A potentiometer wire has length of $$5 \mathrm{~m}$$ and resistance of $$16 \Omega$$. The driving cell has an e.m.f. of $$5 \mathrm{~V}$$ and an internal resistance of $$4 \Omega$$. When the two cells of e.m.f.s $$1.3 \mathrm{~V}$$ and $$1.1 \mathrm{~V}$$ are connected so as to assist each other and then oppose each other, the balancing lengths are respectively

Four massless springs whose force constants are $$2 \mathrm{~K}, 2 \mathrm{~K}, \mathrm{~K}$$ and $$2 \mathrm{~K}$$ respectively are attached to a mass $$\mathrm{M}$$ kept on a frictionless plane as shown in figure, If mass $$M$$ is displaced in horizontal direction then frequency of oscillating system is

About black body radiation, which of the following is the wrong statement?

Two coils have a mutual inductance of $$0.004 \mathrm{~H}$$. The current changes in the first coil according to equation $$\mathrm{I}=\mathrm{I}_0 \sin \omega \mathrm{t}$$, where $$\mathrm{I}_0=10 \mathrm{~A}$$ and $$\omega=50 ~\pi \mathrm{~rad} ~\mathrm{s}^{-1}$$. The maximum value of e.m.f. in the second coil in volt is