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

If $L: ax + by + c = 0$ is a variable straight line,where $a, b$ and $c$ are the second,fourth and seventh terms of an $AP$ respectively,then $L$ passes through the fixed point -

$A$ light beam is traveling from Region $I$ to Region $IV$ (Refer Figure). The refractive indices in Region $I, II, III$ and $IV$ are $n_0, \frac{n_0}{2}, \frac{n_0}{6}$ and $\frac{n_0}{8}$,respectively. The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

Newton's law of cooling is a special case of

The amount of heat energy required to raise the temperature of $1\, g$ of Helium at $NTP$ from $T_1\, K$ to $T_2\, K$ is