JEE Main 2022 (Online) 27th July Morning Shift

In the above reaction product B is :

In the following reaction

The \(\%\) yield for reaction I is \(60 \%\) and that of reaction II is \(50 \%\). The overall yield of the complete reaction is __________ \(\%\). [nearest integer]

Given below are two statements: one is labelled as Assertion A and, the other is labelled as Reason R.
Assertion A: [6] Annulene, [8] Annulene and cis-[10] Annulene, are respectively aromatic, not-aromatic and aromatic.

Reason R: Planarity...

Optical activity of an enantiomeric mixture is \(+12.6^{\circ}\) and the specific rotation of \((+)\) isomer is \(+30^{\circ}\). The optical purity is __________\(\%\).

A sugar 'X' dehydrates very slowly under acidic condition to give furfural which on further reaction with resorcinol gives the coloured product after sometime. Sugar 'X' is

Given below are two statements.
Statement I: \(\mathrm{O}_{2}, \mathrm{Cu}^{2+}\), and \(\mathrm{Fe}^{3+}\) are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field.
Statement II: \(\mathrm{NaCl}\) a...

Amongst the following, the number of oxide(s) which are paramagnetic in nature is
$$\mathrm{Na}_{2} \mathrm{O}, \mathrm{KO}_{2}, \mathrm{NO}_{2}, \mathrm{~N}_{2} \mathrm{O}, \mathrm{ClO}_{2}, \mathrm{NO}, \mathrm{SO}_{2}, \mathrm{Cl}_{2} \m...

According to MO theory, number of species/ions from the following having identical bond order is ________.
\(\mathrm{CN}^{-}, \mathrm{NO}^{+}, \mathrm{O}_{2}, \mathrm{O}_{2}^{+}, \mathrm{O}_{2}^{2+}\)

\(2 \mathrm{NO}+2 \mathrm{H}_{2} \rightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O}\)
The above reaction has been studied at \(800^{\circ} \mathrm{C}\). The related data are given in the table below

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Match List I with List II.

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Match List I with List II.

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The conductivity of a solution of complex with formula \(\mathrm{CoCl}_{3}\left(\mathrm{NH}_{3}\right)_{4}\) corresponds to 1 : 1 electrolyte, then the primary valency of central metal ion is __________.

Given below are two statements.
Statement I : Iron (III) catalyst, acidified \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) and neutral \(\mathrm{KMnO}_{4}\) have the ability to oxidise \(\mathrm{I}^{-}\) to \(\mathrm{I}_{2}\) independen...

The total number of \(\mathrm{Mn}=\mathrm{O}\) bonds in \(\mathrm{Mn}_{2} \mathrm{O}_{7}\) is __________.

Match List I with List II.

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Given below are two statements.
Statement I : Hydrogen peroxide can act as an oxidizing agent in both acidic and basic conditions.
Statement II : Density of hydrogen peroxide at \(298 \mathrm{~K}\) is lower than that of $$\mathrm{D}_{2} \ma...

At \(310 \mathrm{~K}\), the solubility of \(\mathrm{CaF}_{2}\) in water is \(2.34 \times 10^{-3} \mathrm{~g} / 100 \mathrm{~mL}\). The solubility product of \(\mathrm{CaF}_{2}\) is ____________ $$\times 10^{-8}(\mathrm{~mol} / \mathrm{L})^{...

In the titration of \(\mathrm{KMnO}_{4}\) and oxalic acid in acidic medium, the change in oxidation number of carbon at the end point is ___________.

Which of the following methods are not used to refine any metal?
A. Liquation
B. Calcination
C. Electrolysis
D. Leaching
E. Distillation
Choose the correct answer from the options given below:

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Activated charcoal adsorbs SO2 more efficiently than CH4.
Reason R : Gases with lower critical temperatures are readily adso...

Given below are two statements.
Statement I: The chlorides of \(\mathrm{Be}\) and \(\mathrm{Al}\) have Cl-bridged structure. Both are soluble in organic solvents and act as Lewis bases.
Statement II: Hydroxides of \(\mathrm{Be}\) and $$\mat...

Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?

The incorrect statement is

Match List I with List II.

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Boiling point of a \(2 \%\) aqueous solution of a non-volatile solute A is equal to the boiling point of \(8 \%\) aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is

\(250 \mathrm{~g}\) solution of \(\mathrm{D}\)-glucose in water contains \(10.8 \%\) of carbon by weight. The molality of the solution is nearest to
(Given: Atomic Weights are, $$\mathrm{H}, 1 \,\mathrm{u} ; \mathrm{C}, 12 \,\mathrm{u} ; \m...

In Carius method of estimation of halogen, \(0.45 \mathrm{~g}\) of an organic compound gave \(0.36 \mathrm{~g}\) of \(\mathrm{AgBr}\). Find out the percentage of bromine in the compound.
(Molar masses : $$\mathrm{AgBr}=188 \mathrm{~g} \math...

\(20 \mathrm{~mL}\) of \(0.02 \,\mathrm{M} \,\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) solution is used for the titration of \(10 \mathrm{~mL}\) of \(\mathrm{Fe}^{2+}\) solution in the acidic medium.
The molarity of $$\mathrm{Fe}^{2+}...

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Energy of \(2 \mathrm{s}\) orbital of hydrogen atom is greater than that of \(2 \mathrm{s}\) orbital of lithium.
Reason R: En...

The molar heat capacity for an ideal gas at constant pressure is \(20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\). The change in internal energy is \(5000 \mathrm{~J}\) upon heating it from \(300 \mathrm{~K}\) to $$500 \mathrm{~K}...

If the plane \(P\) passes through the intersection of two mutually perpendicular planes \(2 x+k y-5 z=1\) and \(3 k x-k y+z=5, k<3\) and intercepts a unit length on positive \(x\)-axis, then the intercept made by the plane \(P\) on the $$y$...

Let the line \(\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4}\) intersect the plane containing the lines \(\frac{x-4}{1}=\frac{y+1}{-2}=\frac{z}{1}\) and \(4 a x-y+5 z-7 a=0=2 x-5 y-z-3, a \in \mathbb{R}\) at the point $$P(\alpha, \beta, \gamm...

Let \(M\) and \(N\) be the number of points on the curve \(y^{5}-9 x y+2 x=0\), where the tangents to the curve are parallel to \(x\)-axis and \(y\)-axis, respectively. Then the value of \(M+N\) equals ___________.

The area of the smaller region enclosed by the curves \(y^{2}=8 x+4\) and \(x^{2}+y^{2}+4 \sqrt{3} x-4=0\) is equal to

The remainder when \((2021)^{2022}+(2022)^{2021}\) is divided by 7 is

If the circle \(x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}\) passes through the point \((6,1)\) and its centre lies on the line \(x-2 c y=8\), then the length of intercept made by the circle on \(x\)-axis is :

Let the minimum value \(v_{0}\) of \(v=|z|^{2}+|z-3|^{2}+|z-6 i|^{2}, z \in \mathbb{C}\) is attained at \({ }{z}=z_{0}\). Then \(\left|2 z_{0}^{2}-\bar{z}_{0}^{3}+3\right|^{2}+v_{0}^{2}\) is equal to :

Let \(S=\left\{z \in \mathbb{C}: z^{2}+\bar{z}=0\right\}\). Then \(\sum\limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))\) is equal to ______________.

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined as
\(f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in \mathbb{R}\) where \([t]\) is the greatest integer less than or equal to \(t\). If $$\mathop {\lim }\limits_{x \t...

Let \(I=\int_{\pi / 4}^{\pi / 3}\left(\frac{8 \sin x-\sin 2 x}{x}\right) d x\). Then

Let a function \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined as :
$$f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|) d t, & x>4 \\ x^{2}+b x & , x \leq 4\end{cases}$$
where \(\mathrm{b} \in \mathbb{R}\). If \(f\) is continuous at $$x=4...

Let \(y=y_{1}(x)\) and \(y=y_{2}(x)\) be two distinct solutions of the differential equation \(\frac{d y}{d x}=x+y\), with \(y_{1}(0)=0\) and \(y_{2}(0)=1\) respectively. Then, the number of points of intersection of \(y=y_{1}(x)\) and $$y=...

Let \(y=y(x)\) be the solution curve of the differential equation
\(\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x^2}} \right)dy + \left( {4xy - 4\sqrt 2 x\sin \left( {{x^2} - {\pi \over 4}} \right)} \right)dx = 0\), $$0 < x < \sqrt ...

If the length of the latus rectum of the ellipse \(x^{2}+4 y^{2}+2 x+8 y-\lambda=0\) is 4 , and \(l\) is the length of its major axis, then \(\lambda+l\) is equal to ____________.

Let \(f, g: \mathbb{N}-\{1\} \rightarrow \mathbb{N}\) be functions defined by \(f(a)=\alpha\), where \(\alpha\) is the maximum of the powers of those primes \(p\) such that \(p^{\alpha}\) divides \(a\), and \(g(a)=a+1\), for all $$a \in \ma...

Let \(f(x)=2 x^{2}-x-1\) and \(\mathrm{S}=\{n \in \mathbb{Z}:|f(n)| \leq 800\}\). Then, the value of \(\sum\limits_{n \in S} f(n)\) is equal to ___________.

Let a vertical tower \(A B\) of height \(2 h\) stands on a horizontal ground. Let from a point \(P%\) on the ground a man can see upto height \(h\) of the tower with an angle of elevation \(2 \alpha\). When from \(P\), he moves a distance $...

An ellipse \(E: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) passes through the vertices of the hyperbola \(H: \frac{x^{2}}{49}-\frac{y^{2}}{64}=-1\). Let the major and minor axes of the ellipse \(E\) coincide with the transverse and conjug...

For \(k \in \mathbb{R}\), let the solutions of the equation \(\cos \left(\sin ^{-1}\left(x \cot \left(\tan ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)\right)\right)\right)=k, 0<|x|<\frac{1}{\sqrt{2}}\) be \(\alpha\) and \(\beta\), wher...

\((p \wedge r) \Leftrightarrow(p \wedge(\sim q))\) is equivalent to \((\sim p)\) when \(r\) is