Under hydrolytic conditions, the compounds used for the preparation of linear polymer and for chain termination, respectively, are

The increasing order of atomic radii of the following group $13$ elements is

The number of aldol reaction(s) that occurs in the given transformation is :

Which among the following statement(s) is (are) true for the extraction of aluminium from bauxite?

The initial rate of hydrolysis of methyl acetate$\left(1\mathrm{M}\right)$ by a weak acid $(\mathrm{HA}, 1\mathrm{M})$ is $1/{100}^{\mathrm{th}}$ of that by a strong acid $\left(\mathrm{HX}, 1\mathrm{M}\right)$, at $25°\mathrm{C}$. The ${\mathrm{K}}_{\mathrm{a}}$ of $\mathrm{HA}$ is

In \(1 \mathrm{~L}\) saturated solution of \(\mathrm{AgCl}\left[K_{\mathrm{sp}} \mathrm{AgCl}=1.6 \times 10^{-10}\right], 0.1\) mole of \(\mathrm{CuCl}\left[K_{\mathrm{sp}}(\mathrm{CuCl})=1.0 \times 10^{-6}\right]\) is added. The resultant concentration of \(\mathrm{Ag}^{+}\)in the solution is \(1.6 \times 10^{-x}\). The value of \(x\) is

For the reduction of \(\mathrm{NO}_3^{-}\)ion in an aqueous solution \(E^{\circ}\) is \(+0.96 \mathrm{~V}\). Values of \(E^{\circ}\) for some metal ions are given below.
\(
\begin{aligned}
& \mathrm{V}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{V} ; E^{\circ}=-1.19 \mathrm{~V} \\
& \mathrm{Fe}^{3+}(a q)+3 e^{-} \longrightarrow \mathrm{Fe} ; \mathrm{E}^{\circ}=-0.04 \mathrm{~V} \\
& \mathrm{Au}^{3+}(a q)+3 e^{-} \longrightarrow \mathrm{Au} ; E^{\circ}=+1.40 \mathrm{~V}
\end{aligned}
\)
\(
\mathrm{Hg}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Hg} ; E^{\circ}=+0.86 \mathrm{~V}
\)
The pair(s) of metals that is (are) oxidised by \(\mathrm{NO}_3^{-}\)in aqueous solution is (are)

A real gas behaves like an ideal gas if its

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8:15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $100$, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are:

For 3 x 3 matrices M and N, which of the following statement(s) is (are) not correct?

A black body of temperature \(T\) is inside chamber of temperature \(T_0\). Now, the closed chamber is slightly opened to sun such that temperature of black body \((T)\) and chamber \(\left(T_0\right)\) remains constant.

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A tertiary alcohol \(H\) upon acid catalysed dehydration gives a product \(I\). Ozonolysis of I leads to compounds \(\mathrm{J}\) and \(\mathrm{K}\). Compound \(\mathrm{J}\) upon reaction with
\(\mathrm{KOH}\) gives benzyl alcohol and a compound \(\mathrm{L}\), where \(\mathrm{K}\) on reaction with \(\mathrm{KOH}\) gives only \(M\).

Question:
The structures of compounds \(J, K\) and \(L\), respectively, are

Let \(P(6,3)\) be a point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\). If the normal at the point \(P\) intersects the \(X\)-axis at \((9,0)\), then the eccentricity of the hyperbola is