$6.023 \times 10^{22}$ molecules are present in $10 \text{ g}$ of a substance '$X$'. The molarity of a solution containing $5 \text{ g}$ of substance '$X$' in $2 \text{ L}$ solution is ........... $\times 10^{-3} \text{ M}$.

$\frac{\sin 5 \theta}{\sin \theta}$ is equal to

The eccentricity of the ellipse $x^2+4y^2+2x+16y+13=0$ is

$A$ particle of mass $1 \times 10^{-26} \ kg$ and charge $1.6 \times 10^{-19} \ C$ travelling with a velocity $1.28 \times 10^6 \ ms^{-1}$ along the positive $X$-axis enters a region in which a uniform electric field $E$ and a uniform magnetic field of induction $B$ are present. If $E = -102.4 \times 10^3 \ \hat{k} \ NC^{-1}$ and $B = 8 \times 10^{-2} \ \hat{j} \ Wbm^{-2}$,the direction of motion of the particle is:

In a transistor circuit,when the base current is increased by $50 \mu A$ keeping the collector voltage fixed at $2 \ V$,the collector current increases by $1 \ mA$. The current gain of the transistor is

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is