A system consists of N number of particles, N » 1. Each particle can have only one of the two energies E1 or E1 + ε (ε > 0). If the system is in equilibrium at a temperature T, the average number of particles with energy E_{1} is
A mass m, lying on a horizontal, frictionless surface, is connected to one end of a spring. The other end of the spring is connected to a wall, as shown in the figure. At t = 0, the mass is given an impulse.
The time dependence of the displacement and the velocity of the mass (in terms of non zero constants A and B) are given by
1 Crore+ students have signed up on EduRev. Have you? Download the App 
A particle with energy E is incident on a potential given by
The wave function of the particle for E > V_{0}, in the region x > 0 (in terms of positive constants A, B and C) is
The electric field of a light wave is given by The polarization
state of the wave is
Consider the coordinate transformation The relation between the area elements dx'dy' and dxdy is given by dx’dy’ = Jdxdy. The value of J is
The trace of a 2 × 2 matrix is 4 and its determinant is 8. If one of the eigenvalues is 2(1 + i), the other eigenvalue is
Temperature dependence of resistivity of a metal can be described by
A proton from outer space is moving towards earth with velocity 0.99c as measured in earth’s frame. A spaceship, traveling parallel to the proton, measures proton’s velocity to be 0.97c. The approximate velocity of the spaceship, in the earth’s frame, is
A charge φ is at the center of two concentric spheres. The outward electric flux through the inner sphere is φ while that through the outer sphere is 2φ. The amount of charge contained in the region between the two spheres is
At room temperature, the speed of sound in air is 340 m/sec. An organ pipe with both ends open has a length L= 29 cm. An extra hole is created at the position L/2. The lowest frequency of sound produced is
A system comprises of three electrons. There are three single particle energy levels accessible to each of these electrons. The number of possible configurations for this system is
A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing is
A Zener regulator has an input voltage in the range 15V 20V and a load current in the range of 5 mA 20 mA. If the Zener voltage is 6.8V, the value of the series resistor should be
The variation of binding energy per nucleon with respect to the mass number of nuclei is shown in the figure.
Consider the following reactions:
A rigid triangular molecule consists of three non collinear atoms joined by rigid rods. The constant pressure molar specific heat (Cp) of an ideal gas consisting of such molecules is
A satellite moves around the earth in a circular orbit of radius R centered at the earth. A second satellite moves in an elliptic orbit of major axis 8R, with the earth at one of the foci. If the former takes 1 day to complete a revolution, the latter would take
A positively charged particle, with a charge q, enters a region in which there is a uniform electric field E and a uniform magnetic field B both directed parallel to the positive y axis. At t = 0, the particle is at the origin and has a speed v0 directed along the positive x axis. The orbit of the particle, projected on the x z plane, is a circle. Let T be the time taken to complete one revolution of this circle. The y coordinate of the particle at t = T is given by
Vibrations of diatomic molecules can be represented as those of harmonic oscillators. Two halogen molecules X_{2} and Y_{2} have fundamental vibrational frequencies vX = 16.7 × 10^{12} Hz and vY = 26.8 × 10^{12} Hz, respectively. The respective force constants are KX = 325 N/m and KY = 446 N/m. The atomic masses of F, Cl and Br are 19.0, 35.5 and 79.9 atomic mass unit respectively.
The halogen molecules X_{2} and Y_{2} are
A hollow, conducting spherical shell of inner radius R_{1} and outer radius R_{2} encloses a charge q inside, which is located at a distance d (< R_{1}) from the centre of the spheres. The potential at the centre of the shell is
Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, is
Which of the following circuits represent the Boolean expression
A conducting wire is in the shape of a regular hexagon, which is inscribed inside an imaginary circle of radius R, as shown. A current I flows through the wire. The magnitude of the magnetic field at the center of the circle is
An observer is located on a horizontal, circular turntable which rotates about a vertical axis passing through its center, with a uniform angular speed of 2 rad/sec. A mass of 10 grams is sliding without friction on the turntable. At an instant when the mass is at a distance of 8 cm from the axis, it is observed to move towards the center with a speed of 6 cm/sec. The net force on the mass, as seen by the observer at that instant, is
Miller indices of a plane in cubic structure that contains all the directions [100], [011] and [111] are
Seven uniform disks, each of mass .. and radius .., are inscribed inside a regular hexagon, as shown. The moment of inertia of this system of seven disks, about an axis passing through the central disk and perpendicular to the plane of the disks, is
A nucleus has a size of 10^{–15} m. Consider an electron bound within a nucleus. The estimated energy of this electron is of the order of
Consider a vector field Let C be the circle x^{2} + y^{2} = 4 on the plane z = 2, oriented counter clockwise. The value of the contour integral
Consider the equation with the boundary condition y(1) = 1. Out of the following, the range of x in which y is real and finite, is
The Fourier series for an arbitrary periodic function with period 2.. is given by For the particular periodic function shown in the figure, the value of a_{0} is
The phase of the complex number (1 + i)i in the polar representation is
29 docs48 tests

29 docs48 tests
