If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements,then the number of relations from $A$ to $B$ is

If $f(x) = \sin^2 \left( \frac{\pi}{8} + \frac{x}{2} \right) - \sin^2 \left( \frac{\pi}{8} - \frac{x}{2} \right)$,then the period of $f$ is

Lactose is a disaccharide of

$A$ weak acid $HX$ has the dissociation constant $1 \times 10^{-5} \text{ } M$. It forms a salt $NaX$ on reaction with alkali. The percentage hydrolysis of $0.1 \text{ } M$ solution of $NaX$ is ............... $\%$

The wavelength of ${K_\alpha }$ $X-$rays produced by an $X-$ray tube is $0.76 \ \mathring A$. The atomic number of the anode material of the tube is:

$A$ ball is allowed to fall from a height of $10\, m$. If there is $40\%$ loss of energy due to impact,then after one impact,the ball will rise to a height of ......... $m$.