The differential equation of all circles, passing through the origin and having their centres on the $$\mathrm{X}$$-axis, is

$$\int_\limits0^1 \cos ^{-1} x d x=$$

Two trains, each $$30 \mathrm{~m}$$ long are travelling in opposite directions with velocities $$5 \mathrm{~m} / \mathrm{s}$$ and $$10 \mathrm{~m} / \mathrm{s}$$. They will cross after

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '$$\mathrm{A}$$' to that of air column in pipe '$$\mathrm{B}$$' is