The correct statements about the oxoacids, ${\mathrm{HClO}}_4\mathrm{ }\mathrm{and}\mathrm{ }\mathrm{HClO}$ are,

In the following monobromination reaction, the number of possible chiral products is

For the reaction sequence given below, the correct statement(s) is(are)

Among the complex ions,
\(\left[\mathrm{Co}\left(\mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{NH}_{2}\right)_{2} \mathrm{Cl}_{2}\right]^{+},\)\(\left[\mathrm{CrCl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{OH})_{2}\right]^{+}\), \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{CN})_{4}\right]^{-},\)\(\left[\mathrm{Co}(\mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{NH}_{2})_{2}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}\right]^{2+}\) and \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right]^{2+}\), the number of complex ion(s) that show(s) cis-trans isomerism is

Newman projections $\mathrm{P},\mathrm{Q},\mathrm{R}$ and $\mathrm{S}$ are shown below:

Which one of the following options represent identical molecules?

In the following carbocation, \(\mathrm{H} / \mathrm{CH}_3\) that is most likely to migrate to the positively charged carbon is

For the following reaction $2\mathrm{X}+\mathrm{Y}\stackrel{\mathrm{k}}{\to }\mathrm{P}$ the rate of reaction is $\frac{\mathrm{d}\left[\mathrm{P}\right]}{\mathrm{dt}}=\mathrm{k}\left[\mathrm{X}\right]$. Two moles of $\mathrm{X}$ are mixed with one mole of $\mathrm{Y}$ to make $1.0 \mathrm{L}$ of solution. At $50 \mathrm{s}, 0.5$ mole of $\mathrm{Y}$ is left in the reaction mixture. The correct statement(s) about the reaction is(are) $($Use: $\ln 2=0.693)$

Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option.

List - I	List - II
(P) \(XeF _2\)	(1) Trigonal bipyramidal and two lone pair of electrons
(Q) \(XeF _4\)	(2) Tetrahedral and one lone pair of electrons
(R) \(XeO _3\)	(3) Octahedral and two lone pair of electrons
(S) \(XeO _3 F_2\)	(4) Trigonal bipyramidal and no lone pair of electrons
	(5) Trigonal bipyramidal and three lone pair of electrons

Let $P$ be the image of the point$(3,1,7)$ with respect to the plane $x-y+z=3.$ Then the equation of the plane passing through $P$ and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is

For an isosceles prism of angle $A$ and refractive index $\mu$ it is found that, the angle of minimum deviation is ${ \delta }_m=A$. Which of the following options is/are correct?

The carboxyl functional group \((-\mathrm{COOH})\) is present in

Let \(H_1, H_2, \ldots, H_n\) be mutually exclusive events with \(P\left(H_i\right)>0, i=1,2, \ldots, n\). Let \(E\) be any other event with \(0 < P(E) < 1\).
Statement I \(P\left(H_i / E\right)>P\left(E / H_i\right) P\left(H_i\right)\) for \(i=1,2, \ldots, n\).
Statement II \(\sum_{i=1}^n P\left(H_i\right)=1\)

Statement I The curve \(y=-\frac{x^2}{2}+x+1\) is symmetric with respect to the line \(x=1\)
Statement II A parabola is symmetric about its axis.