JEE Main 2022 (Online) 28th June Morning Shift

The correct structure of product 'A' formed in the following reaction.

is

Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?

Which of the following structure are aromatic in nature?

Stability of \(\alpha\)-Helix structure of proteins depends upon

The hybridization of P exhibited in PF5 is spxdy. The value of y is __________.

For a first order reaction A \(\to\) B, the rate constant, k = 5.5 \(\times\) 10\(-\)14 s\(-\)1. The time required for 67% completion of reaction is x \(\times\) 10\(-\)1 times the half life of reaction. The value of x is _____________ (Nea...

Which amongst the following is not a pesticide?

Identify the major product formed in the following sequence of reactions:

A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K), gives a/an

Given below are two statements :
Statement I : [Ni(CN)4]2\(-\) is square planar and diamagnetic complex, with dsp2 hybridization for Ni but [Ni(CO)4] is tetrahedral, paramagnetic and with sp3-hybridication for Ni.
Statement II : [NiCl4]2$$...

Number of complexes which will exhibit synergic bonding amongst, \([Cr{(CO)_6}]\), \([Mn{(CO)_5}]\) and \([M{n_2}{(CO)_{10}}]\) is ___________.

Which one of the lanthanoids given below is the most stable in divalent form?

The quantity of electricity in Faraday needed to reduce 1 mol of Cr2O\(_7^{2 - }\) to Cr3+ is ____________.

The major product (P) in the reaction

is

Which one of the following compounds is inactive towards SN1 reaction?

Dihydrogen reacts with CuO to give :

The solubility product of a sparingly soluble salt A2X3 is 1.1 \(\times\) 10\(-\)23. If specific conductance of the solution is 3 \(\times\) 10\(-\)5 S m\(-\)1, the limiting molar conductivity of the solution is \(x \,\times\) 10\(-\)3 S m2...

Given are two statements one is labelled as Assertion A and other is labelled as Reason R.
Assertion A : Magnesium can reduce Al2O3 at a temperature below 1350\(^\circ\)C, while above 1350\(^\circ\)C, while above 1350\(^\circ\)C aluminium c...

Nitrogen gas is obtained by thermal decomposition of :

Given below are two statements :
Statement I : The pentavalent oxide of group-15 element, E2O5, is less acidic than trivalent oxide, E2O3, of the same element.
Statement II : The acidic character of trivalent oxide of group 15 elements, E2O...

Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above "E" in the group is

Which one of the following is NOT a copolymer?

The formula of the purple colour formed in Laissaigne's test for sulphur using sodium nitroprusside is :

A 2.0 g sample containing MnO2 is treated with HCl liberating Cl2. The Cl2 gas is passed into a solution of KI and 60.0 mL of 0.1 M Na2S2O3 is required to titrate the liberated iodine. The percentage of MnO2 in the sample is _____________. ...

In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is _________ % (nearest integer)
(Relative atomic masses of Ag and Br are 108u and 80u, respectively).

The incorrect statement about the imperfections in solids is :

The vapour pressures of two volatile liquids A and B at 25\(^\circ\)C are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is $${x \over {17}}$...

If the work function of a metal is 6.63 \(\times\) 10\(-\)19J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ____________ nm. (Nearest integer)
[Given : h = 6.63 \(\times\) 10\(-\)34 J s, and c = ...

The Zeta potential is related to which property of colloids?

4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 2.0 L. The amount of heat absorbed in this expansion is ____________ L atm.

If two distinct point Q, R lie on the line of intersection of the planes \(- x + 2y - z = 0\) and \(3x - 5y + 2z = 0\) and \(PQ = PR = \sqrt {18}\) where the point P is (1, \(-\)2, 3), then the area of the triangle PQR is equal to :

The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing through the intersection of the planes \(5x + 8y + 13z - 29 = 0\) and \(8x - 7y + z - 20 = 0\) and the points (2, 1, 3) and (0, 1, 2), respectively, is :

Let the plane \(P:\overrightarrow r \,.\,\overrightarrow a = d\) contain the line of intersection of two planes \(\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 6\) and $$\overrightarrow r \,.\,\left( { - 6...

The number of real solutions of \({x^7} + 5{x^3} + 3x + 1 = 0\) is equal to ____________.

Let l be a line which is normal to the curve y = 2x2 + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to ___________.

The area of the region S = {(x, y) : y2 \(\le\) 8x, y \(\ge\) \(\sqrt2\)x, x \(\ge\) 1} is

If \(\sum\limits_{k = 1}^{31} {\left( {{}^{31}{C_k}} \right)\left( {{}^{31}{C_{k - 1}}} \right) - \sum\limits_{k = 1}^{30} {\left( {{}^{30}{C_k}} \right)\left( {{}^{30}{C_{k - 1}}} \right) = {{\alpha (60!)} \over {(30!)(31!)}}} }\), where ...

The number of positive integers k such that the constant term in the binomial expansion of \({\left( {2{x^3} + {3 \over {{x^k}}}} \right)^{12}}\), x \(\ne\) 0 is 28 . l, where l is an odd integer, is ______________.

If the tangents drawn at the points \(O(0,0)\) and \(P\left( {1 + \sqrt 5 ,2} \right)\) on the circle \({x^2} + {y^2} - 2x - 4y = 0\) intersect at the point Q, then the area of the triangle OPQ is equal to :

Let the lines \(y + 2x = \sqrt {11} + 7\sqrt 7\) and \(2y + x = 2\sqrt {11} + 6\sqrt 7\) be normal to a circle \(C:{(x - h)^2} + {(y - k)^2} = {r^2}\). If the line \(\sqrt {11} y - 3x = {{5\sqrt {77} } \over 3} + 11\) is tangent to the ...

The number of elements in the set {z = a + ib \(\in\) C : a, b \(\in\) Z and 1 < | z \(-\) 3 + 2i | < 4} is __________.

Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral \(\int\limits_0^1 {[ - 8{x^2} + 6x - 1]dx}\) is equal to :

Let the solution curve \(y = y(x)\) of the differential equation
\(\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]x{{dy} \over {dx}} = x + \left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]y\)
pa...

Let y = y(x) be the solution of the differential equation \(x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0\), \(x > 1\), with \(y(2) = - 2\). Then y(3) is equal to :

Let a function f : N \(\to\) N be defined by
\(f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,} & {n = 3,7,11,15,......} \cr {{{n + 1} \over 2},} & {n = 1,5,9,13,......} \cr } } \right.\)
then, f is

Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let \({\pi \over 8}\) and \(\theta\) be the angles of elevation from C to P and A, respectively. If ...

Let the eccentricity of the hyperbola \(H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) be \(\sqrt {{5 \over 2}}\) and length of its latus rectum be \(6\sqrt 2\). If \(y = 2x + c\) is a tangent to the hyperbola H, then the value...

Let f : R \(\to\) R be defined as
\(f(x) = \left[ {\matrix{ {[{e^x}],} & {x < 0} \cr {a{e^x} + [x - 1],} & {0 \le x < 1} \cr {b + [\sin (\pi x)],} & {1 \le x < 2} \cr {[{e^{ - x}}] - c,} & {x \ge 2} \cr } } \right.\)
w...

Let p, q, r be three logical statements. Consider the compound statements
\({S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)\) and
\({S_2}:p \to (q \vee r)\)
Then, which of the following is NOT true?

If the system of linear equations
\(2x + 3y - z = - 2\)
\(x + y + z = 4\)
\(x - y + |\lambda |z = 4\lambda - 4\)
where, \(\lambda\) \(\in\) R, has no solution, then