The number of $5$-digit numbers that are not divisible by $5$ and consist of different odd digits is:

If $f(x) = \frac{x}{1+x}$ and $g(x) = f(f(x))$, then $g^{\prime}(x)$ is equal to

If $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}}$,then $\lim_{x \to \infty} f(x)$ is

The heat evolved for the rise of water when one end of the capillary tube of radius $r$ is immersed vertically into water is (Assume surface tension $= T$ and density of water to be $\rho$)

Two persons $A$ and $B$ are located in the $X-Y$ plane at the points $(0,0)$ and $(0,10)$ respectively. (The distances are measured in $MKS$ units). At time $t=0$,they start moving simultaneously with velocities $\overrightarrow{v}_A = 2\hat{j} \text{ m/s}$ and $\overrightarrow{v}_B = 2\hat{i} \text{ m/s}$ respectively. The time after which $A$ and $B$ are at their closest distance is

If $Alpha$,$Beta$,and $\Gamma$ rays carry the same momentum,which has the longest wavelength?