JEE Main 2021 (Online) 16th March Evening Shift

The structure of X is :

In the above reaction, the reagent ''A'' is :

The secondary structure of protein is stabilised by:

A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is _________ m...

Ammonolysis of Alkyl halides followed by the treatment with NaOH solution can be used to prepare primary, secondary and tertiary amines. The purpose of NaOH in the reaction is :

Which of the following is least basic?

[Ti(H2O)6]3+ absorbs light of wavelength 498 nm during a d \(-\) d transition. The octahedral splitting energy for the above complex is ____________ \(\times\) 10\(-\)19 J. (Round off to the Nearest Integer). h = 6.626 \(\times\) 10\(-\)34 ...

Fex2 and Fey3 are known when x and y are :

Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all the three, high spin system.(Atomic numbers Ce = 58, Gd = 64 and Eu = 63)(a) (NH4)2[Ce(NO3)6](b) Gd(NO3)3 and (c) Eu(NO3)3

A 5.0 m mol dm\(-\)3 aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell of cell constant 1.3 cm\(-\)1. The molar conductivity of this solution is ___________ mSm2 mol\(-\)1. (Round off to the Nearest Integer).

The green house gas/es is (are) :(A) Carbon dioxide(B) Oxygen(C) Water vapour(D) MethaneChoose the most appropriate answer from the options given below :

Identify the reagent(s) 'A' and condition(s) for the reaction

An unsaturated hydrocarbon X on ozonolysis gives A. Compound A when warmed with ammonical silver nitrate forms a bright silver mirror along the sides of the test tube. The unsaturated hydrocarbon X is :

The correct statements about H2O2 are :(A) used in the treatment of effluents.(B) used as both oxidising and reducing agents.(C) the two hydroxyl groups lie in the same plane.(D) miscible with water.Choose the correct answer from the option...

Sulphurous acid (H2SO3) has Ka1 = 1.7 \(\times\) 10\(-\)2 and Ka2 = 6.4 \(\times\) 10\(-\)8. The pH of 0.588 M H2SO3 is __________. (Round off to the Nearest Integer).

Which of the following reduction reaction CANNOT be carried out with coke?

The INCORRECT statement regarding the structure of C60 is :

The characteristics of elements X, Y and Z with atomic numbers, respectively, 33, 53 and 83 are :

Identify the elements X and Y using the ionisation energy values given below :



Ionization energy (kJ/mol)






1\({st}\)
2\({nd}\)


X
495
4563


Y
731
1450

Which of the following polymer is used in the manufacture of wood laminates?

Match List - I with List - II :



List - I Test/Reagents/Observation(s)

List - II Species detected




(a)
Lassaigne's Test
(i)
Carbon


(b)
Cu(II) oxide
(ii)
Sulphur


(c)...

In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at 287 K and 758 mm of Hg pressure. The percentage composition of nitrogen in the compound is __________. (Round off to the Nearest...

Statement I : Sodium hydride can be used as an oxidising agent.Statement II : The lone pair of electrons on nitrogen in pyridine makes it basic.Choose the CORRECT answer from the options given below :

Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is __________ \(\times\) 1021. (Round off to the Nearest Integer). [Given : NA = 6.023 \(\times\) 1023]

At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and 2 moles of B are mixed. Assuming that this solution is ideal, the vapour pressure of the mixture is ___________ kPa. (Round off to the Nearest Integer).

The exact volumes of 1 M NaOH solution required to neutralise 50 mL of 1 M H3PO3 solution and 100 mL of 2 M H3PO2 solution, respectively, are :

When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution, _________ \(\times\) 10\(-\)5 moles of lead sulphate precipitate out. (Round off to the Nearest Integer).

The number of orbitals with n = 5, m1 = +2 is ___________. (Round off to the Nearest Integer).

The INCORRECT statements below regarding colloidal solutions is :

At 25\(^\circ\)C, 50 g of iron reacts with HCl to form FeCl2. The evolved hydrogen gas expands against a constant pressure of 1 bar. The work done by the gas during this expansion is _________ J. (Round off to the Nearest Integer).[Given : ...

If the foot of the perpendicular from point (4, 3, 8) on the line \({L_1}:{{x - a} \over l} = {{y - 2} \over 3} = {{z - b} \over 4}\), l \(\ne\) 0 is (3, 5, 7), then the shortest distance between the line L1 and line $${L_2}:{{x - 2} \over ...

If (x, y, z) be an arbitrary point lying on a plane P which passes through the points (42, 0, 0), (0, 42, 0) and (0, 0, 42), then the value of the expression $$3 + {{x - 11} \over {{{(y - 19)}^2}{{(z - 12)}^2}}} + {{y - 19} \over {{{(x - 11...

If the distance of the point (1, \(-\)2, 3) from the plane x + 2y \(-\) 3z + 10 = 0 measured parallel to the line, \({{x - 1} \over 3} = {{2 - y} \over m} = {{z + 3} \over 1}\) is \(\sqrt {{7 \over 2}}\), then the value of |m| is equal to ...

The maximum value of \(f(x) = \left| {\matrix{ {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\cos 2x} \cr {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\cos 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr } } \right|,x \in R\) is...

Let f be a real valued function, defined on R \(-\) {\(-\)1, 1} and given by f(x) = 3 loge \(\left| {{{x - 1} \over {x + 1}}} \right| - {2 \over {x - 1}}\).Then in which of the following intervals, function f(x) is increasing?

Let n be a positive integer. Let $$A = \sum\limits_{k = 0}^n {{{( - 1)}^k}{}^n{C_k}\left[ {{{\left( {{1 \over 2}} \right)}^k} + {{\left( {{3 \over 4}} \right)}^k} + {{\left( {{7 \over 8}} \right)}^k} + {{\left( {{{15} \over {16}}} \right)}^...

Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2\({\sqrt 2 }\) and 2\({\sqrt 5 }\), respectively. Then the shortest distance from origin to a tangent to this circle which is perp...

The least value of |z| where z is complex number which satisfies the inequality \(\exp \left( {{{(|z| + 3)(|z| - 1)} \over {||z| + 1|}}{{\log }_e}2} \right) \ge {\log _{\sqrt 2 }}|5\sqrt 7 + 9i|,i = \sqrt { - 1}\), is equal to :

Consider the integral \(I = \int_0^{10} {{{[x]{e^{[x]}}} \over {{e^{x - 1}}}}dx}\), where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :

Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that \(\int_0^1 {P(x)dx}\) = 1 and P(x) leaves remainder 5 when it is divided by (x \(-\) 2). Then the value of 9(b + c) is equal to :

Let C1 be the curve obtained by the solution of differential equation \(2xy{{dy} \over {dx}} = {y^2} - {x^2},x > 0\). Let the curve C2 be the solution of \({{2xy} \over {{x^2} - {y^2}}} = {{dy} \over {dx}}\). If both the curves pass through...

If y = y(x) is the solution of the differential equation \({{dy} \over {dx}}\) + (tan x) y = sin x, \(0 \le x \le {\pi \over 3}\), with y(0) = 0, then \(y\left( {{\pi \over 4}} \right)\) equal to :

If the points of intersections of the ellipse \({{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1\) and the circle x2 + y2 = 4b, b > 4 lie on the curve y2 = 3x2, then b is equal to :

For real numbers \(\alpha\), \(\beta\), \(\gamma\) and \(\delta\), if \(\int {{{({x^2} - 1) + {{\tan }^{ - 1}}\left( {{{{x^2} + 1} \over x}} \right)} \over {({x^4} + 3{x^2} + 1){{\tan }^{ - 1}}\left( {{{{x^2} + 1} \over x}} \right)}}dx}\)...

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy $${\sin ^{ - 1}}\left( {{{3x} \over 5}} \right) + {\sin ^{ - 1}}\left( {{{4x} \over 5}} \right) = {\sin ^{ - 1}}x$...

Let f : S \(\to\) S where S = (0, \(\infty\)) be a twice differentiable function such that f(x + 1) = xf(x). If g : S \(\to\) R be defined as g(x) = loge f(x), then the value of |g''(5) \(-\) g''(1)| is equal to :

Let \(\alpha\) \(\in\) R be such that the function $$f(x) = \left\{ {\matrix{
{{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){{\sin }^{ - 1}}(1 - \{ x\} )} \over {\{ x\} - {{\{ x\} }^3}}},} & {x \ne 0} \cr
{\alpha ,} & {x = 0} \cr

} } \...

Let f : R \(\to\) R and g : R \(\to\) R be defined as \(f(x) = \left\{ {\matrix{ {x + a,} & {x < 0} \cr {|x - 1|,} & {x \ge 0} \cr } } \right.\) and $$g(x) = \left\{ {\matrix{
{x + 1,} & {x < 0} \cr
{{{(x - 1)}^2} + ...

Let \(A = \left[ {\matrix{ {{a_1}} \cr {{a_2}} \cr } } \right]\) and \(B = \left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr } } \right]\) be two 2 \(\times\) 1 matrices with real entries such that A = XB, where $$X = {1 \ove...

Let C be the locus of the mirror image of a point on the parabola y2 = 4x with respect to the line y = x. Then the equation of tangent to C at P(2, 1) is :