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

The electric field at a place is given by $\overrightarrow E = E_0 \widehat i \, V/m$. $A$ particle of charge $+q_0$ moves from point $A(0, a)$ to $B(a, 0)$ along a circular path. Find the work done by the electric field in this motion.

Which of the following elements shows a stable $+2$ oxidation state?

On electrolysis of aqueous solution of $KI$ in presence of platinum electrodes,which of the following statements are correct?
$(a)$ Hydrogen gas is released at cathode
$(b)$ Oxygen gas is released at anode
$(c)$ $pOH$ of solution decreases
$(d)$ There is deposition of potassium at cathode

$A$ rubber cube of side $5 ~cm$ has one face fixed,while a tangential force $1800 ~N$ is applied on its opposite face. If the modulus of rigidity of rubber is $2.4 \times 10^6 ~N/m^2$,then the lateral displacement of the strained face is . . . . . . (in $mm$)

Which of the following substances leads to the inhibition of the central nervous system?