The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $$1 \mathrm{~mm}$$. The main scale reading is $$2 \mathrm{~cm}$$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $$\mathrm{g}$$, the density of the sphere is:

Critical angle of incidence for a pair of optical media is $$45^{\circ}$$. The refractive indices of first and second media are in the ratio:

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:

(Assume h = 6.63 $$\times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}$$ and $$\mathrm{m}_{\mathrm{p}}=1836$$ times $$\mathrm{m}_{\mathrm{e}}$$ )

Correct Bernoulli's equation is (symbols have their usual meaning) :