If the wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5 \times 10^{-6} \ m$ and $10^{-4} \ m$ respectively,the ratio of their temperatures is:

Two vibrating tuning forks produce progressive waves given by $Y_1 = 4 \sin(500 \pi t)$ and $Y_2 = 2 \sin(506 \pi t)$. The number of beats produced per minute is:

If $A = \{2, 4, 5\}$ and $B = \{7, 8, 9\}$,then $n(A \times B)$ is equal to:

The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

In Young's double slit experiment,the two slits act as coherent sources of equal amplitude $A$ and wavelength $\lambda$. In another experiment with the same setup,the two slits are sources of equal amplitude $A$ and wavelength $\lambda$,but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is:

$A$ magnetic needle lying parallel to a magnetic field is turned through $60^{\circ}$. The work done on it is $W$. The torque required to maintain the magnetic needle in the position mentioned above is