The equation of a wave is y = 5 sin  ; where x is in cm and t is in second. The maximum velocity of the wave will be

• 1 ms^-1

• 2 ms^-1

• 1.5 ms^-1

• 1.25 ms^-1

12.

Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency ${\mathrm{v}}_1$ and the other with frequency ${\mathrm{v}}_2$ The ratio $\raisebox{1ex}{${\mathrm{v}}_1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{v}}_2$}\right.$ is

• 2

• 4

• 8

• 1

1 mole of an ideal gas at an initial temperature of T K does 6R joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, then final temperature of the gas will be

• ( T - 4 ) K

• ( T + 4 ) K

• ( T - 2.4 ) K

• ( T + 2.4 ) K

Consider a compound slab consisting of two different materials having equal lengths, thicknesses and thermal conductivities K and 2K respectively. The equivalent thermal conductivity of the slab is

• $\sqrt{2} \mathrm{K}$

• 3 K

• $\frac{4}{3} \mathrm{K}$

• $\frac{2}{3}\mathrm{K}$

A black body has a wavelength of A at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be

• $\frac{2\mathrm{\lambda }}{3}$

• $\frac{3\mathrm{\lambda }}{2}$

• $\frac{4\mathrm{\lambda }}{9}$

• $\frac{9\mathrm{\lambda }}{4}$

If Young's double slit experiment is performed i water instead of air, then

• no fringes would be seen

• fringe width would decrease

• fringe width would increase

• fringe width would remain unchanged

A charge q is located at the centre of a cube. The electric flux through any face is

• $\frac{4 \mathrm{\pi q}}{6 \left(4{\mathrm{\pi \epsilon }}_{\mathrm{o}}\right)}$

• $\frac{\mathrm{\pi q}}{6 \left(4{\mathrm{\pi \epsilon }}_{\mathrm{o}}\right)}$

• $\frac{\mathrm{q}}{6 \left(4{\mathrm{\pi \epsilon }}_{\mathrm{o}}\right)}$

• $\frac{2\mathrm{\pi q}}{6 \left(4{\mathrm{\pi \epsilon }}_{\mathrm{o}}\right)}$

Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference ${\mathrm{V}}_{\mathrm{A}} - {\mathrm{V}}_{\mathrm{B}} = {\mathrm{V}}_{\mathrm{B}} -{\mathrm{V}}_{\mathrm{C}}$ If t₁ and t₂ be the distances between them, then              

• t₁ = t₂

• t₁ > t₂

• t₁ < t₂

• t₁ ≤ t₂

Three capacitors of capacitances 1 µF, 2µF and 4μF are connected first in a series combination and then in a parallel combination. The ratio their equivalent capacitances will be

• 2 : 49

• 49 : 2

• 4 : 49

• 49 : 4

At room temperature, copper has free electron density of 8.4 x 10²⁸ m^-3,  The electron drift velocity in a copper conductor of cross-section area of 10^-6 m² and carrying a current of 5.4 A will be

• 4 ms^-1

• 0.4 ms^-1

• 4 ms^-1

• 0.4 mm s^-1