What will be the volume of $CO_2$ at $NTP$ obtained on heating $10 \ g$ of ($90\%$ pure) limestone (in $L$)?

Two ions having masses in the ratio $1: 1$ and charges $1: 2$ are projected into a uniform magnetic field perpendicular to the field with speeds in the ratio $2: 3$. The ratio of the radii of circular paths along which the two particles move is :

If $A(2,-1)$ and $B(6,5)$ are two points,the ratio in which the foot of the perpendicular from $P(4,1)$ to $AB$ divides $AB$ is:

For the energy levels in an atom,which one of the following statements is correct?

If $y = \cos^{-1}\left(\frac{a^2-x^2}{a^2+x^2}\right) + \sin^{-1}\left(\frac{2ax}{a^2+x^2}\right)$, then $\frac{dy}{dx}$ is equal to

The radiant energy from the sun incident normally at the surface of the earth is $20 \ kcal/m^2-min$. What would have been the radiant energy incident normally on the earth if the sun had a temperature twice of the present one? (in $kcal/m^2-min$)