An ideal transformer has $100$ turns in the primary and $250$ turns in the secondary. The peak value of the $AC$ voltage in the primary is $28\ V$. The $r.m.s.$ secondary voltage is nearest to $....V$.

The probability that a number selected at random from the set of numbers ${1, 2, 3, \ldots, 100}$ is a cube, is

What is the concentration of $20$ volume $H_2O_2$ in $g/L$?

$A$ spherical black body of radius $12 \, cm$ radiates $450 \, W$ of power at $500 \, K$. If the radius is halved and the temperature is doubled,the power radiated will be ........ $W$.

Two ideal slits $S_1$ and $S_2$ are at a distance $d$ apart and are illuminated by light of wavelength $\lambda$ passing through an ideal source slit $S$ placed on the line through $S_2$ as shown. The distance between the plane of the slits and the source slit is $D$. $A$ screen is held at a distance $D$ from the plane of the slits. The minimum value of $d$ for which there is darkness at $O$ is

For better survival of the human population,which of the following steps is most important?