A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced emf is

• once per revolution

• twice per revolution

• four times per revolution

• six times per revolution

A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when

• frequency of the AC source is decreased

• number of turns in the coil is reduced

• a capacitance of reactance X_C =X_L is included in the same circuit

• an iron rod is inserted in the coil

The condition under which a microwave oven heats up a food item containing water molecules most efficiently is

• the frequency of the microwave must match the resonant frequency of the water molecules

• the frequency of the microwave has no relation with natural frequency of water molecules

• microwave are heat waves, so always produce heating

• infrared waves produce heating in a microwave oven

Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

• $\frac{5}{27}$

• $\frac{3}{23}$

• $\frac{7}{29}$

• $\frac{9}{31}$

The half-life of a radioactive isotope X is 20 yr. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

• 40 yr

• 60 yr

• 80 yr

• 100 yr

A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV)

• 2.67 MeV

• 26.7 MeV

• 6.675 MeV

• 13.35 MeV

For photoelectric emission from certain metal the cut-off frequency is v. If radiation of frequency 2v impinges on the metal plate, the maximumpossible velocity of the emitted electron will be (m is the electron mass)

• $\sqrt{\frac{\mathrm{hv}}{\left(2\mathrm{m}\right)}}$

• $\sqrt{\frac{\mathrm{hv}}{\mathrm{m}}}$

• $\sqrt{\frac{2\mathrm{hv}}{\mathrm{m}}}$

• $2\sqrt{\frac{\mathrm{hv}}{\mathrm{m}}}$

38.

The wavelength λ_e of an electron and λ_p of a photon of same energy E are related by

• λ_p ∝ λ_e²

• λ_p ∝ λ_e

• ${\mathrm{\lambda }}_{\mathrm{p}} \propto \sqrt{{\mathrm{\lambda }}_{\mathrm{e}}}$

• ${\mathrm{\lambda }}_{\mathrm{p}} \propto \frac{1}{\sqrt{{\mathrm{\lambda }}_{\mathrm{e}}}}$

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices µ₁ and µ₂ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

• $\frac{\mathrm{R}}{2\left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}$

• $\frac{\mathrm{R}}{2\left({\mathrm{\mu }}_1 - {\mathrm{\mu }}_2\right)}$

• $\frac{\mathrm{R}}{\left({\mathrm{\mu }}_1 - {\mathrm{\mu }}_2\right)}$

• $\frac{2\mathrm{R}}{\left({\mathrm{\mu }}_2 - {\mathrm{\mu }}_1\right)}$

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be

• 5 cm

• 2.5 cm

• 1.67 cm

• 1.5 cm