The angle of prism is $$A$$ and one of its refracting surface is silvered. Light rays falling at an angle of incidence '$$2 \mathrm{A}$$' on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index of the material of the prism is

The maximum velocity of a particle performing S.H.M. is '$$\mathrm{V}$$'. If the periodic time is made $$\left(\frac{1}{3}\right)^d$$ and the amplitude is doubled, then the new maximum velocity of the particle will be

A conducting wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $$=25 \sqrt{2} \Omega$$, acceleration due to gravity $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{~B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}$$ )

For an electron moving in the $$\mathrm{n}^{\text {th }}$$ Bohr orbit the deBroglie wavelength of an electron is