For the circuit shown below, determine the current I. Assume silicon diodes with a forward voltage drop of 0.7 V. (E₁ = 20 V → 2.2 kΩ resistor → two silicon diodes in anti-parallel → E₂ = 4 V)

In a universal shift register, the input labelled D_SR is used when

The operating principle of a Gunn diode is based on

A 4-bit synchronous (parallel) counter has a flip-flop propagation delay of 50 ns and a maximum logic path containing one AND gate with a propagation loss delay of 20 ns. Determine the maximum operating frequency (f_max) of the counter.

The maximum power conversion efficiency (η) of a solar cell is best represented by which of the following expression? (Where : V_OC = Open Circuit Voltage ; I_SC = Short Circuit Current ; ff = fill factor ; P_in = incident solar power)

The magnetic susceptibility (χ′_m) is related to the magnetic permeability μ′ through the expression (in CGS system)

The magnetic moment of diamagnetic material is given by (e-charge of electron, m-mass of electron, r-radius of orbit, H-magnetic field applied to the normal of the orbit)

Magnetic field H is measured in 1 amp-turn/m is equivalent to how many oersteds?

Curie-Weiss law is given by (Given C′ − Curie constant)

Specific heat (Cv) at constant volume is given by the relation

Eddy currents are induced in

An infinitely long wire carries a current of 1 A. What will be the value of magnetic field due to it at a distance of 2 cm from the wire? (μ₀ = 4π × 10⁻⁷ MKS)

Magnetic field due to a current I carrying circular loop at its center is B. Now if the current through the loop is reduced to half, the magnetic field

Poisson’s equation in terms of the vector potential and the current density is given by ∇²A⃗ = −μ₀J⃗. If J⃗ → 0 at infinity, the solution of this equation is of the type

The magnetic flux associated with a loop is given by φ = 4 cos 5πt, where t is in second and φ is in Wb. The maximum magnitude of the emf induced in it at t = 1.5 s will be _______ V.

A triangular waveform varying from −5 V to +5 V is applied to the non-inverting (+) input of an op-amp comparator. The inverting input is held at +2 V. The output waveform will

Calculate the output voltage for the circuit of figure. The inputs are V₁ = 50 mV sin(1000t) and V₂ = 10 mV sin(3000t). (Inverting summing amplifier using IC 741: R_f = 330 kΩ, R₁ = 33 kΩ for V₁, R₂ = 10 kΩ for V₂, supply ±9 V)

Which addressing mode is used in the instruction MVI A, # 55 H?

Which of the following correctly describes the Data Bus Width and the Program Counter (PC) width of the standard 8051 microcontroller?

Which of the following 8085 microprocessor instructions does not affect any of the status flags?

If the x, y co-ordinates are rotated counter clockwise through an angle φ, keeping r⃗ fixed the transformed x-component is

Matrices are primarily used to represent

An eigenvector of a matrix is a vector that

Which of the following equations contain a source term −ρ/ε₀? (Where symbols have their usual meanings)

The standard generating function for Bessel’s functions of integral order is

The contribution of Coulomb energy in the semi-empirical mass formula of a nucleus of mass number A and atomic number Z is of the form (a = constant)

Given that ₃Li⁷ = 7.01816 amu, ₃Li⁶ = 6.01692 amu, ₀n¹ = 1.00893 amu. The binding energy of a neutron in a ₃Li⁷ nucleus is

Volume of a nucleus in an atom is proportional to the

If the nuclear radius of ²⁷Al is 3.6 Fermi, the approximate nuclear radius of ⁶⁴Cu in Fermi is

Nuclear forces are

Rydberg’s constant is

An atom has L = 2, S = 1/2 and J = 3/2, what is its state?

A translatory force experienced in Stern-Gerlach experiment is given as

The Zeeman shift is denoted as

An X-ray machine uses an accelerating potential of 50,000 volts. The shortest wavelength present in X-ray produced is

According to Bose-Einstein statistics, f_BE is equal to

Three particles are to be distributed in four energy levels a, b, c and d. When particles are bosons, then all possible ways of this distribution are

_______ is called life time of the microstate. (Where, N = No. of microstates)

A molecule of a gas moves equal distances ‘l’ between collisions with equal probability in any direction. After a total of N such displacements, what is the mean square displacement R² of the molecule from its starting point?

An ensemble in which each system has the same fixed energy as well as the same number of particles, is called

Consider the following statements about Newton’s laws of motion.

For conservative force F, consider the following statements.

How does a one dimensional harmonic oscillator oscillates in phase space?

Kepler’s second law states that “The radius vector joining a planet to the sun sweeps out area at a rate that is independent of its position in the orbit”. It implies that the

A particle moving in a central force field at r = 0, describes a spiral r = e^−θ. The magnitude of force is proportional to

When current through a closed loop is 2 mA, its self-inductance is 25 mH. If the current is doubled, its self-inductance will become

Which of the following equation is a general solution to the Laplace equation in one dimension?

Which fundamental law of Physics is represented by continuity equation?

Let the unit vector along the direction of polarization of transverse electromagnetic wave is n̂ and that in the direction of its propagation is k̂. Then n̂ · k̂ =

The differential equation for a wave, propagating along z-axis, is given by ∂²f/∂z² = 25π² ∂²f/∂t². What is its speed?

The sum of Boltzmann factors over all states is called

If the partition function is given by Z, then mean energy Ē is given by

The diffusion co-efficient is directly proportional to

A system which can exchange only energy with the surroundings is called _______ system.

The phenomenon that takes place with no change in entropy and volume at constant temperature and pressure is called _______ order phase transitions.

Fermi factor (where E-energy of allowed state, E₀-Fermi energy) is given by

The kinetic energy of a free electron is (Quantum mechanical approach) is given as (P-momentum of electron and m is a mass of the electron)

Fermi energy for intrinsic semiconductors is given by (Where Ev-energy of valence band, Ec-energy of conduction band)

The binding (ionization) energy (En) of donor or acceptor impurity levels in an extrinsic semiconductor (The equation obtained from the hydrogen model) is given by (Where symbols have their usual meaning)

For a typical germanium crystal at room temperature, n_e is the order of 2 × 10¹⁵ electron/cm³ and μ = 3600 cm²/(volt-sec), then conductivity is given by (charge of electron = −1.602 × 10⁻¹⁹ C), (Where n_e is number of charge carriers and μ is the mobility)

The angular momentum of the electron in hydrogen atom can possibly be

Neglecting the variation of mass with velocity, the wavelength associated with an electron having kinetic energy E, is proportional to

The uncertainty principle holds for

The de-Broglie wavelength for an electron of energy 150 eV is

The value of the commutator [L_z, L²] is

The common mode voltage for a differential amplifier is V₀ = 8 V. Given input voltage V₁ = 6 V, then value of other input voltage V₂ is

A 8-bit A/D converter has a full scale analog input voltage of +5 V. For a resolution of 8-bit and full scale error 0.02% of full scale, what is the total possible error?

The latching behaviour of an SCR is primarily due to

An eight-bit binary ripple up counter with a modulus of 256 is holding the count 01111111. What will be the count after 135 clock pulses be?

If the average velocity of an electron in GaAs is V_d ≃ 1 × 10⁷ cm/s at a field of 10⁴ V cm⁻¹ and the effective mass of the electron is 0.07 m_e, the electron mobility (μ) and mean time (t) between electron scattering events will be

Zero-crossing detector is also known as

A differential amplifier has +100 mV applied to non-inverting end and +250 mV applied to inverting end. The output is 1.5 V. The gain of the amplifier is

A differential amplifier has a common mode gain of 0.02. It has +200 mV signals applied to each of its inputs. The amplitude of output signal is

Fourier series is for N = 1, 2, 3, …

The probable error in measuring the horizontal distance x of a tower is ± a and that in measuring its height y is ± b. What will be the probable error in evaluating the tangent of the angle subtended by it at distance x on the ground?

The weighting function for the orthogonality of Hermite polynomials is

Which of the following statement is true regarding Fourier series?

The coefficient of (z − z₀)⁻¹ in Laurent expansion is called the

The transformation philosophy of tensors is based on the fact that

A group is called abelian if

For coupling of three angular momentum 1, 3/2 and 5/2, total number of eigen states will be

In Born approximation, the cross-section of scattering depends on

For the motion of a Dirac particle in a central force field, we have (Where J⃗ = L⃗ + S⃗ and H is the Hamiltonian)

If α⃗ and β⃗ are Dirac matrices, then the value of (α⃗·β⃗)(α⃗·c⃗) will be (Where c⃗ is arbitrary matrices)

According to Quantum mechanics, the energy levels of a particle executing one-dimensional simple harmonic motion are

Deuteron is the two nucleon bound system consisting of

Nuclear forces are

The ground state of the deuteron is a

According to the shell model, the ground state of ¹⁵₈O nucleus is

The spin and parity of ₄Be⁹ nucleus, as predicted by the shell model, are respectively

The shift in stark effect is denoted as

The quantity eh/4π mpc is known as

Stokes and antistokes lines are observed in

In electronic spectra for rotational structure of P-branch, the following statement is true

The splitting of spectral lines in the presence of magnetic field when the energy due to spin-orbit coupling is less than that due to magnetic field is

A particle is scattered by a rigid elastic sphere of radius r. What will be the total scattering cross-section?

A rigid body has principal moment of inertia I₁, I₂ and I₃. If I₁ = I₂ and I₃ = 0, then the rigid body is called

Which quantity is always conserved in torque free motion of a rigid body?

A particle of mass m is attached to a thin uniform rod of length a and mass 4m, at a point located at a distance a/4 from the center of the rod, towards the lower end. The moment of inertia of rod-particle system, about an axis passing through the upper end of the rod and perpendicular to its length will be

If the Lagrangian of a mechanical system does not depend explicitly on time, which of the following quantities is conserved?

The modulation index (β) for frequency modulation is defined as

A carrier wave of frequency 10 MHz and peak value 10 V is amplitude modulated by a 5 KHz sine wave of amplitude 6 V. What is the value of modulation index?

A temperature transducers exhibit non-linear behavior. The order in which they exhibit non-linearity (highest to lowest) is

Which of the following optical transducers is an active transducers?

From the following data calculate value of y as a linear function of x using method of least squares.

The solutions of Maxwell's equations

If for the air-glass interface, n₁ = 1 and n₂ = 1.5, the value of reflection coefficient will be

When a ray of light is incident on an air-glass interface at Brewster's angle (θ_p), the angle between the reflected ray and the refracted ray is

_______ waves cannot occur in a hollow wave guide.

A waveguide has a square cross-section of dimensions 3 mm × 3 mm. What will be its cutoff frequency for the TE₁₀ mode?

If J⃗₁ and J⃗₂ are angular momenta of two non-interacting systems and J⃗ represent the sum of J⃗₁ and J⃗₂ (i.e. J⃗ = J⃗₁ + J⃗₂), then

A particle is moving in a negative potential field which vanishes at infinity. The spectrum of negative energy eigenvalues of the particle will be

The value of a a⁺ a a⁺a⁺ a

The Fermi Golden rule of time dependent perturbation gives the transition of

The first order perturbation energy is given by

Hamilton's canonical equations of motion for a conservative system are

A hypothetical train moving with the speed of 0.6C passes by the platform without being slowed down. An observer on the platform note that the length of the train is just equal to the length of the platform which is 200 meter. What is the length of platform as measured by the observer in the train?

How fast must an electron move in order that its relativistic mass is equal to twice its rest mass?

The Galilean transformation is obtained from the Lorentz transformation under which of the following conditions?

What is the equivalent mass m of a photon of wavelength λ?

Which is Moseley's law?

The mass of hydrogen atom is 1.6 × 10⁻²⁷ kg. The reduced mass of hydrogen molecule will be

The symbols have their usual meanings. The following relation is obeyed in LASER

For fine structure of X-ray levels, the energy of the system is given as

The value of Rydberg constant for heavy mass (M) is R_M and thus following order is correct, for variation of R_M with mass number

The transformation of ice into water at 0°C and 1 atmospheric pressure is an example of _______ order phase transition.

The entropy S in terms of partition function Z and the mean energy Ē are related with the expression

The particles whose spin angular momenta are (n + ½)ħ, where n = 0, 1, 2, 3, ..., are called

The equilibrium number of photons in the radiation cavity is directly proportional to (Where V = Volume of cavity)

In simple random walk problem, the mean square deviation (Δn₁)² =

The bisection method is guaranteed to converge if

The finite difference method is particularly suitable for

The truncation error of the trapezoidal rule is proportional to

Which statement is true about the Poisson distribution?

The probability distribution function of normal distribution is defined over the interval

The mean deviation (D̄) in terms of deviations from the mean value of n reading is

The heat generated by a linear IC-741 is 200 mw. If thermal resistance is 150° C/W and the ambient temperature is 25° C, then the device temperature is

Common Mode Rejection Ratio (CMRR) of a differential amplifier is given by (A_d → voltage gain of difference signal and A_c → voltage gain of common mode signal)

Basic instrumentation amplifier using three Op-Amp should have characteristics

For IC-741 Op-Amp following parameters are given. Quiescent collector current I_c = 9.5 μA, C_c = 30 PF, Peak amplitude of input voltage V_m = 1.5 V, so the slew rate is

Which of the following disintegration series of the heavy elements will give ²⁰⁹Bi as a stable nucleus?

Nuclear fusion required high temperature because

The thermal ionization formula was proposed by

The reaction e⁺ + e⁻ → μ⁺ + π⁻ is forbidden because of

Atomic mass of an element is 232 and its atomic number is 90. The end product of this radioactive element is an isotope of lead (atomic mass 208 and atomic number 82). The number of alpha and beta particles emitted as

The Hall coefficient (R_H) is given by (Where symbols have their usual meaning)

If the crystal is at constant pressure P, then the Gibbs free energy G is given by the relation

In Fermi energy-the transitional energy (E_trans) and momentum (P_trans) are related by the expression (Where m is the mass of electron)

The kinetic energy (KE) for metals, where m* is an effective mass is given by the expression

The Pauli paramagnetic susceptibility (χ) is given by the expression (Where symbols have their usual meaning)