The value of $\cos^{-1}\left(\cos\frac{5\pi}{3}\right) + \sin^{-1}\left(\cos\frac{5\pi}{3}\right)$ is

The limiting points of the co-axial system containing the two circles $x^2+y^2+2x-2y+2=0$ and $25(x^2+y^2)-10x-80y+65=0$ are

The internal energy change in a system that has absorbed $2 \, kcal$ of heat and done $500 \, J$ of work is ........... $J$.

$A$ glass capillary tube of inner diameter $0.28 \ mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel (in $N/m^2$) is:
(Surface tension of water $= 0.07 \ N/m$,Atmospheric pressure $= 10^5 \ N/m^2$)

Which one of the following symbols and its representation,used in human pedigree analysis is correct?

The energy of an electromagnetic radiation is $19.875 \times 10^{-13} \ erg$. What is its wave number in $cm^{-1}$? $(h = 6.625 \times 10^{-27} \ erg \ sec, c = 3 \times 10^{10} \ cm \ sec^{-1})$