In the hydrogen atom spectrum, the ratio of the energy for the transition n = 3 → n = 1 to that of n = 4 —>n = 1 is
The ^{32}P radio isotope used in leukemia theraphy has t_{1/2} = 14.26 days, what % of ^{32}P remains after 35 days
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The wave function ψ of a quantum mechanical system described by a Hamiltonian can be written as a linear combination of φ_{1}and φ_{2} which are the eigen functions of H with eigen values E_{1} and E_{2} respectively . At t = 0, the system is prepared in the state
and then allowed to evolve with time. The wave function at time t = will be
An engine absorb heat at a temperature of 1000 K and rejects heat at 600 K. If the engine operates at maximum possible efficiency, the amount of work performed by the engine for 2000 J heat input is
One mole of a perfect gas is heated at a constant pressure of 1 atm from 0°C to 100°C. What is the change in internal energy?
For an assembly of molecules (molar mas = M) at temperature T, the standard deviation of maxweller’s speed is approximately
Two uniform thin rods of equal length 2L and masses M_{1} and M_{2} are joined together along the length. The moment of inertia of the combined rod of length 4L about an axis passing through the mid point and perpendicular to the length of the rod is
A particle is constrained in a onedimensional box of length 2a with potential
Energy difference between level n = 3 and n = 2 is
A person of mass m stands at one end of a plank of mass M and length L. the plank is lying on a smooth horizontal surface, what is distance moves by the plank as the person walks on it to reach the other end.
A particle of mass m is located in a unidimensional potential field where the potential energy of the particle depends on the coordinate x as U(x) = U_{0} (1  cos a x ) ; U_{0} and a are constants. Then the period of small oscillations that the particle performs about the equilibrium position.
If the electrostatic potential at point (x,y) is given by V (x,y) = [ 4x + 9y] volts, the electrostatic energy density at that point (in J/m^{3}) is
A solid sphere of mass m callides head on with identical sphere at rest. If the coefficient of restitution is e. The loss in kinetic energy
An insulated gas jar of mass M which is equal to the molecular mass of the enclosed gas moves with certain K. E. when the jar is stopped, the increment of temperature of the gas is ΔT. The K .E . of the system before stopping is , where adiabatic exponent of the gas.
The input in the below circuit to get output one is
If the amplitude of a damped  oscillator becomes one  third in 2 minutes, what will be the amplitude of oscillation as compared to initial one after 6 minutes ?
The relation between angular frequency ω and wave number K for given type of waves is . The wave number K_{0} for which the phase velocity equals the group velocity is
A ray of light passes through four transparent media with refractive indices μ_{1},μ_{2},μ_{3} and u_{4} as shown in Fig. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have
For a pure substance, the slope of the plot of Gibbs free energy (G) against T at constant pressure is
The space  time coordinates of two events as measured by O are x_{1}= 6 x 10^{4} m,y_{1} = z_{1} = Om, t_{1}’ = 2 x 10^{4}sec and x_{2}= 12 x 10^{4}m, t_{2}= 1 x 10^{4}sec. What must be the velocity of O’ with respect to O if O’ measures the two events to occur simultaneously ?
are the Pauli matrices. The expression equal to
The electric field component of a plane electromagnetic wave travelling in vacuum is given by The Poynting vector for the wave is
The xy plane is the boundary between free space and a magnetic material with relative permeability μ. The magnetic field in the free space is The magnetic field in the magnetic material is
An infinite, conducting slab kept in a horizontal plane carries a uniform charge density σ . Another infinite slab of thickness t, made of a linear dielectric material of dielectric constant K, is kept above the conducting slab. The bound charge density on the upper surface of the dielectric slab is _______ .
Two parallel plates of a capacitor, separated by 2 mm, are at a potential difference of 20V. A dielectric sheet of dielectric constant 2 and thickness 1 mm is inserted between the plates. How does the potential difference between the two plates change ?
If waves in an ocean travel with a phase velocity then what is the group velocity V_{g} of the ‘wave packet’ of these waves ?
A transistor with β = 100 is used in C E configuration.The collector circuit resistance is 1k Ω & V_{cc} = 20v. Assuming V_{be} = 0. Find the value of collector to base resistance such that quiescent collector emitter voltage is 4V.
Calculate the collector current in Voltage divider method with the following data
A truth table is given as, then the correct logic expression corresponding to it is
A mass m, moves in a circular orbit of radius r_{0} under the influence of a central force whose potential is Then
A series of sine and cosines of multiples x; which will represent x + x^{2} in the interval π < x < π then
Which of the following are statement is/are correct :
Consider the following statements regarding the magnitude of barrier potential of a pn junction. Which of the following statements is/are Correct ?
Consider the following statements related to an oscillator; Among these statements which of the following are Correct ?
A Carnot engine operating between two temperatures 727°c and 27°c is supplied heat energy at the rate of 500 Joule / cycle. Sixty percent of the work output is used to drive a refrigerator, which reject heat to the surrounding at 27°c. If the refrigerator removes 1050 Joule of heat per cycle from the low temperature reservoir. Then
An ideal diatomic gas at pressure p_{i} and volume v_{i} double its volume adiabatically. Then
Two holes 1 and 2 are made at depths h and 16h respectively. Both the holes are circular but radius of hole 1 is two times that of hole 2
A rocket of enitial mass m_{0} is ejecting gas at the constant rate α and a constant velocity v_{0} with respect to it and that it moves vertically upward in a constant gravitational field. Then the velocity of rocket v and travelled distance by the rocket x is
For a scalar function φ satisfying the Laplace equation , has
In a certain inertial frame two light pulses are emitted at point 10 km apart and separated in time 10 ms. An observer moving at a speed V along the line joining these points notes that the pulses are simultaneous. Therefore V is_____(in C).
Let be orthonormal functions . Find the value of n which normalise the function
The number of independent solutions of the equation
are _______ .
A planet is revolving around a star in an elliptic orbit. The ratio of the farthest distance to the closest distance of the planet from the star is 4. The ratio of kinetic energies of the planet at the closest to farthest position is ______ .
Steam at 100°C is mixed with 1500 grams of water at 15°C so that the final temperature of the mixture is 80°C. The mass of steam is _____ .(in grams)
The mean free path of the particles of a gas at a temperature T_{0} and pressure P_{0} has a value λ_{1} . If the pressure increased to 1.5 P_{0} and the temperature is reduced to 0.75 T_{0}. Then = _____ .
A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same train. Find out the ratio of the velocity of train B to that of train A.
Find out the rms value of the emf given by E = 8 sin ωt + 6 sin 2 ωt volt?
Unpolarised light of intensity l_{0} gets polarised as it emerges from a polarizer. It then passes through an analyser. The intensity of light emerging from the analyser is Find out the angle between the polarising direction of the polarizer and analyser (in degree)?
If each square cm, of sun’s surface radiates energy at the rate of 1.5 x 10^{3} cal. sec^{1}cm^{2 }and Stefan’s constant is 5.7 x 10^{8} joule sec^{1 }.m^{2}(K)^{4}. Find out the temperature of the sun’s surface in degree Celsius?
Find out the minimum number of AND GATE require to solve the logic expression
A ball impinges directly into another ball at rest by the impact, if half of the initial kinetic energy is destroyed in the collision, find the coefficient of restitution.
10 gm. of steam at 100°C is blown into 90 gms. of water at 0°C contained in a calorimeter of water equivalent 10 gms. The whole of the steam is condensed. Calculate the increase in the entropy of the system, (in cal/K)
The value of the magnetic field required to maintain non  relativistic protons of energy 1 MeV in a circular orbit of radius 100mm is _____Tesla.
A point charge is placed between two semi infinite conducting plates which are inclined at an angle of 60º with respect to each other. The number of image charges is ______ .
A solid sphere of Radius R has a charge density, given by
where r is the radial coordinate and p_{0}, a and R are positive constants. If the magnitude of the electric field at r = is 1.25 times that at r = R, then the value of a is
40040 volt (rms) transformer is used with a full wave rectifier circuit with each diode having internal resistance of 1Ω . If load resistance is 19Ω then the dc load current is _______________________ (in Amperes ) .
The current flowing through a certain Pn junction at room temperature when reversebiased (bias voltage being very large in comparison to V_{T}) is 0.15μA. Determine the current (in μA) flowing through the diode when applied voltage is 0.12V. (V_{T} = 26 mV)
An operational amplifier with negative feedback has voltage gain of 150. It is found that without feedback, an input signal of 50 mV is required to produce a given output; where as with feedback, the input signal must be 0.5V for the same output calculate the value of β.
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