An inductive circuit contains a resistance of $10\,\Omega$ and an inductance of $2.0\,H$. If an $AC$ voltage of $120\,V$ and frequency $60\,Hz$ is applied to this circuit,the current would be nearly ................$A$.

If $y=y(x)$ is the solution of the differential equation $\left(\frac{2+\sin x}{y+1}\right) \frac{d y}{d x}+\cos x=0$ with $y(0)=1$,then $y\left(\frac{\pi}{2}\right)$ is equal to

$1+\frac{1+2}{2 !}+\frac{1+2+2^2}{3 !}+\ldots$ is equal to

In an experiment with $15$ observations on $x$,the following results were available: $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:

$A$ photoelectric cell is connected to a source of variable potential difference. The resulting photoelectric current $(\mu A)$ is plotted against the applied potential difference $(V)$. The graph with the broken line represents the data for a given frequency and intensity of the incident radiation. If the frequency is increased and the intensity is reduced, which of the following graphs (represented by unbroken lines) corresponds to the new situation?

In which of the following reactions is hydrogen gas not liberated?