GATE 2022 Electrical Engineering

For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is

The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, is

If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is ______. (round off to nearest integer).

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order. Consider the following statements : $$\bullet$$...

The transfer function of a real system, H(s), is given as: $$H(s) = {{As + B} \over {{s^2} + Cs + D}}$$, where A, B, C and D are positive constants. This system cannot operate as

As you grow older, an injury to your __________ may take longer to ___________.

In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m. What is the distance between P and Q (in m) when P wins the race?

Given below are two statements and four conclusions drawn based on the statements. Statement I : Some bottles are cups. Statement II : All cups are knives. Conclusion I : Some bott...

The most commonly used relay, for the protection of an alternator against loss of excitation, is

Altruism is the human concern for the well being of others. Altruism has been shown to be motivated more by social bonding, familiarity and identification of belongingness to a gro...

There are two identical dice with a single letter on each of the faces. The following six letters : Q, R, S, T, U and V, one on each of the faces. Any of the six outcomes are equal...

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges Rs.150 for delivery. There are no delivery charges for ord...

The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transported three-phase transmission line, from the given choices are

The open loop transfer function of a unity gain negative feedback system is given by $$G(s) = {k \over {{s^2} + 4s - 5}}$$. The range of k for which the system is stable, is

Consider a 3 $$\times$$ 3 matrix A whose (i, j)-th element, a i,j = (i $$-$$ j) 3 . Then the matrix A will be

A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Whi...

A long conducting cylinder having a radius b is placed along the z-axis. The current density is $$\overrightarrow J = {J_a}{r^3}\widehat z$$ for the region r

A MOD-2 and a MOD-5 up-counter when cascaded together results in a MOD _________ counter. (in integer).

An inductor having a Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of the circuit is ________. (round off to nearest integer...

The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of 20 ns, is ________. (round off to one decima...

The voltage at the input of an AC-DC rectifier is given by $$v(t) = 230\sqrt 2 \sin \omega t$$ where $$\omega = 2\pi \times 50$$ rad/s. The input current drawn by the rectifier is...

The frequencies of the stator and rotor currents flowing in the three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is ________. (round of...

Let the probability density function of a random variable x be given as f(x) = ae $$-$$2|x| The value of a is _________.

e 4 denotes the exponential of a square matrix A. Suppose $$\lambda$$ is an eigen value and v is the corresponding eigen-vector of matrix A. Consider the following two statements:...

Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt} $$. Then f(x) decreases in the interval.

Consider a matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 2} \cr 0 & 1 & 1 \cr } } \right]$$. The matrix A satisfies the equation 6A $$-$$1 = A 2 + cA + dI, where c and d...

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by Plant 1 : C 1 = 350 + 6P 1 + 0.004P$$_1^2$$ Plant 2 : C 2 = 450 + aP 2 + 0.003P$$_2^2$$ wher...

If the magnetic field intensity ($$\overrightarrow H $$) in a conducting region is given by the expression, $$\overrightarrow H = {x^2}\widehat i + {x^2}{y^2}\widehat j + {x^2}{y^2...

Let $$f(x,y,z) = 4{x^2} + 7xy + 3x{z^2}$$. The direction in which the function f(x, y, z) increases most rapidly at point P = (1, 0, 2) is

Let $$\overrightarrow E (x,y,z) = 2{x^2}\widehat i + 5y\widehat j + 3z\widehat k$$. The value of $$\mathop{\int\!\!\!\int\!\!\!\int}\limits_{\kern-5.5pt V} {(\overrightarrow \nabla...

Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in...

A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular ac...

A 3-phase grid-connected voltage source converter with DC link voltage of 1000 V is switched using sinusoidal Pulse Width Modulation (PWM) technique. If the rid phase current is 10...

A 280 V, separately excited DC motor with armature resistance of 1 $$\Omega$$ and constant field excitation drives a load. The load torque is proportional to the speed. The motor d...

A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times o...

A single-phase full-bridge diode rectifier feeds a resistive load of 50 $$\Omega$$ from a 200 V, 50 Hz single phase AC supply. If the diodes are ideal, then the active power, in wa...

A star-connected 3-phase, 400 V, 50 kVA, 50 Hz synchronous motor has a synchronous reactance of 1 ohm per phase with negligible armature resistance. The shaft load on the motor is...

Let a causal LTI system be governed by the following differential equation $$y(t) + {1 \over 4}{{dy} \over {dt}} = 2x(t)$$, where x(t) and y(t) are the input and output respectivel...

A balanced Wheatsone bridge ABCD has the following arm resistances : R AB = 1 k$$\Omega$$ $$\pm$$ 2.1%; R BC = 100 $$\Omega$$ $$\pm$$ 0.5%; R CD is an unknown resistance; R DA = 30...

Let an input x(t) = 2 sin(10$$\pi$$t) + 5 cos(15$$\pi$$t) + 7 sin(42$$\pi$$t) + 4 cos(45$$\pi$$t) is passed through an LTI system having an impulse response, $$h(t) = 2\left( {{{\s...

The discrete time Fourier series representation of a signal x[n] with period N is written as $$x[n] = \sum\nolimits_{k = 0}^{N - 1} {{a_k}{e^{j(2kn\pi /N)}}} $$. A discrete time pe...