Let f(x, y) = x^{3} − 2y^{3} . The curve along which ∇^{2}f = 0 is
A curve is given by The unit vector of the tangent to the curve at t =1 is
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There are three planets in circular orbits around a star at distances a, 4a and 9a, respectively. Attime t = t_{0}, the star and the three planets are in a straight line. The period of revolution of theclosest planet is T. How long after t_{0} will they again be in the same straight line?
A current I is flowing through the sides of an equilateral triangle of side a. The magnitude of the magnetic field at the centroid of the triangle is
Two vehicles A and B are approaching an observer O at rest with equal speed as shown in the figure. Both vehicles have identical sirens blowing at a frequency fs . The observer hears these sirens at frequency f_{A} and f_{B}, respectively from the two vehicles. Which one of the following is correct?
Three infinite plane sheets carrying uniform charge densities −σ, 2σ, 3σ are placed parallel to the
xz plane at y = a, 3a, 4a , respectively. The electric field at the point (0, 2a, 0) is
Two boxes A and B contain an equal number of molecules of the same gas. If the volumes are V_{A}
and V_{B}, and λ_{A} and λ_{B} denote respective mean free paths, then
Let T_{g} and T_{e} be the kinetic energies of the electron in the ground and the third excited states of ahydrogen atom, respectively. According to the Bohr model, the ratio T_{g}/ T_{e }is
Which one of the following arrangements of optical components can be used to distinguish between
an unpolarised light and a circularly polarised light?
Which one of the following graphs shows the correct variation of v_{o} with v_{i}? Here, v_{d} is the voltage
drop across the diode and the OpAmp is assumed to be ideal.
Which one of the figures correctly represents the TS diagram of a Carnot engine?
The plane of polarisation of a plane polarized light rotates by 60^{° }after passing through a waveplate. The passaxis of the wave plate is at an angle α with respect to the plane of polarisation of theincident light. The wave plate and α are
A rectangular loop of dimensions l and w moves with a constant speed of v through a region containing a uniform magnetic field B directed into the paper and extending a distance of 4w. Which of the following figures correctly represents the variation of emf (ε) with the position (x) of the front end of the loop?
The equation of state for one mole of a nonideal gas is given by PV = A where the coefficients A and B are temperature dependent. If the volume changes from V_{1} to V_{2} in an isothermal process, the work done by the gas is
An ideal gas consists of three dimensional polyatomic molecules. The temperature is such that only
one vibrational mode is excited. If R denotes the gas constant, then the specific heat at constant
volume of one mole of the gas at this temperature is
A long solenoid is carrying a time dependent current such that the magnetic field inside has the form is along the axis of the solenoid. The displacement current at the
point P on a circle of radius r in a plane perpendicular to the axis
Consider an ensemble of thermodynamic systems, each of which is characterized by the samenumber of particles, pressure and temperature. The thermodynamic function describing theensemble is
Given a spherically symmetric charge density ρ(r) (k being a constant), the electric field for r < R is (take the total charge as Q)
An infinitely long solenoid, with its axis along , carries a current I. In addition there is a uniform line charge density λ along the axis. If is the energy flux, in cylindrical coordinates then
Consider two waves y_{1} = a cos(ωt − kz) and y_{2} = a cos[(ω + Δω)t − (k + Δk)z]. The group velocity of the superposed wave will be (Δω ≪ ω and Δk ≪ k)
Consider a convex lens of focal length f. A point object moves towards the lens along its axis between 2f and f. If the speed of the object is V_{O}, then its image would move with speed V_{I}. Whichof the following is correct?
A disc of radius R_{1} having uniform surface density has a concentric hole of radius R_{2} < R_{1}. If its
mass is M, the principal moments of inertia are
The function is expanded as a Fourier series of the form
Which one of the following curves correctly represents (schematically) the solution for the equation
The mean momentum of a nucleon in a nucleus of mass number A and atomic number Z depends on A, Z as
Consider the transformation to a new set of coordinatesfrom rectangular Cartesian coordinates (x, y), where In the coordinate system, the area element dxdy is
A particle of mass m is in a one dimensional potential
At some instant its wave function is given by
are the ground and the first excited states, respectively. Identify the correct statement.
A raindrop falls under gravity and captures water molecules from atmosphere. Its mass changes atthe rate λm(t), where λ is a positive constant and m(t) is the instantaneous mass. Assume thatacceleration due to gravity is constant and water molecules are at rest with respect to earth beforecapture. Which of the following statements is correct?
A particle P of mass m is constrained to move on the surface of a cylinder under a force as
shown in figure (k is the positive constant). Which of the following statements is correct? (Neglect
friction.)
29 docs48 tests

29 docs48 tests
