An inductor of $2\,H$ and a resistance of $10\,\Omega$ are connected in series with a battery of $5\,V$. The initial rate of change of current is.....$A/s$.

The cold junction of a thermocouple is maintained at $10\,^{\circ}C$. No thermo $e.m.f.$ is developed when the hot junction is maintained at $530\,^{\circ}C$. The neutral temperature is ................ $^{\circ}C$.

$A$ $100 \ mL$ solution of $0.1 \ N$ $HCl$ was titrated with $0.2 \ N$ $NaOH$ solution. The titration was discontinued after adding $30 \ mL$ of $NaOH$ solution. The remaining titration was completed by adding $0.25 \ N$ $KOH$ solution. The volume of $KOH$ required for completing the titration is $............ \ mL$.

The following graph shows two isotherms for a fixed mass of an ideal gas. The ratio of $r.m.s.$ speed of the molecules at temperatures $T_1$ and $T_2$ is

$ICBN$ stands for

$A$ circle with center at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$. The radius of the circle is