In Young's double slit experiment, $$8^{\text {th }}$$ maximum with wavelength '$$\lambda_1$$' is at a distance '$$d_1$$' from the central maximum and $$6^{\text {th }}$$ maximum with wavelength '$$\lambda_2$$' is at a distance '$$\mathrm{d}_2$$'. Then $$\frac{\mathrm{d}_2}{\mathrm{~d}_1}$$ is

The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to

The efficiency of a heat engine is '$$\eta$$' and the coefficient of performance of a refrigerator is '$$\beta$$'. Then

A conducting sphere of radius $$0.1 \mathrm{~m}$$ has uniform charge density $$1.8 \mu \mathrm{C} / \mathrm{m}^2$$ on its surface. The electric field in free space at radial distance $$0.2 \mathrm{~m}$$ from a point on the surface is ( $$\varepsilon_0=$$ permittivity of free space)