Ammonia can be dried by

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$,then $\left(1+a^2 x^2\right) y^{\prime \prime}+2 a^2 x y^{\prime}$ is equal to

$A$ load of $1 ~kg$ weight is attached to one end of a steel wire of area of cross-section $3 ~mm^2$ and Young's modulus $10^{11} ~N/m^2$. The other end is suspended vertically from a hook on a wall,then the load is pulled horizontally and released. When the load passes through its lowest position,the fractional change in length is $(g = 10 ~m/s^2)$.

The number of common tangent$(s)$ to the circles $x^2 + y^2 + 2x + 8y - 23 = 0$ and $x^2 + y^2 - 4x - 10y + 19 = 0$ is:

Identify the chiral molecule from the following.

Which of the following hydrides is the least stable?