The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

The variance of the first $50$ even natural numbers is

The $K_{\alpha}$ $X$-ray emission line of tungsten occurs at $\lambda = 0.021 \, nm$. The energy difference between $K$ and $L$ levels in this atom is about:

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$,then $\left(1+a^2 x^2\right) y^{\prime \prime}+2 a^2 x y^{\prime}$ is equal to

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 ~cm$,the total length of the hollow cylinder is: (in $~cm$)

$A$ body is executing Simple Harmonic Motion. At a displacement $x$ its potential energy is $E_1$ and at a displacement $y$ its potential energy is $E_2$. The potential energy $E$ at displacement $(x + y)$ is