The differential equation satisfying y(0) = 1, y(π) = 0 has
If S is the surface (x 1)^{2} + (y  2)^{2 }+ (z  3)^{2} = 1 enclosing volume V, and , then the value of integral is equal to
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The expectation value of energy when the state of the harmonic oscillator is described by the following wave function
where ψ_{0}(x,t) and ψ_{2}(x,t) are wave functions for the ground state and second excited state respectively :
While using second latent heat equation , the specific heat of steam is negative in the following condition :
For silver, the specific heat at constant pressure in the range of 50 K to 100 K is given by C_{p} = 0.076 T  0.00026 T^{2}  0.15 cal mol^{1 }deg^{1 }where T is the kelvin temperature. If 2 mole of silver are heated from 50 K to 100 K. Calculate the change in entropy
A particle describes a circular orbit under the influence of an attractive central force directed toward a point at the center. The force inversely proportional to
An astronaut moves in a super spaceship travelling at a speed of 0.64C. The astronaut observes a photon approaching him from space. The speed of photon with respect to the astronaut i s ________ .
Half life of a radioactive materials is 4 days. After 20 days, the fraction remaining undecayed will be 
After being hit, a golf ball reaches a maximum height 60 m with a speed of 30 m / sec. Right after being hit, the speed of the ball is (take g = 10 m/sec^{2})
The vector field in cylindrical polar coordinates is
One mole of monoatomic ideal gas is initially at pressure P_{0} and volume V_{0}. The gas then undergoes a three  stage cycle consisting of the following processes:
(A) An isothermal expansion till it reaches volume 2 V_{0} and heat Q flows into the gas.
(B) An isobaric compression back to the original volume V_{0}
(C) An isochoric increase in pressure till the original pressure P_{0} is regained. The efficiency of this cycle can be expressed as
The normalized wave function of a particle can be written as
Where (x) are the normalized energy eigenfunction of a given Hamiltonian. The value of N is
The commutator of two matrices A and B are defined as
[A, B] = AB  BA
{A, B} = AB + BA
If [A,B] = 0. We can write [A,B,C] =
A Solid cylinder of height H, radius R and density P, floats vertically on the surface of a liquid of density_{p}The cylinder will be set into oscillatory motion when a small instantaneous downward force is applied. The frequency of oscillation is
Consider a hollow charged shell of inner radius a and outer radius b. The volume charge density is (K is constant) in the region a < r < b. The magnitude of the electric field produced at distance r > a is
The wave function of a state of the hydrogen atom is given by where , denotes the normalized eigenfunction in the usual notation. The expectation value of L_{z} in the state
A planet of mass m moves in the gravitational field of the sun (mass M). If the semimajor and semiminor axis of the orbit are a and b respectively. The angular momentum of the planet is
Consider an infinite conducting sheet in the xyplan with a time dependent current density kt where K is a constant. The vector potential at (x,y,z) is given by The magnetic field is
Water is flowing through a tube as shown. The cross section area at A & C are equal and greater than the crosssectional area at B. If the flow is steady, then the pressure on the walls at B is
A gas of N noninteracting particles is in thermal equilibrium at temperature T. Each particle can be in any of the possible nondegenerate states of energy . The average energy per particle of the gas, when <<< 1, is
A plane electromagnetic wave is propagating in a lossless dielectric. The electric field is given by
where c is the speed of light in vacuum, E_{0}, A, and K_{o}, are constants and and are unit vectors along the xaxis and zaxis
The relative dielectric constant of the medium and the constant A are
A plane polarized electromagnetic wave in free space at time t = 0 is given The magnetic field is given by
A circular loop of mass M and radius a rolls without slipping with constant angular speed ω along the horizontal xaxis in the xy plane. When the centre of the hoop is at a distance d = from the origin, the magnitude of the total angular momentum of the loop about the origin is
A particle is incident with a constant energy E on a one dimensional potential barrier as shown in the figure. The wave function in regions I and II are respectively
The frequency response curve of a damped forced oscillator will be of the form (Ramplitude and V_{R} frequency ratio) :
A voltage applied to an XRay tube being increased η = 1.5 times, the shortwave limit of an XRay continuous spectrum shifts by Δλ = 26 pm. Find the initial voltage applied to the tube.
Metallic copper is know to form cubic crystals and the lattice constant is measured from Xray diffraction studies to be about 0.36 nm. If the specific gravity of copper is 8.96 and its atomic weight is 63.5, one can conclude that
In a simple cubic structure of lattice constant a, one plane among a set of parallel planes intercepts x,y, and z axis 2a, a and a respectively. The interplanar spacing is
Consider a doped semiconductor having the electron and the hole mobilities μ_{n} and μ_{p }respectively. Its intrinsic carrier density is n_{i} The hole concentration p for which the conductivity is minimum at a given temperature is
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