An inductor coil is connected to a capacitor and an AC source of rms voltage \(8 \mathrm{~V}\) in series. The rms current in the circuit is \(16 \mathrm{~A}\) and is in phase with emf. If this inductor coil is connected to \(6 \mathrm{~V}\) DC battery, the magnitude of steady current is

A proton moving with a velocity of \(8 \times 10^5 \mathrm{~ms}^{-1}\) enters a uniform magnetic field normal to the direction of the magnetic field. If the radius of the circular path of the proton in the magnetic field is 8.3 cm, then the magnitude of the magnetic field is \(\left(\right.\) Charge of proton \(=1.6 \times 10^{-19} \mathrm{C}\) and mass of the proton \(\left.=1.66 \times 10^{-27} \mathrm{~kg}\right)\)

The error in the measurement of force acting normally on a square plate is \(3 \%\). If the error in the measurement of the side of the plate is \(1 \%\), then the error in the determination of the pressure acting on the plate is

The escape velocity of a body on the earth's surface is \(v_e\).A body is thrown up with a speed \(\sqrt{5} v_e\).Assuming that the sun and planets do not influence the motion of the body, velocity of the body at infinite distance, is :

Calculate the minimum thickness of a soap film ( \(n=1.33)\) that results in constructive interference in reflected light, if the film is illuminated with light whose wavelength in free space is \(532 \mathrm{~nm}\).

The potential difference \(V\) across the filament of the bulb shown in the given Wheatstone bridge varies as \(V=i(2 i+1)\), where ' \(t\) ' is the current in ampere through the filament of the bulb. The emf of the battery \(\left(V_{\mathrm{a}}\right)\) so that the bridge becomes balanced is

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?

An aluminium (resistivity \(\rho=2.2 \times 10^{-8} \Omega\)-m) wire of a diameter \(1.4 \mathrm{~mm}\) is used to make a \(4 \Omega\) resistor. The length of the wire is

A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If \(R\) is the radius of the earth, maximum height attained by the body from the surface of the earth is

A uniform disc of mass \(100 \mathrm{~kg}\) and radius \(2 \mathrm{~m}\) is rotating at \(1 \mathrm{rad} / \mathrm{s}\) about a perpendicular axis passing through its centre. A boy of mass \(60 \mathrm{~kg}\) standing at the centre of the disk suddenly jumps to a point which is \(1 \mathrm{~m}\) from the centre of the disc. The final angular velocity of the boy (in \(\mathrm{rad} / \mathrm{s}\) ) is

A message signal of frequency \(10 \mathrm{kHz}\) and peak voltage of \(15 \mathrm{~V}\) is used to modulate a carrier frequency of \(1 \mathrm{MHz}\) and peak voltage of \(30 \mathrm{~V}\). Determine the modulation index.

As per kinetic theory of gases which of the following statements is / are true?
a) Temperature of a gas is a measure of average kinetic energy of a molecule
b) Temperature of a gas depends on the nature of the gas
c) Heavier molecule has lower average speed
d) Lighter molecule has lower average speed

A thin converging lens of focal length \(f=25 \mathrm{~cm}\) forms the image of an object on a screen placed at a distance of \(75 \mathrm{~cm}\) from the lens. The screen is moved closer to the lens by a distance of \(25 \mathrm{~cm}\). The distance through which the object has to be shifted, so that its image on the screen in sharp again is