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)

If $$\mathrm{I}_0$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be the intensity when the slit width is doubled?

Two circular coils made from same wire but radius of $$1^{\text {st }}$$ coil is twice that of $$2^{\text {nd }}$$ coil. If magnetic field at their centres is same then ratio of potential difference applied across them is ($$1^{\text {st }}$$ to $$2^{\text {nd }}$$ coil)