The angular momentum of an electron in a stationary state of \(\mathrm{Li}^{2+}(\mathrm{Z}=3)\) is \(\frac{3 h}{\pi}\). The radius and energy of that stationary state are respectively

A subshell $\mathrm{n}=3, \mathrm{l}=2$ can accommodate maximum of

The elevation in boiling point of a solution of \(10 \mathrm{~g}\) of a binary electrolyte (of molecular mass 100) in \(100 \mathrm{~g}\) of water is \(\Delta T_b\). Then, the value of \(K_b\) for water is

Acetone on addition to methyl magnesium bromide forms a complex, which on decomposition with acid gives \(X\) and \(\mathrm{Mg}(\mathrm{OH}) \mathrm{Br}\). Which one of the following is \(X\) ?

What will be the molality of the solution containing \(18.25 \mathrm{~g}\) of \(\mathrm{HCl}\) gas in \(500 \mathrm{~g}\) of water?

From the following, identify the reactions which are responsible for depletion of ozone layer.
\(\begin{aligned}
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{NO}_2(g) \rightarrow \mathrm{ClONO}_2(g) \\
& \mathrm{CF}_2 \mathrm{Cl}_2(g) \xrightarrow{\text { uv }} \mathrm{Cl}(g)+\dot{\mathrm{CF}}_2 \mathrm{Cl}(g) \\
& \dot{\mathrm{Cl}}(g)+\mathrm{CH}_4(g) \rightarrow \mathrm{HCl}(g)+\dot{\mathrm{C}} \mathrm{H}_3(g) \\
& \dot{\mathrm{C}} \mathrm{l}(\mathrm{g})+\mathrm{O}_3(g) \rightarrow \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}_2(g) \\
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}(g) \rightarrow \dot{\mathrm{C}} \mathrm{l}(g)+\mathrm{O}_2(g)
\end{aligned}\)

Maximum number of electrons possible with spin quantum number \(+\frac{1}{2}\) with principal quantum number \(\mathrm{n}=4\) in an atom is

If \(\int \frac{\mathrm{dx}}{1-\sin ^4 \mathrm{x}}=\mathrm{A} \tan \mathrm{x}+\mathrm{B} \operatorname{Tan}^{-1}(\sqrt{2} \tan \mathrm{x})+\mathrm{C}\), then \(\mathrm{A}^2-\mathrm{B}^2=\)

If \(P+Q+R=\frac{\pi}{4}\), then
\(\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos \left(\frac{\pi}{8}-R\right)=\)

The constant ' \(\mathcal{C}\) ' of Lagrange's mean value theorem for the function \(f(x)=\frac{2 x+3}{4 x-1}\) defined on \([1,2]\) is

If \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are non-zero real numbers and if the equations \((a-1) x=y+z,(b-1) y=z+x,(c-1) z=x+y\) have a non-trivial solution, then \(a b+b c+c a=\)

\[
\lim _{x \rightarrow 9} \frac{(2.5)^{81-x^2}-(0.4)^{x+9}}{x+9}=
\]

The volume of \(0.02 \mathrm{M}\) acidified permanganate solution required for complete reaction of \(60 \mathrm{~mL}\), of \(0.01 \mathrm{M} \mathrm{I}^{-}\)ion solution to form \(\mathrm{I}_2\) in \(\mathrm{mL}\) is