Two different radioactive elements with half lives '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' have undecayed atoms '$$\mathrm{N}_1$$' and '$$\mathrm{N}_2$$' respectively present at a given instant. The ratio of their activities at that instant is

The equation of wave motion is $$Y=5 \sin (10 \pi t -0.02 \pi x+\pi / 3)$$ where $$x$$ is in metre and $$t$$ in second. The velocity of the wave is

A potentiometer wire of length $$4 \mathrm{~m}$$ and resistance $$5 ~\Omega$$ is connected in series with a resistance of $$992 ~\Omega$$ and a cell of e.m.f. $$4 \mathrm{~V}$$ with internal resistance $$3 ~\Omega$$. The length of $$0.75 \mathrm{~m}$$ on potentiometer wire balances the e.m.f. of

Select the correct statement from the following.