31.

In the given figure what will be the coefficient of mutual inductance

     

• 

• 

• 

• 

An L-C-R series circuit with a resistance of 100 Ω is connected to 200 V (AC source) and angular frequency 300 rad/s. When only the capacitor is removed, then the current lags behind the voltage by 60°. When only the inductor is removed the current leads the voltage by 60°. The average power dissipated in original L-C-R circuit is

• 50 W

• 100 W

• 200 W

• 400 W

The concentric, conducting spherical shells X, Y and Z with radii r, 2r and 3r, respectively. X and Z are connected by a conducting wire and Y is uniformly charged to charge Q as shown in figure. Charges on shells X and Z will be

• ${\mathrm{q}}_{\mathrm{x}} = \frac{-\mathrm{Q}}{4}, {\mathrm{q}}_{\mathrm{z}} = \frac{\mathrm{Q}}{4}$

• ${\mathrm{q}}_{\mathrm{x}} = \frac{\mathrm{Q}}{4}, {\mathrm{q}}_{\mathrm{z}} = \frac{-\mathrm{Q}}{4}$

• ${\mathrm{q}}_{\mathrm{x}} = \frac{\mathrm{Q}}{4} , {\mathrm{q}}_{\mathrm{z}} = \frac{\mathrm{Q}}{4}$

• ${\mathrm{q}}_{\mathrm{x}} = \frac{-\mathrm{Q}}{6}, {\mathrm{q}}_{\mathrm{z}} = \frac{\mathrm{Q}}{4}$

Two batteries of emf 3V and 6 V with internal resistances 2 Ω and 4 Ω are connected in a circuit with resistance of 10 Ω as shown in figure. The current and potential difference between the points P and Q are

• $\frac{3}{16} \mathrm{A} \mathrm{and} \frac{8}{15} \mathrm{V}$

• $\frac{16}{3} \mathrm{A} \mathrm{and} \frac{15}{8} \mathrm{V}$

• $\frac{3}{16} \mathrm{A} \mathrm{and} 8 \mathrm{V}$

• $\frac{3}{16} \mathrm{A} \mathrm{and} \frac{15}{8} \mathrm{V}$

The charges on two spheres are + 7 µC and -5C respectively. They experience a force F. If each of them is given an additional charge of -2 µC, then the new force of attraction will

• F

• $\frac{\mathrm{F}}{2}$

• $\frac{\mathrm{F}}{\sqrt{3}}$

• 2F

A rod made up of metal is 1.2 m long and 0.8 cm in diameter. Its resistance is 3.5 x 10^-3 Ω. Another disc made of the same metal is 2.0 cm in diameter and 1.25 mm thick. What is the resistance between the round faces of the disc?

• 1.35x 10^-8 Ω

• 2.70 x 10^-7 Ω

• 5.82 × 10^-7 Ω

• 8.10 × 10^-5 Ω

A body is moving along a rough horizontal surface with an initial velocity of 10 ms^-1.  If the body comes to rest after travelling a distance of 12m, then the coefficient of sliding friction will be

• 0.5

• 0.2

• 0.4

• 0.6

A circular current carrying coil has a radius R. The distance from the centre of the coil, on the axis, where B will be  $\frac{1}{8}$  of its value at the centre of the coil is

• $\frac{\mathrm{R}}{\sqrt{3}}$

• $\sqrt{3} \mathrm{R}$

• 2 $\sqrt{3}$ R

• $\frac{2 \mathrm{R}}{\sqrt{3}}$

A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy

• l > lll> ll > lV

• l > ll > lll > lV

• l > lV > ll > lll

• lll > lV > l > ll

In the given figure, the capacitors C₁, C₃, C₄, C₅ have a capacitance 4 µF each. If the capacitor C₂ has a capacitance 10 μF, then effective capacitance between A and B will be 

• 2 μF

• 6 μF

• 4 μF

• 8 μF