The dispersion relation for electromagnetic waves travelling in a plasma is given as w^{2} = c^{2}k^{2} + w_{p}^{2}, where c and w_{p} are constants. In this plasma, the group velocity is :
Consider the following circuit with two identical Si diodes. The input ac voltage waveform has the peak voltage V_{p} = 2V, as shown.
The voltage waveform across PQ will be represented by :
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A current I = 10A flows in an infinitely long wire along the axis of a hemisphere (see figure). The value over the hemispherical surface as shown in the figure is :
Consider two, single turn, co planar, concentric coils of radii R_{1} and R_{2} with R_{1} >> R_{2}. The mutual inductance between the two coils is proportional to
If the Boolean function Z = PQ + PQR + PQRS + PQRST + PQRSTU, then Z is :
Shown in the figure is a combination of logic gates. The output values at P and Q are correctly represented by which of the following ?
Which of the following is due to inhomogeneous refractive index of earth’s atmosphere ?
For the three matrices given below, which one of the choices is correct ?
A plane in a cubic lattice makes intercepts of a, a/2 and 2a/3 with the three crystallographic axes, respectively. The Miller indices for this plane are :
Which one of the following schematic curves best represents the variation of conductivity s of a metal with temperature T ?
Consider an inertial frame S' moving at speed c/2 away from another inertial frame S along the common x x' axis, where c is the speed of light, As observed from S', a particle is moving with speed c/2 in the y' direction, as shown in the figure. The speed of the particle as seen from S is:
Consider a uniform thin circular disk of radius R and mass M. A concentric square of side R/2 is cut out from the disk (see figure). What is the moment of inertia of the resultant disk about an axis passing through the centre of the disk and perpendicular to it ?
Consider a system of N particles obeying classical statistics, each of which can have an energy 0 or E. The system is in thermal contact with a reservoir maintained at a temperature T. Let k denote the Boltzmann constant. Which one of the following statements regarding the total energy U and the heat capacity C of the system is correct ?
The integral of the vector (standard notation for cylindrical coordinates is used) over the volume of a cylinder of height L and radius R0 :
Consider Rydberg (Hydrogenlike) atoms in a highly excited state with n around 300. The wavelength of radiation coming out of these atoms for transitions to the adjacent states lies in the range:
A uniform rigid meter scale is held horizontally with one of its end at the edge of a table and the other supported by hand. Some coins of negligible mass are kept on the meter scale as shown in the figure.
As the hand supporting the scale is removed, the scale starts rotating about its edge on the table and the coins start moving. If a photograph of the rotating scale is taken soon after, it will look closest to :
Consider two identical, finite, isolated systems of constant heat capacity C at temperatures T_{1} and T_{2}, (T_{1} > T_{2}). An engine works between them until their temperatures become equal. Taking into account that the work performed by the engine will be maximum (=W_{max}) if the process is reversible (equivalently, the entropy change of the entire system is zero), the value of W max is:
A white dwarf star has volume V and contains N electrons so that the density of electrons is Taking the temperature of the star to be 0K, the average energy per electron in the star where m is the mass of the electron. The electronic pressure in the star is:
A pendulum is made of a massless string of length L and a small bob of negligible size and mass m. It is released making an angle q0 (<<1 rad) from the vertical. When passing through the vertical, the string slips a bit from the pivot so that its length increases by a small amount d(d << L) in negligible time. If it swings up to angle q1 one the other side before starting to swing back, then to a good approximation which of the following expressions is correct?
To demonstrate Bernoulli’s principle, an instructor arranges two circular horizontal plates of radii b each with distance d(d << b) between them (see figure). The upper plate has a hole of radius a in the middle. On blowing air at a speed v0 through the hole so that the flow rate of air is pa2v0, it is seen that the lower plate does not fall. If the density of air is r, the upward force on the lower plate is well approximated by the formula (assume that the region with r < a does not contribute to the upward force and the speed of air at the edges is negligible) :
KCl has the NaCl type structure which is fcc with two atom basis, one at (0, 0, 0) and the other at Assume that the atomic form factors of K+ and Cl– are identical. In an X ray diffraction experiment on KCl, which of the following (h k l) peaks will be observed?
Which one of the following graphs represents the derivative of the function most closely (graphs are schematic and not drawn to scale)?
Bar magnet of magnetic moment 200 Am2 is suspended in a magnetic field of intensity 0.25N/Am. The couple required to deflect it through 30° is
Consider a thin long insulator coated conducting wire carrying current I. It is now wound once around an insulating thin disc of radius R to bring the wire back on the same side, as shown in the figure. The magnetic field at the centre of the disc is equal to:
Consider two coherent point source (S_{1} and S_{2}) separated by a small distance along a vertical line and two screens P_{1} and P_{2} placed as shown in figure. Which one of the choices represents the shapes of the interference fringes at the central regions on the screens ?
The electric field of an electromagnetic wave is given by
The value of β is (c is the speed of light) :
Unpolarized light is incident on a combination of a polarizer, a λ/2 plate and a λ/4 plate kept one after the other. What will be the output polarization for the following configurations?
Configuration 1: Axes of the polarizer, the λ/2 plate and the λ/4 plate are all parallel to each other.
Configuration 2: The λ/2 plate is rotated by 45º with respect to configuration 1.
Configuration 3: The λ/4 plate is rotated by 45º with respect to configuration 1.
For the Fourier series of the following function of period 2π
the ratio (to the nearest integer) of the Fourier coefficients of the first and the third harmonic is:
An n p n transistor is connected in a circuit as shown in the figure. If I_{C} = 1mA, b = 50, V_{BE} = 0.7V, and the current through R_{2} is 10I_{B}, where I_{B} is the base current. Then the ratio R_{1}/R_{2} is :
A rectangular loop of dimension L and width w moves with a constant velocity v away from an infinitely long straight wire carrying a current I in the plane of the loop as shown in the figure below. Let R be the resistance of the loop. What is the current in the loop at the instant the nearside is at a distance r from the wire?
A photon of frequency u strikes an electron of mass m initially at rest. After scattering at an angle φ, the photon loses half of its energy. If the electron recoils at an angle θ, which of the following is(are) true?
For an atomic nucleus with atomic number Z and mass number A, which of the following is (are) correct ?
Consider a one dimensional harmonic oscillator of angular frequency ω. If 5 identical particles occupy the energy levels of this oscillator at zero temperature, which of the following statement(s) about their ground state energy E_{0} is(are) correct ?
For a point dipole moment pˆ = pz located at the origin, which of the following is(are) correct?
A dielectric sphere of radius R has constant polarization so that the field inside the sphere Then, which of the following is (are) correct ?
Consider a circular parallel plate capacitor of radius R with separation d between the plates (d << R). The plates are placed symmetrically about the origin. If a sinusoidal voltage
V = V_{0} sinωt is applied between the plates, which of the following statement(s) is(are) true?
The linear mass density of a rod of length L varies from one end to the other as
where x is the distance from one end with tensions T1 and T2 in them (see figure), and l0 is a constant.
The rod is suspended from a ceiling by two massless strings. Then, which of the following statement(s) is(are) correct?
An object of mass m with non zero angular momentum l is moving under the influence of gravitational force of a much larger mass (ignore drag). Which of the following statement(s) is(are) correct?
A particle of mass m fixed in space is observed from rotating about its z axis with angular speed w. The particle is in the frames xy plane at a distance R from its origin. If the Coriolis and centrifugal forces on the particle are respectively, then (all the symbols have their standard meaning and refer to the rotating frame),
An isolated box is divided into two equal compartments by a partition (see figure). One compartment contains a van der Waals gas while the other compartment is empty. The partition between the two compartments is now removed. After the gas has filled the entire box and equilibrium has been achieved, which of the following statement(s) is(are) correct?
An intrinsic semiconductor of band gap 1.25 eV has an electron concentration 1010 cm^{–3} at 300 K. Assume that its band gap is independent of temperature and that the electron concentration depends only exponentially on the temperature. If the electron concentration at 200 K is Y × 10^{N} cm^{–3} (1 < Y < 10; N = integer), then the value of N is ________.
A particle of unit mass is moving in a one dimensional potential V(x) = x^{2} – x^{4}. The minimum mechanical energy (in the same units as V(x)) above which the motion of the particle cannot be bounded for any given initial condition is _________.
(Specify your answer to two digits after the decimal point.)
In a coaxial cable, the radius of the inner conductor is 2 mm and that of the outer one is 5 mm. The inner conductor is at a potential of 10V, while the outer conductor is grounded. The value of the potential at a distance of 3.5 mm from the axis is ___________.
(Specify your answer to two digits after the decimal point.)
Sand falls on a conveyor belt at the rate of 1.5 kg/s. If the belt is moving with a constant speed of 7m/s, the power needed to keep the conveyor belt running is ________.
(Specify your answer to two digits after the decimal point.)
A particle of mas m is placed in a three dimensional cubic box of side a. What is the degeneracy of its energy level with energy
(Express you answer as an integer.)
The wave number of an electromagnetic wave incident on a metal surface is (20π + 750i)m^{–1} inside the metal, where i = √1 . The skin depth of the wave in the metal is _________.
(Specify your answer in mm to two digits after the decimal point.)
Consider a Carnot engine operating between temperatures of 600K and 400K. The engine performs 1000 J of work per cycle. The heat (in Joules) extracted per cycle from the high temperature reservoir is __________.
(Specify your answer to two digits after the decimal point.)
Unpolarized light of intensity I_{0} passes through a polarizer P_{1}. The light coming out of the polarizer falls on a quarter wave plate with its optical axis at 45º with respect to the polarization axis of P_{1} and then passes through another polarizer P_{2} with its polarization axis perpendicular to that of P_{1}.
The intensity of the light coming out of P_{2} is I. The ratio I_{0}/ I is _______.
Specify your answer to two digits after the decimal point.)
An anti reflection film coating of thickness 0.1µm is to be deposited on a glass plate for normal incidence of light of wavelength 0.5µm. What should be the refractive index of the film? (Specify your answer to two digits after the decimal point.)
Intensity versus distance curve for a double slit diffraction experiment is shown in the figure below. If the width of each of the slits is 0.7µm, what is the separation between the two slits in micrometers?
(Specify your answer to two digits after the decimal point.)
The volume integral of the function over the region (0 ≤ r ≤ 2, 0 ≤ q ≤ p/3 and 0 ≤ j ≤ 2p) is ___________.
(Specify your answer to two digits after the decimal point.)
A sphere of radius R has a uniform charge density r. A sphere of smaller radius R/2 is cut out from the original sphere, as shown in the figure below. The center of the cut out sphere lies at After the smaller sphere has been cut out, the magnitude of the electric field at The value of the integer n is ______.
In planar co ordinates, an object’s position at time t is given as (r, θ) = The magnitude of its acceleration in m/s2 at t = 0 (to the nearest integer) is __________.
Consider two particles moving along the x axis. In terms of their coordinates x1 and x_{2}, their velocities are given as respectively. When they start moving from their initial locations of x_{1}(0) = 1 and x_{2}(0) = –1, the time dependence of both x_{1} and x_{2} contains a term of the form eat, where a is a constant. The value of a (an integer) is _________.
For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.
(Specify your answer to two digits after the decimal point.)
Starting with the equation TdS = dU + pdV and using the appropriate Maxwell’s relation along with the expression for heat capacity C_{p} (see useful information), the derivative for a substance
can be expressed in terms of its specific heat Cp, density r, coefficient of volume expansion b and temperature T. For ice, Cp = 2010 J/kg K, r = 10^{3} kg/m^{3} and b = 1.6 × 10^{4}/°K. If the value of at 270 K is N × 10^{7} Pa/K, then the value of N is _________.
(Specify your answer to two digits after the decimal point.)
In an electron microscope, electrons are accelerated through a potential difference of 200kV. What is the best possible resolution of the microscope?
(Specify your answer to two digits after the decimal point.)
Consider the differential equation y" + 2y' + y = 0. If y(0) = 0 and y'(0) = 1, then the value of y(2) is _________.
(Specify your answer to two digits after the decimal point.)
An Op Amp is connected in a circuit with a Zener diode as shown in the figure. The value of resistance R in kW for obtaining a regulated output V0 = 9V is _________. (Specify your answer to two digits after the decimal point.)
At t = 0, a particle of mass m having velocity v0 starts moving through a liquid kept in a horizontal tube and experiences a drag force It covers a distance L before coming to rest. If the times take to cover the distances L/2 and L/4 are t_{2} and t_{4}, respectively, then the ratio (ignoring gravity) is _________. (Specify your answer to two digits after the decimal point.)
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