Electrical Engineering GATE 2022 Questions with Answer

Ques 40 Engineering Mathematics

Consider a 3x3 matrix A whose (i,j)-th element, a_i,j = (i-j)³. Then the matrix A will be

Ques 41 Engineering Mathematics

e^A denotes the exponential of a square matrix A. Suppose λ is an eigenvalue and v is the corresponding eigen-vector of matrix A. Consider the following two statements:
Statement 1: e^λ is an eigenvalue of e^A.
Statement 2: v is an eigen-vector of e^A.
Which one of the following options is correct?

Ques 42 Engineering Mathematics

Let f(x) = ∫₀^x e^t(t-1)(t-2)dt. Then f(x) decreases in the interval

Ques 43 Engineering Mathematics

Consider a matrix
The matrix A satisfies the equation 6A^-1 = A² + cA + dI where c and d are scalars and I is the identity matrix. Then (c+d) is equal to

Ques 44 Engineering Mathematics

Let f(x,y,z) = 4x² + 7xy + 3xz². The direction in which the function f(x,y,z) increases most rapidly at point P=(1,0,2) is

Ques 45 Engineering Mathematics

Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region R?

Ques 46 Engineering Mathematics

Let E⃗(x,y,z) = 2x²î + 5yĵ + 3zk̂. The value of ∫∫∫_V(∇⃗⋅E⃗)dV where V is the volume enclosed by the unit cube defined by 0≤x≤1, 0≤y≤1, and 0≤z≤1, is

Ques 47 Engineering Mathematics

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

Ques 48 Power Electronics

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. Which power device is best suited for this purpose?

Ques 49 Power Electronics

A single-phase full-bridge diode rectifier feeds a resistive load of 50 Ω from a 200 V, 50 Hz single phase AC supply. If the diodes are ideal, then the active power, in watts, drawn by the load is ________. (round off to nearest integer).

Ques 50 Power Electronics

The voltage at the input of an AC-DC rectifier is given by v(t)=230√2 sin(ωt) where ω=2πx50 rad/s. The input current drawn by the rectifier is given by i(t)=10sin(ωt-π/3) + 4sin(3ωt-π/6) + 3sin(5ωt-π/3). The input power factor, (rounded off to two decimal places), is ________ lag.

Ques 51 Power Electronics

Consider an ideal full-bridge single-phase DC-AC inverter with a DC bus voltage magnitude of 1000 V. The inverter output voltage v(t) shown below, is obtained when diagonal switches of the inverter are switched with 50% duty cycle. The inverter feeds a load with a sinusoidal current given by, i(t) = 10sin(ωt - π/3)A, where ω = 2π/T. The active power, in watts, delivered to the load is ________. (round off to nearest integer)

Ques 52 Power Electronics

For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is I_dc=15A and is ripple free. The thyristors are fired with a delay angle of 45°. The amplitude of the fundamental component of the source current, in amperes, is ________. (round off to two decimal places)