The molar heat capacity of water at constant pressure is $75 \, J \, K^{-1} \, mol^{-1}$. When $1.0 \, kJ$ of heat is supplied to $100 \, g$ of water,which is free to expand,the increase in temperature of water is $...... \, K$.

$A$ constant volume gas thermometer shows pressure readings of $50 \, cm$ and $90 \, cm$ of mercury at $0^{\circ} C$ and $100^{\circ} C$ respectively. When the pressure reading is $60 \, cm$ of mercury,the temperature is ......... $^{\circ} C$.

$A$ common emitter transistor amplifier has a current gain of $50$. If the load resistance is $4 \ k\Omega$ and input resistance is $500 \ \Omega$,the voltage gain of the amplifier is

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

$A$ variable plane passes through a fixed point $(1, 2, 3)$. The foot of the perpendicular from the origin to the plane lies on:

Two wires are made of the same material and have the same volume. Wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$,how much force is needed to stretch wire $2$ by the same amount $\Delta x$?