Class 12th

An inductance coil has a reactance of 100Ω. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45°. The self-inductance of the coil is:

The figure shows a region of length 'l' with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 * 10⁵ ms⁻¹ making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, 'l' is close to (mass of proton = 1.67 * 10⁻²⁷ kg, charge of the proton = 1.6 * 10⁻¹⁹C)

When the temperature of metal wire is increased from 0°C to 10°C, its length increases by 0.02%. The percentage change in its mass density will be close to:

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm⁻¹, density = 667 kg m⁻³) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opposite sides of the capillary) make an angle of 60° with one another. Then h is close to (g = 10 ms⁻²)

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of µ?I/π is:

A 750 Hz, 20 V (rms) source is connected to a resistance of 100Ω, an inductance of 0.1803H and a capacitance of 10µF all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C. (assume no loss of heat to the surroundings) is close to:

In the circuit shown in the figure, the total charge is 750 µC and the voltage across capacitor C? is 20 V. Then the charge on capacitor C? is

In a Young's double slit experiment, light of 500 nm is used to produce an interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to:

A charged particle carrying charge 1µC is moving with velocity (2î + 3ĵ + 4k) ms⁻¹. If an external magnetic field of (5î + 3ĵ – 6k) * 10⁻³T exists in the region where the particle is moving then the force on the particle is F⃗ * 10⁻⁹ N. The vector F⃗ is:

In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is