Electrical Engineering GATE 2021 Questions with Answer

Ques 27 Electromagnetics

One coulomb of point charge moving with a uniform velocity $10\tox m/s$ enters the region $x \geq 0$ having a magnetic flux density $β = (10y\tox + 10x\toy + 10\toz)$ T. The magnitude of force on the charge at $x = 0 +$ is _______ N.
( $\tox,$ $\toy,$ and $\toz$ are unit vectors along x-axis, y-axis, and z-axis, respectively.)

100 is the correct answer.

Ques 28 Electromagnetics

Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field $E\_{2}$ in the gap to the original electric field $E\_{1}$ is

5 is the correct answer.

Ques 29 Electromagnetics

A 1 μC point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 μC is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is _______ mJ. (Round off to 2 decimal places).
Take 1/4πε_o = 9*10⁹ in SI units. All coordinates are in meters.

is the correct answer.

Ques 30 Electronics

In the BJT circuit shown, beta of the PNP transistor is 100. Assume V_BE = -0.7V. The voltage across R_c will be 5 V when R₂ is _______ KΩ. (Round off to 2 decimal places.)

is the correct answer.

Ques 31 Electronics

In the circuit shown, the input V_i is a sinusoidal AC voltage having an RMS value of 230V ± 20%. The worst-case peak-inverse voltage seen across any diode is _______ V. (Round off to 2 decimal places.)

is the correct answer.

Ques 32 Electronics

In the circuit shown, a 5 V Zener diode is used to regulate the voltage across load R₀. The input is an unregulated DC voltage with a minimum value of 6 V and a maximum value of 8 V. The value of R_s is 6 Ω. The Zener diode has a maximum rated power dissipation of 2.5 W. Assuming the Zener diode to be ideal, the minimum value of R₀ is _______ Ω.

is the correct answer.

Ques 33 Engineering Mathematics

Let A be a $10 \times 10$ matrix such that $A 5$ is a null matrix, and let I be the $10 \times 10$ identity matrix. The determinant of $A + I$ is

1 is the correct answer.

Ques 34 Engineering Mathematics

Let p and q be real numbers such that p²+q²=1. The eigenvalues of the matrix are

1 and 1

1 and -1

j and -j

pq and -pq

Ques 35 Engineering Mathematics

Let p(z)=z³+(l+j)z²+(2+j)z+3 , where z is a complex number. Which one of the following is true?

conjugate {p(z)}=p(conjugate{z}) for all z

The sum of the roots of p(z)=0 is a real number

The complex roots of the equation p(z)=0 come in conjugate pairs

All the roots cannot be real

Ques 36 Engineering Mathematics

Let f(x) be a real-valued function such that f^'(x₀)=0 for some x₀∈(0,1) and f^''(x)>0 for all x∈(0,1). Then f(x) has

no local minimum in (0, 1)

one local maximum in (0, 1)

exactly one local minimum in (0, 1)

two distinct local minima in (0, 1)

Ques 37 Engineering Mathematics

Suppose the circles x² + y² = 1 and (x - 1)² + (y - 1)² = r² intersect each other orthogonally at the point (u, v). Then u + v = _______

a is the correct answer.

Ques 38 Engineering Mathematics

In the open interval (0, 1), the polynomial p(x) = x⁴ - 4x³ + 2 has

two real roots

one real root

three real roots

no real roots

Ques 39 Engineering Mathematics

Suppose the probability that a coin toss shows "head" is p, where 0<p<1. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is

p/(1-p)

(1-p)/p

1/p

1/p²

1 2 3 4 5

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Electrical Engineering GATE 2021 Questions with Answer