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If an integral curve of the differential equation = 1 passes (0.0) and (α,1), then α is equal to
The potential φ in Joule of a particle of mass 1 kg moving in x  y plane obey the law of φ = 3x + 4y. Here x and y are in meters. If the particle is at rest at (6m, 8m) at time t = 0, then the work done by conservative force on the particle from the initial position to the instant when it crosses the x  axis is
A solid uniform disc of mass m rolls without slipping down a fixed inclined plank with an acceleration α. The frictional force on the disc due to surface of the plane is
Consider the earth as a uniform sphere of mass M and radius R. Imagine a straight smooth tunnel made through the earth which connects any two points on its surface. The motion of a particle of mass m along this tunnel under the action of gravitation simple harmonic. Determine the time that a particle would take to go from one end to the other through the tunnel.
A glass plate of thickness 30 mm is placed just below a wellfocused microscope for focusing it again the microscope should be moved through a distance of :
The Clausiusclapeyron equation indicates that the increase of pressure increases the melting point.
The magnitude of the deBroglie wavelength λ of electron (e), proton (p), neutron (n) and α  particle (α) all having the some energy of 1 MeV, in the increasing order will follow which of the following sequence :
The frequency of a cyclotron oscillator is 10^{7} Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .
Two identical capacitors A and B shown in the given circuit are joined in series with a battery. If a dielectric slab of dielectric constant K is slipped between the plates of capacitor B and battery remain connected then the energy of capacitor A will
Consider a particle with three possible spin state S = 0 and ±1. There is a magnetic field h present and the energy for a spin state S is hS. The system is at a temperature T. Which of the following statements is true about the entropy S(T) ?
Consider three situations of 6 particles in one dimensional box of width L with hard walls. In case (i), the particles are fermions, in case (ii) they are bosons and in case (iii) they are classical. If the total ground state energy of the six particles in these three cases are E_{F}, E_{B} and E_{cl} respectively, which of the following is correct ?
The electric fields inside (r < R) and outside (r > R) a solid sphere with a uniform volume charge density are given by , respectively, while the electric field outside a spherical shell with a uniform surface charge density is given by being the total charge. The correct ratio of the electrostatic energies for the first case to second case is
Le t where c is the boundary (oriented anticlockwise ) of the region in the first quadrant bounded by y = 0, x^{2} + y^{2} = 1 and x = 0. The value of I is
A quantum mechanical particle in a harmonic oscillator potential has the initial wave function , where ψ_{0} and ψ_{1} are the real wave functions in the ground and first excited state of the harmonic oscillator. For convenience we take m = ℏ = ψ= 1 for the oscillator. What is the probability density of finding the particle at x at time t = π ?
A particle of mass m is thrown upward with velocity v and there is retarding air resistance proportional to the square of the velocity with proportionality constant K. If the particle attains a maximum height after time t, and g is the gravitational acceleration, what is the velocity.
A monochromatic wave propagating in a direction making an angle 30° with the yaxis in the reference frame of source. The source moves at speed v towards the observer. The direction of the (cosine of angle) wave as seen by the observer’s _____ .
A system of two circular coaxial coils carrying equal currents i along same direction having equal radius R and separated by a distance 2R (as shown in figure below). The magnitude of magnetic field at the midpoint P is given by
Consider a system of 4N noninteracting spin particles each fixed in position and carrying a magnetic moment μ . The system is immersed in a uniform magnetic field B. The number of spin down particle for which the entropy of the system will be maximum is
The black body at a temperature of 6000k emits a radiation whose intensity spectrum peaks at 600 nm. If the temperature is reduced to 5% k, the spectrum will peak at
Let be a matrix with real entries. If the sum and the product of all the eigen values of A are 10 and 30, respectively, then a^{2}+b^{2} equals
A 150Ω resister, a l0μf capacitor a 0.1 H inductor are connected in series to an AC source operating at an angular frequency ω, for what ω the combination acts as a pure resistive load.
Consider two electromagnetic plane waves propagating in vacuum with their electric field vectors
then the averaged pointing vector for the resultant wave
A convex lens of focal length 24 cm (μ = 1.5) is totally immersed in water. Its focal length in water is _______ .
Unpoiarized light falls on two polarizing sheets placed on top of the other. What be the angle between the characteristic directions of the sheets if the intensity of the transmitted light is one third intensity of the incident beam_______ .
What is the maximum range along the dashed line attained by the water stream coming out at B from a thin tube of the water tank assembly shown in the figure ?
Assume h = 10m, L = 2m and θ = 30°
Consider the digital circuit shown below in which the input C is always high (1)
The truth table for the circuit can be written as
The entries in the Z column (vertically) are
In the operational amplifier circuit below, the voltage at point A is
In the opamp circuit shown in the figure below, the input voltage V_{1} is 1V. The value of the output V_{o} is
The output, 0, of the given circuit is cases I and II, where
Case I : A, B = 1; C, D = 0; E, F = 1 and G = 0
Case II : A, B = 0; C, D = 0; E, F = 0 and G = 1
are, respectively
A BJT circuit has β = 50 & V_{cc} = 20V & uses a potential divider bias circuit with R_{c} = 2kΩ, R_{1}=100kΩ & R_{2}= 5kΩ. then Assuming V_{be} = 0.2V which of the following statements is/are correct :
The Mobility of e^{} in copper assuming that each atom contribute one free e^{} for conduction (Given :  Resistivity of copper is 1.7x1^{6} ohm  cm , Atomic weight = 63.54 , density = 8.96 gm /c .c ) will be :
For the given which of the following is/are correct
Consider the radioactive transformation a → B →C with decay constant λ_{A} and λ_{B} for elements A and B . C is a stable element . Assume that at t = 0, N_{A} = N , N_{B} = 0 and N_{c} = 0 where N_{A}, N_{B}and N_{C} are the number of atoms of A, B and C respectively. Then which of the following is/are correct
Muons are elementary particles produced in the upper atmosphere. The have a life time of 2.2 us. Consider muons which are travelling vertically towards the earth’s surface at a speed of 0.998 C. For an observer on earth the height of the atmosphere above the surface of the earth is 10.4 km. Which of the following statements are true ?
A uniform rod of mass m = 2kg and length L = 0.5 m is sliding along two mutually perpendicular smooth walls with the two ends P and Q having velocities V_{p} = 4m/sec and V_{Q} = 3m/sec as shown, then
A satellite of mass m is just placed over the surface of earth. In this position mechanical energy of satellite is E_{1} Now it starts orbiting round the earth in a circular path at height h = radius of earth. In this position, kinetic energy, potential energy and total mechanical energy of satellite are K_{2}, U_{2} and E_{2} respectively. Then
Two charges + Q each are fixed at points C and D. Line AB is the bisector line of CD. A third charge +q is moved from A to B, then from B to C
A charged particle is moving along positive yaxis in uniform electric and magnetic fields.
Here E_{0} and B_{0} are positive constants, choose the correct options 
One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure.
Its pressure at A is P_{o}. choose the correct options from the following
The muon has mass and mean lifetime 2.2 ms in its rest frame. The mean distance traversed by a muon of energy before decaying is approximately _____ km.
Consider two point charges q and λq located at points x = a and x = μa respectively. Assuming that sum of two charges is constant than what is value of λ for which the magnitude of electrostatic for is max __________ .
Two particles of identical mass move in circular orbits under a central potential V (r) = Let I_{1} and I_{2} be the angular momenta r_{1} r_{2} be radii of the orbits respectively. If the value of is
A battery powers two circuits C_{1} and C_{2} as shown in the figure
The total current I drawn from the battery is estimated by measuring the currents I_{1} and l_{3} through the individual circuits. If I_{1} and l_{2} are both 200 mA and if the errors in their measurement are 3 mA and 4mA respectively, the error in the estimate of I is mA.
A particle, of unit mass moves along the xaxis under the influence of a potential, V (x) = x (x  2 )^{2} . The particle is found to be in stable equilibrium at the point x = 2. Find out the time period of oscillation of the particle.
A 3 x 3 matrix has elements such that its trace is 11 and its determinant is 36. The eigenvalues of the matrix are all known to be positive integers. The largest eigenvalue of the matrix is _________ .
A p  n junction is formed from germanium of conductivity 0.8 ohm^{1} cm^{1}on p side & 1.6 ohm^{1} cm^{1} on nside. Calculate potential barrier at 300K (in V). (n_{i} = 2.1 x 10^{13} cm^{1}) (Given μ_{p} = 2000 cm^{2}/voltsec and μ_{n} = 4000 cm^{2}/voltsec) (K = 1.38 x 10^{16} erg per °K)
T h e current gain 'α’ of NPN transistor is 0.98. It is connected in the CB mode & gives a reverse saturation current I_{co} =12μA. Then the base current for an emitter current of 2mA will be _______(in μA ).
A gain transistor has a circuit gain of β = 60. If it is connected in a grounded base configuration, what theoretical a.c collector current (in mA) will flow when an a.c current of 2 mA flows through the emitter (Assume the collector potential to be const.)
The output voltage of a certain opamp appears as shown in figure in response to a step input calculate its slow rate
In a onedimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.
ψ_{1} and ψ_{2} are two states defined by
where a is a constant.
The value of a for which y_{2} is orthogonal to y_{1} is ___________ .
The magnetic field (in A m^{1} ) inside a long solid cylindrical conductor of radius a
What is the total current ( in A ) in the conductor ?
The vapour pressure p (in mm of Hg) of a solid, at temperature T, is expressed by in p = 23  3863/T and that of its liquid phase by In p = 19  3063/T. The triple point (in Kelvin) o f the material is __________ .
A system has energy level E_{0}, 2E_{0}, 3E_{0}...... . where the excited states are triply degenerate. Four noninteracting bosons are placed in this system. If the total energy of these bosons is 5E_{0}, the number of microstates is ________ .
A particle of mass 2 kg is moving such that at time t its position, in metre, is given by The angular momentum of the particle at t = 2 s about the origin, in kg m^{2} s^{1}, is _________ .
A car is moving with constant linear acceleration a along horizontal xaxis. A solid sphere of mass M and radius R is found rolling without slipping on the horizontal floor of the car in the same direction as seen from an inertial frame outside the car. The acceleration of the sphere in the inertial frame is ________ .
In a Young’s experiment the upper slit is covered by a thin transparent plate of refractive index 1.1 and the lower slit is covered by another thin transparent plate of refractive index 1.9 but of thickness half the thickness of the first one. It is observed that the point O on the screen, where the central maxima fall before the insertion of the plates, now has 3/4^{th} of the original intensity. It is also observed that what used to be the 4^{th} maxima earlier lies below O whereas the 4^{th} minimum is above O. Calculate the thickness (μm) of the upper plate. Take the wavelength of light to be 7200 A° and neglect any absorption of light.
A beam of planepolarized light falls on a polarizer which rotates about the axis of the ray with angular velocity ω= 21 rad/s. Find the energy (mJ) of light passing through the polarizer per one revolution if the flux of energy of the incident ray is equal to φ = 4.0 m W.
The figure shows the results obtained during a photoelectric effect experiment where the stopping potential is plotted against the frequency of the incident radiation. The work function of the metal is close to _______ (in eV).
Consider a maxwellian distribution of the energy of the molecules of an ideal gas in three dimension . let E_{av} and E_{rms} denote the average energy and the root mean square energy, respectively. The magnitude of ratio is _______
1 docs34 tests

1 docs34 tests
