A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of $15 ms^{-1}.$Then, the frequency of sound that the observer hears in the echo reflected from the cliff is (Take velocity of sound in air = 330$ms^{-1}$)

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 × 10⁻⁴ J by the end of the second revolution after the beginning of the motion?

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is

To get output 1 for the following circuit, the correct choice for the input is A, B, C.

A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then

The intensity of the maximum in a Young’s double-slit experiment is I₀. Distance between two slits is d = 5λ, where λ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance D = 10d?

A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is

An electron of mass m and a photon have the same energy E. The ratio of de Broglie wavelengths associated with them is

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U₁, at wavelength 500 nm is U₂ and that at 1000 nm is U₃. Wien’s constant, b = 2.88 × 10⁶ nmK. Which of the following is correct?

Given the value of Rydberg constant is 10⁷ m⁻¹, the wave number of the last line of the Balmer series in hydrogen spectrum will be

An npn-transistor is connected in common-emitter configuration in a given amplifier. A load resistance of 800 Ω is connected in the collector circuit and the voltage drop across it is 0.8 V. If the current amplification factor is 0.96 and the input resistance of the circuits is 192 Ω, the voltage gain and the power gain of the amplifier will, respectively, be

Out of the following options, which one can be used to produce a propagating electromagnetic wave?

Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to

If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is

An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm, respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance

The ratio of escape velocity at earth (vₑ) to the escape velocity at a planet (vₚ) whose radius and mean density are twice as that of earth is

A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances (a/2) and (2a), respectively, from the axis of the wire is

A capacitor of 2 μF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is

When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is V/4. The threshold wavelength for the metallic surface is

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is

A body of mass 1 kg begins to move under the action of a time-dependent force F = (2t î + 3t² ĵ) N. What power will be developed by the force at the time t?

The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism, respectively, are

An inductor 20 mH, a capacitor 50 μF and a resistor 40 Ω are connected in series across a source of emf V = 10 sin340t. The power loss in the AC circuit is

A particle moves so that its position vector is given by $\vec{r}$ = x cos(ωt) î + y sin(ωt) ĵ, where ω is a constant. Which of the following is true?

Consider the junction diode as ideal. The value of current flowing through AB is

Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. The v varies as a function of the distance x between the spheres, as

A small signal voltage V(t) = V₀ sinωt is applied across an ideal capacitor C. What is the behavior of the current I(t)?

The magnetic susceptibility is negative for

A square loop ABCD carrying a current $i$ is placed near and coplanar with a long straight conductor XY carrying a current $I,$ the net force on the loop will be

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2.$ The ratio $\frac{\lambda_2}{\lambda_1}$ is

When an $\alpha$-particle of mass $m$ moving with velocity $v$ bombards on a heavy nucleus of charge $Ze,$ its distance of closest approach from the nucleus depends on $m$ as

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

From a disc of radius $R$ and mass $M,$ a circular hole of diameter $R,$ whose rim passes through the centre, is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre?

Match the corresponding entries of Column I with Column II (where m is the magnification produced by the mirror)

A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3}$ Wb. The self-inductance of the solenoid is

What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of a radius $R$ so that it can complete the loop?

The molecules of a given mass of a gas have rms velocity of $200$ ms$^{-1}$ at $27^{\circ}C$ and $1.0 \times 10^{5}$ Nm$^{-2}$ pressure. When the temperature and pressure of the gas are, respectively, $127^{\circ}C$ and $0.05 \times 10^{5}$ Nm$^{-2},$ the rms velocity of its molecules in $$ms$^{-1}$ is

The charge flowing through a resistance $R$ varies with time $t$ as $Q = at - bt^2,$ where $a$ and $b$ are positive constants. The total heat produced in $R$ is

A refrigerator works between $4^{\circ}C$ and $30^{\circ}C.$ It is required to remove $600$ calories of heat every second in order to keep the temperature of the refrigerated space constant. (Take 1 cal = 4.2 J). The power required is

A uniform circular disc of radius $50$ cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of $2.0$ rads$^{-2}.$ Its net acceleration in $$ms$^{-2}$ at the end of $2.0$ s is approximately

Coefficient of linear expansion of brass and steel rods are α1 and α2. Lengths of brass and steel rods are l1 and l2, respectively. If (l2 – l1) is maintained same at all temperatures, which one of the following relations holds good?

At what height from the surface of earth the gravitational potential and the value of g are $-5.4 \times 10^7 kg^{-2}$ and $6.0 ms^{-2},$ respectively? (Take the radius of earth as 6400 km.)

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is (latent heat of ice is $3.4 \times 10^5 Jkg^{-2}$ and $g = 10 Nkg^{-1}$).

In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle 30° when light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of

A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of emfs is