Some standard electrode potentials at $298 \mathrm{K}$ are given below: $\begin{array}{ll}{\mathrm{Pb}}^{2+}/\mathrm{Pb}& -0.13 \mathrm{V}\end{array}$ $\begin{array}{ll}{\mathrm{Ni}}^{2+}/\mathrm{Ni}& -0.24 \mathrm{V}\end{array}$ $\begin{array}{ll}{\mathrm{Cd}}^{2+}/\mathrm{Cd}& -0.40 \mathrm{V}\end{array}$ $\begin{array}{ll}{\mathrm{Fe}}^{2+}/\mathrm{Fe}& -0.44 \mathrm{V}\end{array}$ To a solution containing $0.001 \mathrm{M}$ of ${\mathbf{X}}^{2+}$ and $0.1 \mathrm{M}$ of ${\mathbf{Y}}^{2+}$, the metal rods $\mathbf{X}$ and $\mathbf{Y}$ are inserted $($at $298 \mathrm{K})$ and connected by a conducting wire. This resulted in dissolution of $\mathbf{X}$. The correct combination(s) of $\mathbf{X}$ and $\mathbf{Y}$, respectively, is(are) (Given: Gas constant, $\mathrm{R}=8.314 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$, Faraday constant, $\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$)

A trinitro compound, $1,3,5$-tris-($4$-nitrophenyl) benzene, on complete reaction with an excess of $\mathrm{Sn}/\mathrm{HCl}$ gives a major product, which on treatment with an excess of ${\mathrm{NaNO}}_2/\mathrm{HCl}$ at $0°\mathrm{C}$ provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of ${\mathrm{H}}_2\mathrm{O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$. The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is $474 \mathrm{g} {\mathrm{mol}}^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is $172.5 \mathrm{g} {\mathrm{mol}}^{-1}$.
The number of heteroatoms present in one molecule of \(R\) is [Use: Molar mass (in \(\text{g mol} -1\) ): \(H =1,\) \(C =12, N=14, O =16,\) \(Br =80, Cl =35.5\) Atoms other than C and H are considered as heteroatoms]

For the given close packed structure of a salt made of cation $\mathrm{X}$ and anion $\mathrm{Y}$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction $=\frac{\mathrm{packing} \mathrm{efficiency}}{100}$)

Match the following

Statement I Boron always forms covalent bond
Statement II The small size of \(\mathrm{B}^{3+}\) favours formation of covalent bond.

The maximum number of possible isomers (including stereoisomers) which may be formed on mono-bromination of $1$-methylcyclohex- $1$-ene using ${\mathrm{Br}}_2$ and $\mathrm{UV}$ light is ___.

An organic compound undergoes first-order decomposition. The time taken for its decomposition to \(1 /\) 8 and \(1 / 10\) of its initial concentration are \(t_{1 / 8}\) and \(t_{1 / 10}\) respectively. What is the value of \(\left[\frac{t_{1 / 8}}{t_{1 / 10}}\right] \times 10\) ? \(\left(\log _{10} 2=0.3\right)\)

A binary star consists of two stars \(A\) (mass \(2.2 M_S\) ) and \(B\) (mass \(11 M_s\) ), where \(M_S\) is the mass of the sun. They are separated by distance \(d\) and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of \(\operatorname{star} B\) about the centre of mass is

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Let \(A_1, G_1, H_1\) denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For \(n \geq 2\), let \(A_{n-1}\) and \(H_{n-1}\) has arithmetic, geometric and harmonic means as \(A_n, G_n, H_n\), respectively.
Question:
Which of the following statements is correct?

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

Three objects \(A, B\) and \(C\) are kept in a straight line on a frictionless horizontal surface. These have masses \(m, 2 m\) and \(m\), respectively. The object \(A\) moves towards \(B\) with a speed \(9 \mathrm{~ms}^{-1}\) and makes an elastic collision with it. Thereafter, \(B\) makes completely inelastic collision with \(C\). All motions occur on the same straight line. Find the final speed (in \(\mathrm{ms}^{-1}\) ) of the object \(C\).

In the following \([x]\) denotes the greatest integer less than or equal to \(x\). Match the functions in Column I with the properties Column II.

In the Newman projection for 2,2-dimethylbutane

\(X\) and \(Y\) can respectively be