A straight conductor of length l carrying a current I, is bent in the form of a semicircle. The magnetic field (in tesla) at the centre of the semicircle is

• $\frac{{\mathrm{\pi }}^2\mathrm{I}}{\mathrm{l}} \times {10}^{-7}$

• $\frac{\mathrm{\pi I}}{\mathrm{l}} \times {10}^{-7}$

• $\frac{\mathrm{\pi l}}{{\mathrm{l}}^2} \times {10}^{-7}$

• $\frac{{\mathrm{\pi l}}^2}{\mathrm{l}} \times {10}^{-7}$

A coil having an inductance of 0.5 H carries a current which is uniformly varying from 0 to 10 A in 2 s. The emf (in volts) generated in the coil is

• 10

• 5

• 2.5

• 1.25

53.

If an alternating voltage is represented as E = 141 sin (628 t), then the rms value of the voltage and the frequency are respectively

• 141 V, 628 Hz

• 100 V, 50 Hz

• 100 V, 100 Hz

• 141 V, 100 Hz

A step-down transformer is used on a 1000 V line to deliver 20 A at 120 V at the secondary coil. If the efficiency of the transformer is 80%, the current drawn from the line is  

• 3 A

• 30 A

• 0.3 A

• 2.4 A

For the series LCR circuit shown in the figure, what is the resonance frequency and the amplitude of the current at the resonating frequency ?

• 2500 rad s^-1 and $5\sqrt{2} \mathrm{A}$

• 2500 rad s^-1 and 5 A

• 2500 rad s^-1 and $\frac{5}{\sqrt{2}} \mathrm{A}$

• 250 rad s^-1 and $5\sqrt{2} \mathrm{A}$

A red coloured object illuminated by mercury vapour lamp, when seen through a green filter, will appear

• red

• blue

• black

• white

Time taken by sunlight to pass through a window of thickness 4 mm whose refractive index is $\frac{3}{2}$ is

• 2 × 10^-4 s

• 2 × 10⁴ s

• 2 × 10^-11 s

• 2 × 10¹¹ s

Two thin lenses of focal length 20 cm and 25 cm are in contact. The effective power of the combination is

• 4.5 D

• 18 D

• 9 D

• 2.5 D

The magnification of the image when an object is placed at a distance x from the principal focus of a mirror of focal length f

• $\frac{\mathrm{x}}{\mathrm{f}}$

• $1 + \frac{\mathrm{f}}{\mathrm{x}}$

• $\frac{\mathrm{f}}{\mathrm{x}}$

• $1 - \frac{\mathrm{f}}{\mathrm{x}}$

In the Young's double slit experiment, the central maxima is observed t0 be I₀. If one of the slits is covered, then the intensity at the central maxima will become

• $\frac{{\mathrm{I}}_0}{2}$

• $\frac{{\mathrm{I}}_0}{\sqrt{2}}$

• $\frac{{\mathrm{I}}_0}{4}$

• I₀