$A$ real gas behaves like an ideal gas if its

Wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \ Å$ and $\lambda_2 = 5000 \ Å$. The ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$) is:

The triangle formed by the lines $2x^2+xy-6y^2=0$ and $x+y-1=0$ is

Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the midpoint of $PQ.$ The distance $OR$ remains the same for a small change in temperature. The coefficient of linear expansion for $PR$ and $RQ$ is the same,i.e.,$\alpha_2,$ but that for $PQ$ is $\alpha_1.$ Then the relation between $\alpha_1$ and $\alpha_2$ is:

Which of the following sets of quantum numbers belongs to the highest energy orbital?

$A$ ball is falling freely from a height. When it reaches $10 ~m$ height from the ground,its velocity is $v_0$. It collides with the ground,loses $50 \%$ of its energy,and rises back to a height of $10 ~m$. Then the velocity $v_0$ is (in $~m/s$)