JEE Main 2022 (Online) 28th July Morning Shift

Choose the correct option for the following reactions.

Identify the major products A and B for the below given reaction sequence.

Match List - I with List - II.

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Among the following marked proton of which compound shows lowest \(\mathrm{pK}_{\mathrm{a}}\) value?

For the below given cyclic hemiacetal (X), the correct pyranose structure is :

The number of paramagnetic species among the following is ___________.
\(\mathrm{B}_{2}, \mathrm{Li}_{2}, \mathrm{C}_{2}, \mathrm{C}_{2}^{-}, \mathrm{O}_{2}^{2-}, \mathrm{O}_{2}^{+}\) and \(\mathrm{He}_{2}^{+}\)

The number of interhalogens from the following having square pyramidal structure is :
\(\mathrm{ClF}_{3}, \mathrm{IF}_{7}, \mathrm{BrF}_{5}, \mathrm{BrF}_{3}, \mathrm{I}_{2} \mathrm{Cl}_{6}, \mathrm{IF}_{5}, \mathrm{ClF}, \mathrm{ClF}_{5}\)

For kinetic study of the reaction of iodide ion with \(\mathrm{H}_{2} \mathrm{O}_{2}\) at room temperature :
(A) Always use freshly prepared starch solution.
(B) Always keep the concentration of sodium thiosulphate solution less than that o...

For the given first order reaction
\(\mathrm{A} \rightarrow \mathrm{B}\)
the half life of the reaction is \(0.3010 \mathrm{~min}\). The ratio of the initial concentration of reactant to the concentration of reactant at time $$2.0 \mathrm{~m...

Statements about Enzyme Inhibitor Drugs are given below :
(A) There are Competitive and Non-competitive inhibitor drugs.
(B) These can bind at the active sites and allosteric sites.
(C) Competitive Drugs are allosteric site blocking drugs.
...

Identify the correct statement for the below given transformation.

Total number of relatively more stable isomer(s) possible for octahedral complex \(\left[\mathrm{Cu}(\mathrm{en})_{2}(\mathrm{SCN})_{2}\right]\) will be _________.

Match List - I with List - II, match the gas evolved during each reaction.

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Which of the following has least tendency to liberate \(\mathrm{H}_{2}\) from mineral acids?

The disproportionation of \(\mathrm{MnO}_{4}^{2-}\) in acidic medium resulted in the formation of two manganese compounds \(\mathrm{A}\) and \(\mathrm{B}\). If the oxidation state of \(\mathrm{Mn}\) in \(\mathrm{B}\) is smaller than that of...

Match List - I with List - II.

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Given below are two statements:
Statement I : In polluted water values of both dissolved oxygen and \(\mathrm{BOD}\) are very low.
Statement II : Eutrophication results in decrease in the amount of dissolved oxygen.
In the light of the abov...

The metal salts formed during softening of hardwater using Clark's method are :

\(\mathrm{K}_{\mathrm{a}}\) for butyric acid \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{COOH}\right)\) is \(2 \times 10^{-5}\). The \(\mathrm{pH}\) of \(0.2 \,\mathrm{M}\) solution of butyric acid is __________ \(\times 10^{-1}\). (Neare...

Which of the reaction is suitable for concentrating ore by leaching process ?

In which of the following pairs, electron gain enthalpies of constituent elements are nearly the same or identical?
(A) Rb and Cs
(B) Na and K
(C) Ar and Kr
(D) I and At
Choose the correct answer from the options given below :

Terylene polymer is obtained by condensation of :

Which of the following statement is incorrect?

An element M crystallises in a body centred cubic unit cell with a cell edge of \(300 \,\mathrm{pm}\). The density of the element is \(6.0 \mathrm{~g} \mathrm{~cm}^{-3}\). The number of atoms present in \(180 \mathrm{~g}\) of the element is...

\(150 \mathrm{~g}\) of acetic acid was contaminated with \(10.2 \mathrm{~g}\) ascorbic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) to lower down its freezing point by $$\left(x \times 10^{-1}\right)^{\circ} \mathrm{C}...

In the given reaction,
\(X+Y+3 Z \leftrightarrows X YZ_{3}\)
if one mole of each of \(X\) and \(Y\) with \(0.05 \mathrm{~mol}\) of \(Z\) gives compound \(X Y Z_{3}\). (Given : Atomic masses of \(X, Y\) and \(Z\) are 10, 20 and 30 amu, respe...

On complete combustion of \(0.492 \mathrm{~g}\) of an organic compound containing \(\mathrm{C}, \mathrm{H}\) and \(\mathrm{O}\), \(0.7938 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.4428 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) was p...

Identify the incorrect statement from the following.

Match List - I with List - II.

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Which of the following relation is not correct?

The foot of the perpendicular from a point on the circle \(x^{2}+y^{2}=1, z=0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves?

Let \(\mathrm{P}(-2,-1,1)\) and \(\mathrm{Q}\left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)\) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are \(\alpha,-1, \beta\), where both \(\alpha\) and $$\b...

If the minimum value of \(f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0\), is 14 , then the value of \(\alpha\) is equal to :

The remainder when \(7^{2022}+3^{2022}\) is divided by 5 is :

For \(\mathrm{t} \in(0,2 \pi)\), if \(\mathrm{ABC}\) is an equilateral triangle with vertices \(\mathrm{A}(\sin t,-\cos \mathrm{t}), \mathrm{B}(\operatorname{cost}, \sin t)\) and \(C(a, b)\) such that its orthocentre lies on a circle with c...

Let \(C\) be the centre of the circle \(x^{2}+y^{2}-x+2 y=\frac{11}{4}\) and \(P\) be a point on the circle. A line passes through the point \(\mathrm{C}\), makes an angle of \(\frac{\pi}{4}\) with the line \(\mathrm{CP}\) and intersects th...

Let \(S_{1}=\left\{z_{1} \in \mathbf{C}:\left|z_{1}-3\right|=\frac{1}{2}\right\}\) and \(S_{2}=\left\{z_{2} \in \mathbf{C}:\left|z_{2}-\right| z_{2}+1||=\left|z_{2}+\right| z_{2}-1||\right\}\). Then, for \(z_{1} \in S_{1}\) and $$z_{2} \in ...

The minimum value of the twice differentiable function \(f(x)=\int\limits_{0}^{x} \mathrm{e}^{x-\mathrm{t}} f^{\prime}(\mathrm{t}) \mathrm{dt}-\left(x^{2}-x+1\right) \mathrm{e}^{x}\), \(x \in \mathbf{R}\), is :

If \(\int\limits_{0}^{\sqrt{3}} \frac{15 x^{3}}{\sqrt{1+x^{2}+\sqrt{\left(1+x^{2}\right)^{3}}}} \mathrm{~d} x=\alpha \sqrt{2}+\beta \sqrt{3}\), where \(\alpha, \beta\) are integers, then \(\alpha+\beta\) is equal to __________.

Let the solution curve of the differential equation \(x \mathrm{~d} y=\left(\sqrt{x^{2}+y^{2}}+y\right) \mathrm{d} x, x>0\), intersect the line \(x=1\) at \(y=0\) and the line \(x=2\) at \(y=\alpha\). Then the value of \(\alpha\) is :

If \(y=y(x), x \in(0, \pi / 2)\) be the solution curve of the differential equation \(\left(\sin ^{2} 2 x\right) \frac{d y}{d x}+\left(8 \sin ^{2} 2 x+2 \sin 4 x\right) y=2 \mathrm{e}^{-4 x}(2 \sin 2 x+\cos 2 x)\), with $$y(\pi / 4)=\mathrm...

Let \(\alpha, \beta\) and \(\gamma\) be three positive real numbers. Let \(f(x)=\alpha x^{5}+\beta x^{3}+\gamma x, x \in \mathbf{R}\) and \(g: \mathbf{R} \rightarrow \mathbf{R}\) be such that \(g(f(x))=x\) for all \(x \in \mathbf{R}\). If $...

For \(\mathrm{p}, \mathrm{q} \in \mathbf{R}\), consider the real valued function \(f(x)=(x-\mathrm{p})^{2}-\mathrm{q}, x \in \mathbf{R}\) and \(\mathrm{q}>0\). Let \(\mathrm{a}_{1}\), \(\mathrm{a}_{2^{\prime}}\) \(\mathrm{a}_{3}\) and $$\ma...

For the hyperbola \(\mathrm{H}: x^{2}-y^{2}=1\) and the ellipse \(\mathrm{E}: \frac{x^{2}}{\mathrm{a}^{2}}+\frac{y^{2}}{\mathrm{~b}^{2}}=1\), a \(>\mathrm{b}>0\), let the
(1) eccentricity of \(\mathrm{E}\) be reciprocal of the eccentricity ...

Considering only the principal values of the inverse trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)\) is :

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation \(\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)\) is equal to :

Let \(f:[0,1] \rightarrow \mathbf{R}\) be a twice differentiable function in \((0,1)\) such that \(f(0)=3\) and \(f(1)=5\). If the line \(y=2 x+3\) intersects the graph of \(f\) at only two distinct points in \((0,1)\), then the least numbe...

\(\lim\limits_{x \rightarrow 0}\left(\frac{(x+2 \cos x)^{3}+2(x+2 \cos x)^{2}+3 \sin (x+2 \cos x)}{(x+2)^{3}+2(x+2)^{2}+3 \sin (x+2)}\right)^{\frac{100}{x}}\) is equal to ___________.

Let the operations \(*, \odot \in\{\wedge, \vee\}\). If \((\mathrm{p} * \mathrm{q}) \odot(\mathrm{p}\, \odot \sim \mathrm{q})\) is a tautology, then the ordered pair \((*, \odot)\) is :

Let the matrix $$A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]$$ and the matrix \(B_{0}=A^{49}+2 A^{98}\). If \(B_{n}=A d j\left(B_{n-1}\right)\) for all \(n \geq 1\), then $$\operatorname{det}\left(B_{4}\r...