$A$ 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.....$V$.

The total number of atomic orbitals in the fourth energy level of an atom is .......

If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Four particles,each of mass $m$,are gently placed on the ring at opposite points of two perpendicular diameters. The new angular velocity of the ring will be:

At $25 \, ^oC$,the equilibrium $SO_2Cl_2(g) \rightleftharpoons SO_2(g) + Cl_2(g)$ is established in a closed vessel. When $Cl_2$ is added to this equilibrium mixture,which of the following statements is true for the system?
$(1)$ The concentrations of $SO_2Cl_2$ and $SO_2$ change.
$(2)$ More $Cl_2$ is produced.
$(3)$ The concentration of $SO_2$ decreases and $SO_2Cl_2$ increases.

During the mean life of a radioactive element,the fraction that disintegrates is