The distribution of a random variable $X$ is given below:

$X = x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$k$	$\frac{1}{5}$	$2k$	$\frac{3}{10}$	$k$

The value of $k$ is:

An electron moves with speed $2 \times 10^5 \ m/s$ along the positive $x$-direction in the presence of a magnetic field of induction $B = (\hat{i} + 4\hat{j} - 3\hat{k}) \ T$. The magnitude of the force experienced by the electron in newtons is (Charge on the electron $= 1.6 \times 10^{-19} \ C$)

The bond length of $HCl$ molecule is $1.275 \ \mathring{A}$ and its dipole moment is $1.03 \ D$. The ionic character of the molecule (in percent) (charge of the electron $= 4.8 \times 10^{-10} \ esu$) is

$\sin 120^{\circ} \cos 150^{\circ} - \cos 240^{\circ} \sin 330^{\circ}$ is equal to :

Arrange the following set of compounds in order of their decreasing relative reactivity with an electrophile,$E^{+}$:
$(a)$ Chlorobenzene,$2,4-$dinitrochlorobenzene,$p-$nitrochlorobenzene
$(b)$ Toluene,$p-CH_3-C_6H_4-NO_2$,$p-O_2N-C_6H_4-NO_2$

The activation energy for a reaction at the temperature $T \ K$ was found to be $2.303 \ RT \ J \ mol^{-1}$. The ratio of the rate constant to Arrhenius factor is