For the thin convex lens, the radii of curvature are at $$15 \mathrm{~cm}$$ and $$30 \mathrm{~cm}$$ respectively. The focal length the lens is $$20 \mathrm{~cm}$$. The refractive index of the material is :

Two identical conducting spheres P and S with charge Q on each, repel each other with a force $$16 \mathrm{~N}$$. A third identical uncharged conducting sphere $$\mathrm{R}$$ is successively brought in contact with the two spheres. The new force of repulsion between $$\mathrm{P}$$ and $$\mathrm{S}$$ is :

The longest wavelength associated with Paschen series is : (Given $$\mathrm{R}_{\mathrm{H}}=1.097 \times 10^7 \mathrm{SI}$$ unit)

A total of $$48 \mathrm{~J}$$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $$2^{\circ} \mathrm{C}$$. The work done by the gas is: Given, $$\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$.