If $\frac{x-4}{x^2-5x-2k} = \frac{2}{x-2} - \frac{1}{x+k}$,then $k$ is equal to

$A$ radioactive sample $S_1$ having an activity of $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ can be

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$,$P(\bar{A} \cup \bar{B}) = \frac{7}{10}$ and $P(B) = \frac{2}{5}$,then $P(A)$ equals

The reaction $RCOCl + H_2 \xrightarrow{Pd/BaSO_4} RCHO + HCl$ is known as:

$A$ sinusoidal carrier voltage of frequency $1.5 \, MHz$ and amplitude $50 \, V$ is amplitude modulated by a sinusoidal voltage of frequency $10 \, kHz$ producing $50 \% $ modulation. The lower and upper side-band frequencies in $kHz$ are:

Find out the value of $K_C$ for the following reaction from the value of $K_P$
$2NOCl_{(g)} \rightleftharpoons 2NO_{(g)} + Cl_{2(g)}$
[Given : $K_P = 8 \times 10^{12} \ atm$ at $500 \ K$ use $R = 0.08 \ L \ atm \ mol^{-1} \ K^{-1}$ ]