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?
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