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The ratio of the radii of two nuclei of mass numbers A₁ and A₂ will be
After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is
A dry cell has an e.m.f. of 1.5 V and an internal resistance of 0.05 Ω. The maximum current obtainable from this cell for a very short time interval is
When a.d.c. motor operates at 200 V, its initial current is 5 A, but when it runs at maximum speed, the current is only 3 A. What is its back emf ?
Inside a hollow charged spherical conductor, the potential at every point
If identical charges q are placed at each corner at each corner of a cube of side b, then electric potential energy of charge +q, which is placed at centre of the cube, will be
A motorcyclist of mass m is to negotiate a curve of radius r with a speed ν. The minimum value of the coefficient of friction so that this negotiation may take place safely, is
An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by
A perfect black body emits radiation at temperature 300 K. If it radiates 16 times this amount, then its temperature will be
The r.m.s. velocity of a gas molecules is 100√3 m−s^{⁻1}. The most probable velocity of the molecules is
A galvanometer having a resistance of 8 ohm is shunted by a wire of 2 ohm. If the total current is 1 ampere, the part of it passing through the shunt will be
A horizontal pipe line carries water in a streamline flow. At a point along the pipe where crosssectional area is 10 cm^{2}, the velocity of water is 1 ms^{⁻1} and pressure is 2000 Pa. The pressure of water, at another point where crosssectional area is 5 cm^{2}, is (Density of water = 1000 kgm^{⁻3})
A wire can be broken by applying a load of 200 N.The force required to break another wire of the same length and same material, but double in diameter, is
A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t₁ and t₂ seconds respectively, then
In a vertical circle of radius r, at what point in its path a particle has tension equal to zero
Four bodies P, Q, R and S are projected with equal velocities having angles of projection 15^{o}, 30^{o}, 45^{o} and 60^{o} with the horizontal respectively. The body having shortest range is
A diwali rocket is ejecting 0.05 kg of gases per second at a velocity of 400 m/sec. The accelerating force on the rocket is
If tube length of astronomical telescope is 105 cm and magnifying power is 20 for normal setting, calculate the focal length of objective
Which of the following equation does not represent a simple harmonic motion ?
A hollow sphere is filled with water through a small hole in it. It is hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will
An object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm. The image produced is
A flywheel starts from rest and gains a speed of 540 revmin^{⁻1} in 6 s. Angular acceleration of the flywheel will be
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom is
A Carnot engine used first an ideal monoatomic gas and then an ideal diatomic gas. If the source and sink temperature are 411^{o}C and 69^{o}C respectively and the engine extracts 1000 J of heat in each cycle, then area enclosed by the PV diagram is
A simple harmonic oscillator has a mass m, amplitude A frequency n, displacement x and kinetic energy T. The equation T = 2 π 2 n 2 m A − x is dimensionally
When an unpolarized light of intensity I_{0} is incident on a polarizing sheet, the intensity of the light which does not get transmitted is
The moment of inertia of a body (initially at rest) about a given axis is 1.2 kgm^{2}. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rads^{2} must be applied about that axis for a period of
Who was the first to demonstrate the phenomenon of interference of light?
A polyatomic gas (γ=4/3) is compressed to 1/8th of its volume adiabatically. If its initial pressure is P₀, its new pressure will be
The two bulbs as in the above question are connected in series to a 200 volt line. Then
If an open pipe of length l vibrates in fundamental mode, then pressure variation is maximum at
A body of mass 40 kg having velocity 4 m/s collides with another body of mass 60 kg having velocity 2 m/s. If the collision is inelastic, then loss in kinetic energy will be
A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 45^{o} with the initial vertical direction is
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