The structure of $H_2O_2$ is

Nitrobenzene on reduction using zinc in alkaline medium results in $X$. The number of $\sigma$ and $\pi$ bonds in $X$ is

$A$ sinusoidal voltage of peak value $200\, V$ is connected to a diode and resistor $R$ in the circuit shown so that half-wave rectification occurs. If the forward resistance of the diode is negligible compared to $R$,the $rms$ voltage across $R$ is approximately.....$V$.

$A$ narrow parallel beam of light is incident paraxially on a solid transparent sphere of radius $r$ kept in air. What should be the refractive index if the beam is to be focused at the farther surface of the sphere?

The solution of $\frac{dy}{dx} + \frac{1}{3}y = 1$ is

If $f: R \rightarrow R$ is defined by $f(x) = x - [x]$,where $[x]$ is the greatest integer not exceeding $x$,then the set of points of discontinuity of $f$ is