{N}, a_{1}

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Let the mirror image of a circle $$c_{1}: x^{2}+y^{2}-2 x-6 y+\alpha=0$$ in line $$y=x+1$$ be $$c_{2}: 5 x^{2}+5 y^{2}+1

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## Physics

Given below are two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : T

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A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the tim

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If $$\mathrm{t}=\sqrt{x}+4$$, then $$\left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}$$ is :

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A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a

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A ball is projected with kinetic energy E, at an angle of $$60^{\circ}$$ to the horizontal. The kinetic energy of this b

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Two bodies of mass $$1 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ have position vectors $$\hat{i}+2 \hat{j}+\hat{k}$$ and $$-

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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)

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If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the m

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The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves withou

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A spherically symmetric charge distribution is considered with charge density varying as
$$\rho(r)= \begin{cases}\rho_{0

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Given below are two statements.
Statement I : Electric potential is constant within and at the surface of each conductor

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Two metallic wires of identical dimensions are connected in series. If $$\sigma_{1}$$ and $$\sigma_{2}$$ are the conduct

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An alternating emf $$\mathrm{E}=440 \sin 100 \pi \mathrm{t}$$ is applied to a circuit containing an inductance of $$\fra

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A coil of inductance 1 H and resistance $$100 \,\Omega$$ is connected to a battery of 6 V. Determine approximately :
(a)

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Match List - I with List - II :
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The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $$\lambda$$. To double t

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Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second per

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Find the modulation index of an AM wave having $$8 \mathrm{~V}$$ variation where maximum amplitude of the AM wave is $$9

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A travelling microscope has 20 divisions per $$\mathrm{cm}$$ on the main scale while its vernier scale has total 50 divi

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In an experiment to find out the diameter of wire using screw gauge, the following observations were noted :
(A) Screw

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An object is projected in the air with initial velocity u at an angle $$\theta$$. The projectile motion is such that the

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If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that

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The pressure $$\mathrm{P}_{1}$$ and density $$\mathrm{d}_{1}$$ of diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ chang

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One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at cons

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The current I flowing through the given circuit will be __________A.

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A closely wounded circular coil of radius 5 cm produces a magnetic field of $$37.68 \times 10^{-4} \mathrm{~T}$$ at its

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Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen a

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A wire of length $$314 \mathrm{~cm}$$ carrying current of $$14 \mathrm{~A}$$ is bent to form a circle. The magnetic mome

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The X-Y plane be taken as the boundary between two transparent media $$\mathrm{M}_{1}$$ and $$\mathrm{M}_{2}$$. $$\mathr

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If the potential barrier across a p-n junction is $$0.6 \mathrm{~V}$$. Then the electric field intensity, in the depleti

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