1 Crore+ students have signed up on EduRev. Have you? Download the App 
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
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
For the given differential form y^{3}z^{3}dx + 2xyz^{3}dy + 3xy^{2}z^{2}dz Which of following are correct ?
Which of the following statements is/are correct ?
The electron in a hydrogen atom makes a transition n_{1}→ n_{2} where n_{1} and n_{2} are the principle quantum numbers of two states.Assume the bohr model to be valid. The time period of the electron in the initial state is twenty seven times that in the final state. The possible value of n_{1} and n_{2} are
During the melting of a slab of ice at atmospheric pressure :
A particle is moving in two  dimensional potential well
V(x, y) = 0 0 ≤ x ≤ L , 0 ≤ y ≤ 3L
= ∞ elsewhere
Which of the following statement about the ground state energy E_{1} and ground state eigenfunction φ_{0} are true ?
Consider a simple harmonic oscillator made up of a mass attached to a spring. What will not be the effect in the motion if the mass were to stay completely immersed in a liquid?
A circular coil of radius 120 mm with 10 turns is placed with its plane parallel to the earth’s magnetic field. When a current of 0.45 A flows through the coil, a compass needle placed at the centre of the coil is seen to be deflected by an angle of 45° to the plane of the coil. Assign the correct statements.
Consider a region of space in which there are uniform electric and magnetic fields which are mutually parallel. A charged particle released from rest in this region. Then which paths are impossible for this particle.
Consider the following truth table.
The logic expression for F is
In an npn transistor, 95% of emitted electrons reach the collector. If the collector current is 19 mA. Then
The power radiated by sun is 7.6 x 10^{26} W and its radius is 7x 10^{5} km. The magnitude of the Poynting vector (in W /cm^{2}) at the surface of the sun is _____ .
A particle is in a state which is a superposition of the ground state ψ_{0} and the second excited state ψ_{2} of one  dimensional quantum harmonic oscillator. The state is given by . The expectation value of the energy of the particle in this state (in unit of ____________ .
A rod is moving with aspeed of 0.6c in a direction at 30° to its own length . The percentage contraction in the length of the rod is ________ .
X  rays of wavelength 0.28 nm are compton scattered and the scattered beam is observed at an angle of 60° relative to incident beam . The compton wavelength of the electron is 0.00243 nm. The kinetic energy of scattered electrons in eV is ______.
An iceberg is floating in sea water. The density of ice is 0.92 gm/cm^{3} and that of sea water is 1.03 g/cm^{3}. What percentage of the iceberg will be below the surface o f water ______ %.
A 5 kg block is kept on a horizontal platform at rest. At time t = 0, the platform starts moving with a constant acceleration of 1 m /sec^{2}. The coefficient of friction μ between the block and the platform is 0.2. The work done by the force of friction on the block in the fixed reference frame in 10 sec is _______ J.
The temperature difference between hot T_{A} and cold T_{c} reservoirs of two carnot engines A and B are same . If the ratio of the respective efficiencies is equal to then the ratio of the hot reservoir temperature is ____________ .
Two insulating cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at temperature 300 K. The piston A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30K. Then the rise in temperature of the gas in B is ________ .
The directional derivative of the function f = x^{2}  y^{2} + 2Z^{2} at the point P(1, 2, 3) in the direction of line PQ where Q is the poin t (5, 0, 4 ) is ________.
In a YDSE using light, the apparatus has two slits of unequal widths. When only slit1 is open, the maximum observed intensity on the screen is 9I_{0}. When only slit2 is open the maximum observed intensity is 4I_{0}. When the both slits are open, an interference pattern appears on the screen. The ratio o f principle maxima to that of the nearest minima is _________ .
Two blocks are connected by a spring of spring constant K. one block has K 2mass 2m and the other block has 3m. If the ratio = 8sec^{2} , the angular m frequency of vibration ω of the two block spring system in sec^{1} is ________.
The total power emitted by a spherical black body of radius R at a temperature T is P_{1}. Let P_{2} be the total power emitted another spherical black body of Radius 2R kept at temperature T/2. The ratio is_________ .
The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current I is m. If this loop is changed to a circular shape with the same current I passing through it, the magnetic dipole moment becomes nm. The value of n is _______ .
A particle of rest mass M is moving along the positive xdirection. It decays into two photons y_{1} and y_{2} as shown in the figure. The energy of y_{1} is 1 GeV GeV and the energy of y_{2} = 0.84 GeV. The value of M (in units of ) is __________ .
Two particles of identical mass move in circular orbits under a central potential . Let be the angular momenta and r_{1} , r_{2} be the radii of the orbits respectively. If = 2, the value r_{1}/r_{2} is___________ .
The minimum energy of an electron (the rest mass of which is 0.5 MeV) that can emit Cerenkov radiation while passing through water (of refractive index 1.5) is approximately in MeV_________.
A binary star system consists of two stars S_{1} and S_{2} with masses m and 2m respectively separated by a distance r. If both S_{1} and S_{2} individually follow circular orbits around the centre of mass with instantaneous speeds V, and V2 respectively the speeds ratio V_{1}/ V_{2} is____________ .
The minimum energy of a collection of 6 noninteracting electrons of spin and mass m placed in a one dimensional infinite square well potential of width L is _________.
The Zener diode, as shown in the figure below, has zener voltage V_{z}= 15V and power rating of 0.5 W If V_{s} = 40 V. Find the minimum value of R_{s} in Ω that prevents the zener diode from being destroyed.
Assume that the transistor shown in the figure is biased in the active region. Calculate the value of V_{CE}.
1 docs34 tests

1 docs34 tests
