A longitudinal wave is represented by $\mathrm{x} = {\mathrm{x}}_0 \sin 2\mathrm{\pi } (\mathrm{nt} - \mathrm{x}/\mathrm{\lambda })$. The maximum particle velocity will be four times the wave velocity if

• $\mathrm{\lambda } = \frac{{\mathrm{\pi x}}_0}{4}$

• $\mathrm{\lambda } = 2{\mathrm{\pi x}}_0$

• $\mathrm{\lambda } = \frac{{\mathrm{\pi x}}_0}{2}$

• $\mathrm{\lambda } = 4{\mathrm{\pi x}}_0$

A block of ice at temperature -20°C is slowly heated and converted to steam at 100°C. Which of the following diagram is most appropriate ?

Two black bodies at temperatures 327°C and  427°C are kept in an evacuated chamber at 27°C. The ratio of their rates of loss of heat are

• $\frac{6}{7}$

• ${\left(\frac{6}{7}\right)}^2$

• ${\left(\frac{6}{7}\right)}^3$

• $\frac{243}{464}$

A point charge +q is placed at the centre of a cube of side L. The electric flux emerging from the cube is

• $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

• zero

• $\frac{6{\mathrm{qL}}^2}{{\mathrm{\epsilon }}_0}$

• $\frac{\mathrm{q}}{6{\mathrm{L}}^2{\mathrm{\epsilon }}_0}$

In the figure below, the capacitance of each capacitor is 3 µF. The effective capacitance between A and B is

• $\frac{3}{4} \mathrm{\mu F}$

• 3 µF

• 6 µF

• 5 µF

The reading of the ammeter in the following figure will be

• 0.8 A

• 0.6 A

• 0.4 A

• 0.2 A

A wire of resistance R is elongated n-fold to make a new uniform wire. The resistance of new wire

• nR

• n²R

• 2nR

• 2n²R

28.

The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x. When both the current and radius is doubled the ratio will be

• x/8

• x/4

• x/2

• 2x

The current through a coil of self-inductance L = 2mH is given by i = t²e^-t at time t. How long it will take to make the emf zero ?

• 1 s

• 2 s

• 3 s

• 4 s

The magnetic flux through a loop of resistance 10 Ω is given by ($\mathrm{\varphi }$=5t² − 4t+ 1 Wb). How much current is induced in the loop after 0.2 s ?

• 0.4 A

• 0.2 A

• 0.04 A

• 0.02 A