JEE Main 2021 (Online) 31st August Morning Shift

The major product formed in the following reaction is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Treatment of bromine water with propene yields 1-bromopropan-2-ol.Reason (R) : Attack of water on bromonium ion follo...

The structure of product C, formed by the following sequence of reactions is :

Choose the correct name for compound given below :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R) :Assertion (A) : A simple distillation can be used to separate a mixture of propanol and propanone.Reason (R) : Two liquids with a dif...

Which one of the following compounds contains \(\beta\)-C1-C4 glycosidic linkage?

The number of hydrogen bonded water molecule(s) associated with stoichiometry CuSO4.5H2O is ____________.

For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is ____________. (Integer answer)

According to the following figure, the magnitude of the enthalpy change of the reactionA + B \(\to\) M + N in kJ mol\(-\) is equal to ___________. (Integer answer)

The major products A and B in the following set of reactions are :

The total number of reagents from those given blow, that can convert nitrobenzene into aniline is ___________. (Integer answer)I. Sn \(-\) HClII. Sn \(-\) NH4OHIII. Fe \(-\) HClIV. Zn \(-\) HClV. H2 \(-\) PdVI. H2 \(-\) Raney Nickel

The denticity of an organic ligand, biuret is :

In the structure of the dichromate ion, there is a :

Which one of the following lanthanides exhibits +2 oxidation state with diamagnetic nature? (Given Z for Nd = 60, Yb = 70, La = 57, Ce = 58)

Consider the following cell reaction :\(C{d_{(s)}} + H{g_2}S{O_{4(s)}} + {9 \over 5}{H_2}{O_{(l)}}\) \(\rightleftharpoons\) \(CdS{O_4}.{9 \over 5}{H_2}{O_{(s)}} + 2H{g_{(l)}}\)The value of \(E_{cell}^0\) is 4.315 V at 25\(^\circ\)C. If $$\D...

BOD values (in ppm) for clean water (A) and polluted water (B) are expected respectively :

Which one of the following is the correct PV vs P plot at constant temperature for an ideal gas? (P and V stand for pressure and volume of the gas respectively)

The correct order of reactivity of the given chlorides with acetate in acetic acid is :

Given below are two statements :Statement I : The process of producing syn-gas is called gasification of coal.Statement II : The composition of syn-gas is CO + CO2 + H2 (1 : 1 : 1)In the light of the above statements, choose the most approp...

A3B2 is a sparingly soluble salt of molar mass M (g mol\(-\)1) and solubility x g L\(-\)1. The solubility product satisfies \({K_{sp}} = a{\left( {{x \over M}} \right)^5}\). The value of a is _____________. (Integer answer)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : Aluminium is extracted from bauxite by the electrolysis of molten mixture of Al2O3 with cryolite.Reason (R) : The oxid...

Consider the sulphides HgS, PbS, CuS, Sb2S3, As2S3 and CdS. Number of these sulphides soluble in 50% HNO3 is ___________.

The number of halogen/(s) forming halic (V) acid is ___________.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : Metallic character decreases and non-metallic character increases on moving from left to right in a period.Reason (R) ...

Monomer of Novolac is :

The major component/ingredient of Portland Cement is :

Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing point depression?

The molarity of the solution prepared by dissolving 6.3 g of oxalic acid (H2C2O4.2H2O) in 250 mL of water in mol L\(-\)1 is x \(\times\) 10\(-\)2. The value of x is _____________. (Nearest integer) [Atomic mass : H : 1.0, C : 12.0, O : 16.0...

Ge(Z = 32) in its ground state electronic configuration has x completely filled orbitals with ml = 0. The value of x is ___________.

Select the graph that correctly describes the adsorption isotherms at two temperatures T1, and T2 (T1 > T2) for a gas :(x - mass of the gas absorbed ; m - mass of adsorbent ; P - pressure)

Let the equation of the plane, that passes through the point (1, 4, \(-\)3) and contains the line of intersection of the planes 3x \(-\) 2y + 4z \(-\) 7 = 0 and x + 5y \(-\) 2z + 9 = 0, be \(\alpha\)x + \(\beta\)y + \(\gamma\)z + 3 = 0, the...

The square of the distance of the point of intersection of the line \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z + 1} \over 6}\) and the plane \(2x - y + z = 6\) from the point (\(-\)1, \(-\)1, 2) is __________.

The number of real roots of the equation \({e^{4x}} + 2{e^{3x}} - {e^x} - 6 = 0\) is :

If 'R' is the least value of 'a' such that the function f(x) = x2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then the value of |R \(-\) S| is ____...

If \(\left( {{{{3^6}} \over {{4^4}}}} \right)k\) is the term, independent of x, in the binomial expansion of \({\left( {{x \over 4} - {{12} \over {{x^2}}}} \right)^{12}}\), then k is equal to ___________.

If the variable line 3x + 4y = \(\alpha\) lies between the two circles (x \(-\) 1)2 + (y \(-\) 1)2 = 1 and (x \(-\) 9)2 + (y \(-\) 1)2 = 4, without intercepting a chord on either circle, then the sum of all the integral values of \(\alpha\)...

A point z moves in the complex plane such that \(\arg \left( {{{z - 2} \over {z + 2}}} \right) = {\pi \over 4}\), then the minimum value of \({\left| {z - 9\sqrt 2 - 2i} \right|^2}\) is equal to _______________.

Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If \(\int_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int_0^x {f(t)dt} }\), \(0 \le x \le 1\) and f(0) = 0, then $$\mathop {\lim }\limits_{x \to 0} {1 \over {{x^2}}}\i...

Let [t] denote the greatest integer \(\le\) t. Then the value of \(8.\int\limits_{ - {1 \over 2}}^1 {([2x] + |x|)dx}\) is ___________.

If \(x\phi (x) = \int\limits_5^x {(3{t^2} - 2\phi '(t))dt}\), x > \(-\)2, and \(\phi\)(0) = 4, then \(\phi\)(2) is __________.

If \({{dy} \over {dx}} = {{{2^{x + y}} - {2^x}} \over {{2^y}}}\), y(0) = 1, then y(1) is equal to :

The line \(12x\cos \theta + 5y\sin \theta = 60\) is tangent to which of the following curves?

A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, th...

The integral \(\int {{1 \over {\root 4 \of {{{(x - 1)}^3}{{(x + 2)}^5}} }}} \,dx\) is equal to : (where C is a constant of integration)

The function \(f(x) = \left| {{x^2} - 2x - 3} \right|\,.\,{e^{\left| {9{x^2} - 12x + 4} \right|}}\) is not differentiable at exactly :

If the function $$f(x) = \left\{ {\matrix{
{{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}} \right)} & , & {x < 0} \cr
k & , & {x = 0} \cr
{{{{{\cos }^2}x - {{\sin }^2}x - 1} \over {\sqrt {{x^2} + 1} ...

\(\mathop {\lim }\limits_{x \to 0} {{{{\sin }^2}\left( {\pi {{\cos }^4}x} \right)} \over {{x^4}}}\) is equal to :

Let *, ▢ \(\in\){\(\wedge\), \(\vee\)} be such that the Boolean expression (p * \(\sim\) q) \(\Rightarrow\) (p ▢ q) is a tautology. Then :

If the following system of linear equations2x + y + z = 5x \(-\) y + z = 3x + y + az = bhas no solution, then :

If \({a_r} = \cos {{2r\pi } \over 9} + i\sin {{2r\pi } \over 9}\), r = 1, 2, 3, ....., i = \(\sqrt { - 1}\), then the determinant $$\left| {\matrix{
{{a_1}} & {{a_2}} & {{a_3}} \cr
{{a_4}} & {{a_5}} & {{a_6}} \cr
{{a_7}} & {{a...