A plano-convex lens of refractive index ($$\mu_1^{\prime}$$ fits exactly into a plano-concave lens of refractive index $$\mu_2$$. Their plane surface are parallel to each other. 'R' is the radius of curvature of the curved surface of the lenses. The focal length of the combination is

A cylindrical rod has temperatures '$$T_1$$' and '$$T_2$$' at its ends. The rate of flow of heat is '$$Q_1$$' cal $$\mathrm{s}^{-1}$$. If length and radius of the rod are doubled keeping temperature constant, then the rate of flow of heat '$$\mathrm{Q}_2$$' will be

Energy of electron in the second orbit of hydrogen atom is $$\mathrm{E}$$. The energy of electron '$$\mathrm{E}_3$$' in the third orbit of helium $$(\mathrm{He})$$ atom will be

A series L-C-R circuit containing a resistance of $$120 ~\Omega$$ has angular frequency $$4 \times 10^5 \mathrm{~rad} \mathrm{~s}^{-1}$$. At resonance the voltage across resistance and inductor are $$60 \mathrm{~V}$$ and $$40 \mathrm{~V}$$ respectively, then the value of inductance will be