$\sinh ^{-1} 2 + \sinh ^{-1} 3 = x \Rightarrow \cosh x$ is equal to

If the roots of $x^3-42 x^2+336 x-512=0$ are in increasing geometric progression,then its common ratio is (in $: 1$)

For the gaseous reactions $(I)$ and $(II)$,the equilibrium constants are $X$ and $Y$ respectively.
$I$. $\frac{1}{2} N_{2(g)} + O_{2(g)} \rightleftharpoons NO_{2(g)}$
$II$. $2 NO_{2(g)} \rightleftharpoons N_2 O_{4(g)}$
Using the above reactions,the equilibrium constant $Z$ for the reaction $(III)$ given below is:
$III$. $N_2 O_{4(g)} \rightleftharpoons N_{2(g)} + 2 O_{2(g)}$

$A$ particle $A$ is projected vertically upwards. Another identical particle $B$ is projected at an angle of $45^{\circ}$. Both reach the same maximum height. The ratio of the initial kinetic energy of $A$ to that of $B$ is

The relation between the coefficient of real expansion $(\gamma_r)$ and coefficient of apparent expansion $(\gamma_a)$ of a liquid and the coefficient of linear expansion $(\alpha_g)$ of the material of the container is

In the following common emitter circuit,if $\beta = 100, V_{CE} = 7 \, V, V_{BE} = 0 \, V$ (negligible),and $R_C = 2 \, k\Omega$,then find $I_B$ in $mA$.