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

The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA$ is equal to:

An $AC$ source of angular frequency $\omega$ is fed across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If now the frequency of the source is changed to $\omega/3$ (but maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

The temperature in $K$ at which $\Delta G = 0$ for a given reaction with $\Delta H = -20.5 \ kJ \ mol^{-1}$ and $\Delta S = -50.0 \ J \ K^{-1} \ mol^{-1}$ is:

In the case of alkali metals,the covalent character decreases in the order