Electrical Engineering Gate Yearwise 




Electrical Engineering Gate 2021 Questions with Answer

Ques 27 GATE 2021

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


(100) is the correct answer.

Ques 28 GATE 2021

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 GATE 2021

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 1/4πεo = 9*109 in SI units. All coordinates are in meters.


() is the correct answer.

Ques 30 GATE 2021

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


() is the correct answer.

Ques 31 GATE 2021

In the circuit shown, the input Vi 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 GATE 2021

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 Rs 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 GATE 2021

Let A be a 10 × 10 matrix such that A5 is a null matrix, and let I be the 10 × 10 identity matrix. The determinant of A + I is


(1) is the correct answer.

Ques 34 GATE 2021

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

A

1 and 1

B

1 and -1

C

j and -j

D

pq and -pq


(b) is the correct answer.

Ques 35 GATE 2021

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

A

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

B

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

C

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

D

All the roots cannot be real


(d) is the correct answer.

Ques 36 GATE 2021

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

A

no local minimum in (0, 1)

B

one local maximum in (0, 1)

C

exactly one local minimum in (0, 1)

D

two distinct local minima in (0, 1)


(c) is the correct answer.

Ques 37 GATE 2021

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 GATE 2021

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

A

two real roots

B

one real root

C

three real roots

D

no real roots


(d) is the correct answer.

Ques 39 GATE 2021

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

A

p/(1-p)

B

(1-p)/p

C

1/p

D

1/p2


(c) is the correct answer.

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