The entropy of a system, S, is related to the accessible phase space volume G by S = k_{B}lnG(E, N, V) where E, N and V are the energy, number of particles and volume respectively. From this one can conclude that G
Let dw be the work done in a quasistatic reversible thermodynamic process. Which of the following statements about dw is correct?
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A vector perpendicular to any vector that lies on the plane defined by x + y + z = 5, is
Two events, separated by a (spatial) distance 9 x 10^{9} m, are simultaneous in one inertial frame. The time interval between these two events in a frame moving with a constant speed 0.8 c (where the speed of light c = 3 x 10^{8} m/s) is
Consider three polarizers P_{1} ,P_{2} and P_{3} placed along an axis as shown in the figure
The pass axis of P_{1} and P_{3} are at right angles to each other while the pass axis of P_{2} makes an angle θ with that of P_{1} . A beam of unpolarized light of intensity l_{0} is incident on P_{1} as shown . The intensity of light emerging from P_{3} is
A point particle of mass m carrying an electric charge q is attached to a spring of stiffness constant k. A constant electric field E along the direction of the spring is switched on for a time interval T(whereT Neglecting radiation loss, the amplitude of oscillation after the field is switched off is
A transistor with β = 100 is used in CE configuration. The collector circuit resistance is 1kΩ& V_{∞}= 20v. Assuming V_{be} = 0 find the value of collector to base resistance such that quiescent collector to emitter voltage is 4v
The phenomenon known as ‘Early effect’ in a bipolar transistor refers to a reduction of the effectivebasewidth caused by___
A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is
A particle of mass m is in a potential given by
where a and r_{0 }are positive constants. When disturbed slightly from its stable equilibrium position, it undergoes a simple harmonic oscillation. The time period of oscillation is
A planet of mass m moves in a circular orbit of radius r_{0} in the gravitational potential V(r) = where k is a positive constant. The orbital angular momentum of the planet is
The solution of the differential equation
subject to the boundary conditions y(0) = 1 and y(∞) = 0, is
In an interference pattern formed by two coherent sources, the maximum and the minimum of the intensities are 9I_{0} and I_{0}, respectively. The intensities of the individual waves are
Identify the CORRECT statement for the following vectors
Identify, the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, E_{D }and E_{F} are conduction band, valence band, impurity level and Fermi level, respectively.
A pendulum suspended from the ceiling of the train is at rest. What will be the time period of pendulum if the train accelerates at 10 m/s^{2} (Take g = 10 m/s^{2})
A rod of proper length l_{0} oriented parallel to the xaxis moves with speed 2c/3 along the xaxis in the. Sframe, where c is the speed of the light in free space. The observer is also moving along the xaxis with speed c/2 with respect to the Sframe. The length of the rod as measured by the observer is
Given is a constant vector and r is the position vector. The value of where C is a circle of unit radius centered at origin is _____ .
A system has two energy levels with energies ε and 2ε. The lower is 4fold degenerate while the upper level is doubly degenerate. If there are N noninteracting classical particles in the system, which is in thermodynamic equilibrium at a temperature T, the fraction of particles in the upper level is
A spherical conductor of radius a is placed in a uniform electric field the potential at a point for r > a, is given by
where r is the distance of P from the centre O of the sphere and q is the angle OP makes with the zaxis.
The charge density on the sphere at q = 30° is
The solution of the differential equation for subject to the initial conditions is
A particle of mass m is confined in the potential
Let the wave function of the particle be given by
where y_{0} and y_{1} are the eigen functions of the ground state and the first excited state respectively. The expectation value of the energy is
Two magnetic dipoles of magnitude m each placed in a plane as shown. The energy of interaction is given by
A mass m is constrained to move on a horizontal frictionless surface. It is set in circular m otion with radius r_{0} and angular speed w_{0} by an applied force com municated through an inextensible thread that passes through a hole on the surface as shown in the figure. This force is then suddenly doubled. The magnitude of the radial velocity of the mass
For the BJT circuit shown, assume that the β of the transistor is very large and V_{BE} = 0.7V. The mode of operation of the BJT is ___
If for a silicon npn transistor, the basetoemitter voltage (V_{BE}) is 0.7V and the collectortobase voltage (V_{CB}) is 0.2V. then the transistor is operating in the___
Assuming V_{CEsat} = 0.2V and β= 50. the minimum base current (l_{B}) required to drive the transistor in the given figure to saturation is___
In the voltage regulator shown in the given figure, the load current can vary from 100 mAto 500 mA. Assuming that the Zener diode is ideal (i.e, the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is
A converging lens is used to form an image on screen. When the upper half of the lens is covered by an opaque screen.
A beam of light of wavelength 400 nm and power 1.55 mQ is directed at the cathode of a photoelectric cell, (given he = 1240 ev). If only 10% of the current due to these electrons is i . If the wavelength o f light is now reduced to 200 nm, keeping its power the same, the kinetic energy of the electrons is found to increase by a factor of 5. The stopping potentials for the two wavelength are S_{1} and S_{2}. Then
In a compton experiment the ultraviolet light of wavelength 2000 A° is scattered from an electron at rest. What should be the minimum resolving power of an optical instrument to measure the compton shift. If the observation is made at 60° and 90° with respect to the direction of the incident light ?
XRays of wavelength λ = 0.612 A ° are scattered by free electron (compton collision). Then which of the following statements is/are correct
A particle of mass m and energy E moving in the positive x direction, encounters a one  dimensional potential barrier at x = 0. The barrier is defined by
If the wave function of the particle in the region x < 0 is given as Ae^{lkx} + Be^{ikx}. If = 0.4, then
A resistor of 1KΩ and an inductor of 5mH are connected in series with a battery of emf 4v through a switch. The switch is closed at time t = 0. (use e^{3} = 20)
One mole of an ideal gas (r = 1.5) is at pressure of 100 K P_{a} and a temperature of 300 K. Initial the state of the gas is at the point a of the PV diagram shown. The gas is taken through a reversible cycle a→ b→ c→ a The pressure at point b is 200 K P_{a}. Then
A coil of area 2m^{2} and resistance 4Ω is placed perpendicular to a uniform magnetic field of 4T. The loop is rotated by 90° in 0.1 sec. Choose the correct options
A Voltage 200 cos 100 t is applied to a half wave rectifier with load resistance of 5kΩ . Rectifier may be represented by an ideal diode in series with a resistance of 1kΩ
Then which of the following statements is/are correct :
An unpolarized lightwave is incident from air on a glass surface at the Brewster angle. Calculate the angle (in degree) between the reflected and the refracted wave.
y_{1} and y_{2} are two orthogonal states of a spin 1/2 system. It is given that
where represent the spinup and spindown states, respectively. When the system is in the state y_{2}, its probability to be in the spinup state is __________ .
A one dimensional harmonic oscillator is in the superposition of number states, nn, given by
The average energy of the oscillator in the given state is __________ hw.
A ball of mass m. initially at rest, is dropped from a height of 5 meters. If the coefficient or restitution is 0.9, the speed of the ball just before it hits the floor the second time is approximately________ m/s (take g = 9.8 m/s^{2})
When an ideal monoatomic gas is expanded adiabatically from an initial volume V_{0} to 3V_{0}. its temperature changes from T_{0} to T . Then the ratio is
Let E_{s} denote the contribution of the surface energy per nucleon in the liquid drop model. The ratio is ________ .
A particle moves in a plane with velocity such that The time dependence of the magnitude of the velocity = 5t. It is given that r = 1 ,θ =0 and v _{r} > 0 at t = 0. (In the following, you may use e^{3} ≈ 20.) At what time (in sec.) will θ become 4 radian?
A body of mass 1 kg moves under the influence of a central force, with a potential energy function V(r) = Joule, where r is in meters. It is w l found to move in a circular orbit of radius r = 2 m. (In the following, you may use e^{3} ≈ 20). Find its total energy E. (in mJ)
A cylinder of 1 kg mass and 0.02 m diameter left at the top of an inclined plane of height 1 m rolls down without slipping. (Take g = 9.8 ms^{2}). Find the velocity of center of mass of cylinder on reaching the bottom of inclined plane (in m/sec).
XRays of wavelength λ = 0.612 x 10^{10 }m are scattered by free electrons (Compton collision). Calculate the corresponding kinetic energy in eV imparted to the electron.
A parallel beam of light of diameter 1.8 cm contains two wavelengths 4999.75 Å and 5000.25 Å. The light is incident perpendicularly on a large diffraction grating with 5000 lines per centimeter. Using Rayleigh criterion, find the least order at which the two wavelengths are resolved.
If differential gain of an opamp is A_{vd} = 3500 % & Common mode gain (A_{cM}) = 0.35. Then CMRR will be ______ dB.
The output in the above circuit will be ______ V.
An aircraft, which weights 12000 kg when unloaded , is on a relief mission , carrying 4000 food packets weighing 1 kg each. The plane is gliding horizontally with its engines off at a uniform speed of 540 kmph when the first food packet is dropped. Assume that the horizontal air drag can be neglected and the aircraft keeps moving horizontally. If one food packet is dropped every second , then the distance between the last two packet drops will be _______ m.
In the temperature range 1001000 C, the molar specific heat of a metal varies with temperature T (measured in degrees Celsius) according to the formula C_{p} =(1 + T /5 ) Jdeg C^{1}mol^{1}. If 0.2 Kg of the metal at 300 C, the final equilibrrium temperature, in degree C, will be ________ .
[Assume that no heat is lost to radiation and /or other effects .]
On a planet having the same mass and diameter as the Earth, it is observed that objects weightless at the equator. Find the time period of rotation of this planet in minutes (as defined on the Earth).
The Zener diode in the regulator circuit shown in the figure has a Zener voltage of 5.8 Volts and a Zener knee current of 0.5 mA. The maximum load current drawn from this circuit ensuring proper functioning over the input voltage range between 20 and 30 volts, is _____ mA.
The centre tap full wave singlephase rectifier circuit uses 2 diodes as shown in the given figure. The rms voltage across each diode is _______ V.
If for a transistor, than the value of L_{c} will be ____ mA.
The output voltage for the summing amplifier shown in figure is ______ V.
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