If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle of $\frac{3 \pi}{4}$ with the positive $X$-axis,then the value of $f^{\prime}(3)$ is

$A$ specific volume of $H_2$ requires $24 \ s$ to diffuse out of a container. The time required by an equal volume of $O_2$ to diffuse out under identical conditions is $..... \ s$.

Particles of masses $m, 2m, 3m, \ldots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \ldots, nl$ $cm$ from a fixed point. The distance of the centre of mass of the particles from the fixed point in centimetres is

In the Compton scattering process,the incident $X$-radiation is scattered at an angle of $60^{\circ}$. The wavelength of the scattered radiation is $0.22 \ \mathring{A}$. The wavelength of the incident $X$-radiation in $\mathring{A}$ units is:

How many unit cells are present in $39 \ g$ of potassium that crystallises in body-centred cubic structure? [At. wt. of $K = 39$]

$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$, then $P(X=0)$ is equal to: