Magnetic field at the centre of a circular loop of area ' $A$ ' is ' $B$ '. The magnetic moment of the loop is ' $x B$ '. The value of ' $x$ ' is ( $\mu_0=$ permeability of vacuum or free space)
$\frac{\sqrt{A^3}}{\mu_0 \pi}$
$\frac{2 \sqrt{A}}{\mu_0 \pi}$
$\frac{2}{\mu_0} \sqrt{\frac{\mathrm{~A}^3}{\pi}}$
$\frac{2}{\mu_0} \sqrt{\frac{\mathrm{~A}}{\pi}}$
An ideal gas in a container of volume 500 cc is at a pressure of $2 \times 10^5 \mathrm{~N} / \mathrm{m}^2$. The average kinetic energy of each molecule is $6 \times 10^{-21} \mathrm{~J}$. The number of gas molecules in the container is
$5 \times 10^{25}$
$5 \times 10^{23}$
$25 \times 10^{23}$
$2.5 \times 10^{22}$
Out of the following graphs, the correct graphical relation for LC parallel resonant circuit at resonance is

D
C
B
A
A small steel ball of mass ' M ', radius ' R ' and density ' $\rho$ ' falls with terminal velocity through a tube filled with glycerine of density ' $\sigma$ '. The viscous force acting on the steel ball is ( $\mathrm{g}=$ acceleration due to gravity)
$\mathrm{Mg} \frac{\rho}{\sigma}$
$\mathrm{Mg}(\mathrm{Q}-\sigma)$
$\mathrm{Mg} \rho \sigma$
$M g\left(1-\frac{\sigma}{\rho}\right)$
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