JEE Main 2022 (Online) 29th June Evening Shift

The number of chiral alcohol(s) with molecular formula C4H10O is ________.

In the given reaction,

the number of sp2 hybridised carbon(s) in compound 'X' is ________.

In the given reaction,

The number of \(\pi\) electrons present in the product 'P' is _________.

Which of the following carbocations is most stable?

The structure of protein that is unaffected by heating is

Consider the species CH4, NH\(_4^ +\) and BH\(_4^ -\). Choose the correct option with respect to the these species.

Number of lone pair(s) of electrons on central atom and the shape BrF3 molecule respectively, are

4.0 moles of argon and 5.0 moles of PCl5 are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The Kp for the reac...

A box contains 0.90 g of liquid water in equilibrium with water vapour at 27\(^\circ\)C. The equilibrium vapour pressure of water at 27\(^\circ\)C is 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to...

The equation k = (6.5 \(\times\) 1012s\(-\)1)e\(-\)26000K/T is followed for the decomposition of compound A. The activation energy for the reaction is ________ kJ mol\(-\)1. [nearest integer]
(Given : R = 8.314 J K\(-\)1 mol\(-\)1)

The mixture of chloroxylenol and terpineol is an example of

In Friedel-Crafts alkylation of aniline, one gets

Given below are two statements.
\(\bullet\) Statement I : In CuSO4 . 5H2O, Cu-O bonds are present.
\(\bullet\) Statement II : In CuSO4 . 5H2O, ligands coordinating with Cu(II) ion are O-and S-based ligands.
In the light of the above stateme...

Spin only magnetic moment of [MnBr6]4\(-\) is _________ B.M. (round off to the closest integer)

For the reaction given below :
CoCl3 . xNH3 + AgNO3 (aq) \(\to\)
If two equivalents of AgCl precipitate out, then the value of x will be _____________.

The cell potential for the given cell at 298 K
Pt| H2 (g, 1 bar) | H+ (aq) || Cu2+ (aq) | Cu(s)
is 0.31 V. The pH of the acidic solution is found to be 3, whereas the concentration of Cu2+ is 10\(-\)x M. The value of x is ___________.
(Give...

The stable carbocation formed in the above reaction is

Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H, 4.9% and Br 42.9% gave benzoic acid and p-bromobenzoic acid, respectively on oxidation with KMnO4. Isomer 'A' is optically active and gives a pale yell...

Match List I with List II.

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Aqueous solution of which of the following boron compounds will be strongly basic in nature?

Sulphur dioxide is one of the components of polluted air. SO2 is also a major contributor to acid rain. The correct and complete reaction to represent acid rain caused by SO2 is :

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The first ionization enthalpy for oxygen is lower than that of nitrogen.
Reason R : The four electrons in 2p orbitals of oxy...

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Dacron is an example of polyester polymer.
Reason R : Dacron is made up of ethylene glycol and terephthalic acid monomers.
...

Amongst baking soda, caustic soda and washing soda, carbonate anion is present in :

A white precipitate was formed when BaCl2 was added to water extract of an inorganic salt. Further, a gas 'X' with characteristic odour was released when the formed white precipitate was dissolved in dilute HCl. The anion present in the ino...

Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant (Kb/Kf) is ...

Using the rules for significant figures, the correct answer for the expression \({{0.02858 \times 0.112} \over {0.5702}}\) will be

Which of the following is the correct plot for the probability density \({\psi ^2}\) (r) as a function of distance 'r' of the electron from the nucleus for 2s orbital?

A 42.12% (w/v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the sol in 2 hours is :
[Given : Molar mass : Na = 23.0 g mol\(-\)1 ; Cl = 35.5 g mol\(-\)1]

2.2 g of nitrous oxide (N2O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, \(\Delta\)U is '\(-\)x' J. The value...

Let \({{x - 2} \over 3} = {{y + 1} \over { - 2}} = {{z + 3} \over { - 1}}\) lie on the plane \(px - qy + z = 5\), for some p, q \(\in\) R. The shortest distance of the plane from the origin is :

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line $$\overrightarrow r = - \widehat k + \lambda \left( {\widehat i + \widehat j ...

Let f : R \(\to\) R be a function defined by f(x) = (x \(-\) 3)n1 (x \(-\) 5)n2, n1, n2 \(\in\) N. Then, which of the following is NOT true?

For real numbers a, b (a > b > 0), let
Area \(\left\{ {(x,y):{x^2} + {y^2} \le {a^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} \ge 1} \right\} = 30\pi\)
and
Area $$\left\{ {(x,y):{x^2} + {y^2} \le {b^2}\,and\,{{{x^2}} \over ...

Let n \(\ge\) 5 be an integer. If 9n \(-\) 8n \(-\) 1 = 64\(\alpha\) and 6n \(-\) 5n \(-\) 1 = 25\(\beta\), then \(\alpha\) \(-\) \(\beta\) is equal to

Let the coefficients of x\(-\)1 and x\(-\)3 in the expansion of \({\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5}}}}}} \right)^{15}},x > 0\), be m and n respectively. If r is a positive integer such that $$m{n^2} = {}^{15}{C_r}\,.\,...

Let a triangle ABC be inscribed in the circle \({x^2} - \sqrt 2 (x + y) + {y^2} = 0\) such that \(\angle BAC = {\pi \over 2}\). If the length of side AB is \(\sqrt 2\), then the area of the \(\Delta\)ABC is equal to :

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z \(-\) 1) \(-\) arg(z + 1) = \({\pi \over 4}\) intersect :

Let f be a real valued continuous function on [0, 1] and \(f(x) = x + \int\limits_0^1 {(x - t)f(t)dt}\).
Then, which of the following points (x, y) lies on the curve y = f(x) ?

If \(\int\limits_0^2 {\left( {\sqrt {2x} - \sqrt {2x - {x^2}} } \right)dx = \int\limits_0^1 {\left( {1 - \sqrt {1 - {y^2}} - {{{y^2}} \over 2}} \right)dy + \int\limits_1^2 {\left( {2 - {{{y^2}} \over 2}} \right)dy + I} } }\), then I equa...

If y = y(x) is the solution of the differential equation \(\left( {1 + {e^{2x}}} \right){{dy} \over {dx}} + 2\left( {1 + {y^2}} \right){e^x} = 0\) and y (0) = 0, then $$6\left( {y'(0) + {{\left( {y\left( {{{\log }_e}\sqrt 3 } \right)} \righ...

Let y = y(x), x > 1, be the solution of the differential equation \((x - 1){{dy} \over {dx}} + 2xy = {1 \over {x - 1}}\), with \(y(2) = {{1 + {e^4}} \over {2{e^4}}}\). If \(y(3) = {{{e^\alpha } + 1} \over {\beta {e^\alpha }}}\), then the va...

Let f and g be twice differentiable even functions on (\(-\)2, 2) such that \(f\left( {{1 \over 4}} \right) = 0\), \(f\left( {{1 \over 2}} \right) = 0\), \(f(1) = 1\) and \(g\left( {{3 \over 4}} \right) = 0\), \(g(1) = 2\). Then, the minimu...

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If \(f(g(x)) = 8{x^2} - 2x\) and \(g(f(x)) = 4{x^2} + 6x + 1\), then the value of \(f(2) + g(2)\) is _________.

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60\(^\circ\). The pole subtends an angle 30\(^\circ\) at the top of the tower. Then the height of the tower is :

The value of \(\mathop {\lim }\limits_{x \to 1} {{({x^2} - 1){{\sin }^2}(\pi x)} \over {{x^4} - 2{x^3} + 2x - 1}}\) is equal to:

Negation of the Boolean statement (p \(\vee\) q) \(\Rightarrow\) ((\(\sim\) r) \(\vee\) p) is equivalent to :

Let \(A = \left( {\matrix{ 2 & { - 1} \cr 0 & 2 \cr } } \right)\). If \(B = I - {}^5{C_1}(adj\,A) + {}^5{C_2}{(adj\,A)^2} - \,\,.....\,\, - {}^5{C_5}{(adj\,A)^5}\), then the sum of all elements of the matrix B is

Let \(M = \left[ {\matrix{ 0 & { - \alpha } \cr \alpha & 0 \cr } } \right]\), where \(\alpha\) is a non-zero real number an \(N = \sum\limits_{k = 1}^{49} {{M^{2k}}}\). If \((I - {M^2})N = - 2I\), then the positive integral v...

Let P : y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of \({\pi \over 4}\) with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is :