JEE Main 2022 (Online) 30th June Morning Shift

Paper was held on
Thu, Jun 30, 2022 3:30 AM

## Chemistry

An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm$$

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The number of radial nodes and total number of nodes in 4p orbital respectively are :

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For a solution of the gases A, B, C and D in water at 298 K, the values of Henry's law constant (KH) are 30.40, 2.34, 1.

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The equilibrium constant for the reversible reaction
2A(g) $$\rightleftharpoons$$ 2B(g) + C(g) is K1
$${3 \over 2}$$A(g)

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In which of the following half cells, electrochemical reaction is pH dependent?

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The correct order of electron gain enthalpy ($$-$$ ve value) is :

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$$\Delta$$G$$^\circ$$ vs T plot for the formation of MgO, involving reaction 2Mg + O2 $$\to$$ 2MgO, will look like :

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Match List - I with List - II :
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Correct statement about alkali metal oxides is :

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A $$\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{}^{573\,K}} $$ Red phosphorus $$\mathrel{\mathop{\kern0pt\longrig

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Correct formula of the compound which gives a white precipitate with BaCl2 solution, but not with AgNO3 solution, is :

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Which one of the following chemicals has not been used for the dry cleaning of clothes?

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TLC analysis of a mixture having 3 components (A, B, C) using silica gel as the stationary phase gave following Rf value

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Consider the given chemical reaction
Identify the product P.

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Choose the reaction which is not possible:

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Which among the following will be the major product of the given reaction?

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Consider the above reaction sequence. Identify the component A and component B :

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Match List - I with List - II.
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The sugar produced after complete hydrolysis of DNA is

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The reagent neutral ferric chloride is used to detect the presence of ______________

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Blister copper is produced by reaction of copper oxide with copper sulphide.
2Cu2O + Cu2S $$\to$$ 6Cu + SO2
When 2.86 $$

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Amongst the following, the number of molecule/(s) having net resultant dipole moment is ____________.
NF3, BF3, BeF2, CH

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1.0 mol of monoatomic ideal gas is expanded from state 1 to state 2 as shown in the figure. The magnitude of the work do

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For the reaction P $$\to$$ B, the values of frequency factor A and activation energy EA are 4 $$\times$$ 1013 s$$-$$1 an

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100 mL of 0.3 M acetic acid is shaken with 0.8 g of wood charcoal. The final concentration of acetic acid in the solutio

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In the following brown complex, the oxidation state of iron is +_____________.
$${[Fe{({H_2}O)_6}]^{2 + }} + NO \to \mat

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Spin only magnetic moment ($$\mu$$s) of $${K_3}[Fe{(CN)_6}]$$ is ____________ B.M.
(Nearest integer)

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An organic compound with 51.6% sulfur is heated in a Carius tube. The amount of this compound which will form 0.752 g of

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A hydrocarbon 'X' is found to have molar mass of 80. A 10.0 mg of compound 'X' on hydrogenation consumed 8.40 mL of H2 g

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How many of the following drugs belong to the tranquilizer class _____________ ?
Veronal, Luminal, Propanal, Seconal

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## Mathematics

Let $${S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\}$$ and $

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The real part of the complex number $${{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }}$$

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Let S be the set of all integral values of $$\alpha$$ for which the sum of squares of two real roots of the quadratic eq

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Let $$A = \left[ {\matrix{
1 & { - 2} & \alpha \cr
\alpha & 2 & { - 1} \cr
} } \right]$$ and $$B = \left[

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Let A and B be two square matrices of order 2. If $$det\,(A) = 2$$, $$det\,(B) = 3$$ and $$\det \left( {(\det \,5(det\,A

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For two positive real numbers a and b such that $${1 \over {{a^2}}} + {1 \over {{b^3}}} = 4$$, then minimum value of the

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The value of $$1 + {1 \over {1 + 2}} + {1 \over {1 + 2 + 3}} + \,\,....\,\, + \,\,{1 \over {1 + 2 + 3 + \,\,.....\,\, +

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If xy4 attains maximum value at the point (x, y) on the line passing through the points (50 + $$\alpha$$, 0) and (0, 50

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Let $$f(x) = 4{x^3} - 11{x^2} + 8x - 5,\,x \in R$$. Then f :

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Let m and M respectively be the minimum and the maximum values of $$f(x) = {\sin ^{ - 1}}2x + \sin 2x + {\cos ^{ - 1}}2x

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$$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{r \over {2{r^2} - 7rn + 6{n^2}}}} $$ is equal to :

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Let $${{dy} \over {dx}} = {{ax - by + a} \over {bx + cy + a}},\,a,b,c \in R$$, represents a circle with center ($$\alpha

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Let $$\alpha$$1, $$\alpha$$2 ($$\alpha$$1 2) be the values of $$\alpha$$ fo the points ($$\alpha$$, $$-$$3), (2, 0) and

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Consider three circles:
$${C_1}:{x^2} + {y^2} = {r^2}$$
$${C_2}:{(x - 1)^2} + {(y - 1)^2} = {r^2}$$
$${C_3}:{(x - 2)^2}

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Let the eccentricity of the ellipse $${x^2} + {a^2}{y^2} = 25{a^2}$$ be b times the eccentricity of the hyperbola $${x^2

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The distance of the point (3, 2, $$-$$1) from the plane $$3x - y + 4z + 1 = 0$$ along the line $${{2 - x} \over 2} = {{y

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Let a vector $$\overrightarrow c $$ be coplanar with the vectors $$\overrightarrow a = - \widehat i + \widehat j + \wi

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If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then $${{P(X = 2)} \over

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Let $$\alpha = \tan \left( {{{5\pi } \over {16}}\sin \left( {2{{\cos }^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right)} \r

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The conditional statement
$$((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q))$$ is :

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The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of

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Let for $$f(x) = {a_0}{x^2} + {a_1}x + {a_2},\,f'(0) = 1$$ and $$f'(1) = 0$$. If a0, a1, a2 are in an arithmatico-geomet

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Suppose $$\mathop {\lim }\limits_{x \to 0} {{F(x)} \over {{x^3}}}$$ exists and is equal to L, where
$$F(x) = \left| {\ma

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If for some $$\alpha$$ > 0, the area of the region $$\{ (x,y):|x + \alpha | \le y \le 2 - |x|\} $$ is equal to $${3 \ove

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Let $$f(t) = \int\limits_0^t {{e^{{x^3}}}\left( {{{{x^8}} \over {{{({x^6} + 2{x^3} + 2)}^2}}}} \right)dx} $$. If $$f(1)

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A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some

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Let PQ be a focal chord of length 6.25 units of the parabola y2 = 4x. If O is the vertex of the parabola, then 10 times

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Consider a triangle ABC whose vertices are A(0, $$\alpha$$, $$\alpha$$), B($$\alpha$$, 0, $$\alpha$$) and C($$\alpha$$,

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The probability distribution of X is :
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Let $${S_1} = \{ x \in [0,12\pi ]:{\sin ^5}x + {\cos ^5}x = 1\} $$
and $${S_2} = \{ x \in [0,8\pi ]:{\sin ^7}x + {\cos ^

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## Physics

At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms$$-$$2. At t = 20

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If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each

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The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3$$\rho$$ and 5$$\rho$$ respectively. The r

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Two projectiles P1 and P2 thrown with speed in the ratio $$\sqrt3$$ : $$\sqrt2$$, attain the same height during their mo

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An air bubble of negligible weight having radius r rises steadily through a solution of density $$\sigma$$ at speed v. T

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A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static frictio

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Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The

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The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. W

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A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r1 and r2 respectively. Whe

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Co is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If hal

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A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm

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Which of the following equations correctly represents a travelling wave having wavelength $$\lambda$$ = 4.0 cm, frequenc

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A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accel

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An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5$$\pi$$ $$\times$

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An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $$\Omega$$. If this single copper wir

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In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency (f2) and new q

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Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits

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A source of monochromatic light liberates 9 $$\times$$ 1020 photon per second with wavelength 600 nm when operated at 40

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A speech signal given by 11 sin(2200 $$\pi$$t) V is used for amplitude modulation with a carrier signal given by 44 sin(

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A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by

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A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown

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An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car

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Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown

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The excess pressure inside a liquid drop is 500 Nm$$-$$2. If the radius of the drop is 2 mm, the surface tension of liqu

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Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. Th

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The circuit diagram of potentiometer used to measure the internal resistance of a cell (E) is shown in figure. The key '

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A series LCR circuit with $$R = {{250} \over {11}}\,\Omega $$ and $${X_L} = {{70} \over {11}}\,\Omega $$ is connected ac

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The refractive index of an equilateral prism is $$\sqrt 2 $$. The angle of emergence under minimum deviation position of

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A hydrogen atom in its first excited state absorbs a photon of energy x $$\times$$ 10$$-$$2 eV and excited to a higher e

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The circuit diagram used to study the characteristic curve of a zener diode is connected to variable power supply (0 $$-

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