The current $I$ is flowing through a loop $A B C D A$ as shown in the figure. The magnitude of the magnetic field at the centre ' $O$ ' is $x$ times
$$ \left(\frac{\mu_0 \mathrm{I}}{\mathrm{R}}\right)\left(\mathrm{OD}=\mathrm{R}, \mathrm{DC}=\mathrm{R}, \angle \mathrm{AOD}=90^{\circ}\right) $$
The value of ' $x$ ' is ( $\mu_0=$ permeability of free space)

$\frac{5}{16}$
$\frac{5}{12}$
$\frac{7}{16}$
$\frac{7}{12}$
At what angle should the two forces $2 \overrightarrow{\mathrm{P}}$ and $\sqrt{2} \overrightarrow{\mathrm{P}}$ act so that the resultant force is $\sqrt{10} \overrightarrow{\mathrm{P}}$ ?
$\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
$\cos ^{-1}\left(\frac{1}{2}\right)$
$\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
If the r.m.s. velocity of gas is V at temperature T , then
$\mathrm{VT}^2=$ constant
$\mathrm{V}^2 \mathrm{~T}=$ constant
$\mathrm{V}^2 / \mathrm{T}=$ constant
$\quad \mathrm{VT}=$ constant
Light propagates 2 cm distance in glass of refractive index 1.5 in certain time. In the same time same light propogates a distance of 2.25 cm in a medium. The refractive index of the medium is
$\frac{4}{3}$
$\frac{3}{2}$
$\frac{8}{3}$
$\frac{3}{4}$
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