In an LCR circuit as shown below, both switches are open initially. Later, switch S1 is closed and S2 is kept open. (q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statements is correct?
In an ac generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency ω in a magnetic field B. The maximum value of emf generated in the coil is
A rectangular loop has a sliding connector PQ of length ℓ and resistance RΩ and is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents I1, I2 and I are
Three charges Q, +q and +q are placed at the vertices of a right-angled isosceles triangle as shown in the figure. The net electrostatic energy of the configuration is zero if Q is equal to
A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration 'a' to keep the block stationary. Then, 'a' is equal to
The diameter of a drop of liquid fuel changes with time due to combustion according to the following relationship.
While burning, the drop falls at its terminal velocity under Stokes flow regime. Find the distance that it will travel before complete combustion.
The half-life period of a radioactive element X is the same as the mean life time of another radioactive element Y. Initially, they have the same number of atoms. Then,
An object is 1 metre in front of the curved surface of a plano-convex lens whose flat surface is silvered. A real image is formed 120 cm in front of the lens. What is the focal length of the lens?
Consider a two particle system with particles having masses m1 and m2. The first particle is pushed towards the centre of mass through a distance d. By what distance should the second particle be moved, so as to keep the centre of mass at the same position?
An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1. The other chamber has volume V2 and contains ideal gas at pressure P2 and temperature T2. If the partition is removed without doing any work on the gas, then the final equilibrium temperature of the gas in the container will be
In a hydrogen atom, the electron moves around the nucleus in a circular orbit of radius 5 × 10−11 m. Its time period is 1.5 × 10−16s. The current associated with the electron motion is (charge of electron is 1.6 × 10−19 C)
A cubical vessel open from top of side L is filled with a liquid of density ρ then the torque of hydrostatic force on a side wall about an axis passing through one of bottom edges is-
A certain ideal gas undergoes a polytropic process PVn = constant such that the molar specific heat during the process is negative. If the ratio of the specific heats of the gas be γ, then the range of values of n will be
A ball is projected from the bottom of an inclined plane of inclination 30o, with a velocity of 30 m s−1, at an angle of 30o with the inclined plane. If g = 10 ms−2, then the range of the ball on given inclined plane is
A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be
If the radius of the earth were to shrink by one percent and its mass remains the same, the acceleration due to gravity on the earth's surface would
A black body, at 200 K, is found to have maximum energy at a wavelength of 14 μm. When its temperature is raised to 1000 K, the wavelength at which maximum energy is emitted is
The time constant of charging of the capacitor shown in the diagram is
Spherical wavefronts shown in figure, strike a plane mirror. Reflected wavefronts will be as shown in
A simple pendulum has a time period T1 when on the earth's surface and T2 when taken to a height 2R above the earth's surface where R is the radius of the earth. The value of
The magnetic field due to a current-carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. Its value at the centre of the loop is CμT. What is the value of C?
In a potentiometer experiment, the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of 2Ω, the balancing length becomes 120 cm. The internal resistance of the cell, in ohm, is
The height, in terms of R (radius of Earth), at which the acceleration due to gravity becomes g/9 (where g = acceleration due to gravity on the surface of Earth), is nR. What is the value of n?
A particle executes S.H.M. given by x = 0.24cos(400t − 0.5) in SI units. Find amplitude in cmcm.
The apparent depth of needle lying at the bottom of the tank which is filled with water to a height of 15.5 cm is measured by a microscope to be 8.5 cm. If water is replaced by a liquid of refractive index 1.94 to the same height as earlier, then the displacement of the microscope needed to establish the focus on the needle again is n μmn μm. The value of n is
The radiations from a naturally occurring radioactive substance, as seen after deflection by a magnetic field in one direction, are
Both the molecules possess dipole moment in which of the following pairs?
Which of the following solutions will have pH close to 1.0?
Out of H2S2O3, H2S4O6, H2SO5 and H2S2O8, peroxy acids are
Geometrical shapes of the complexes formed by the reaction of Ni2+ with Cl-, CN- and H2O, respectively, are
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