Electronics & Communication Gate Yearwise 

Electronics and Communication Gate 2023 Questions with Answer

Ques 27 GATE 2023

In an extrinsic semiconductor, the hole concentration is given to be 1.5ni where ni is the intrinsic carrier concentration of 1 × 1010 cm-3. The ratio of electron to hole mobility for equal hole and electron drift current is given as ____ (rounded off to two decimal places).


(0.67) is the correct answer.

Ques 28 GATE 2023

In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at T = 300 K is 1 × 1019 cm-3. The thermal equilibrium hole concentration in silicon at 400 K is ____ × 1013 cm-3 (rounded off to two decimal places).
Given kT at 300 K is 0.026 eV.


(4.63) is the correct answer.

Ques 29 GATE 2023

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 μs. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is ____ μs (rounded off to two decimal places).


(7.37) is the correct answer.

Ques 30 GATE 2023

In the circuit below, the voltage VL is ____ V (rounded off to two decimal places).


(1.45) is the correct answer.

Ques 31 GATE 2023

Which one of the following options represents the given graph?

A

f(x) = x22-|x|

B

f(x) = x2-|x|

C

f(x) = |x|2-x

D

f(x) = x2-x


(B) is the correct answer.

Ques 32 GATE 2023

Let

be two vectors. The value of the coefficient α in the expression v1 = αv2 + e which minimizes the length of the error vector e, is

A

$\frac{7}{2}$

B

$\frac{-2}{7}$

C

$\frac{2}{7}$

D

$\frac{-7}{2}$


(C) is the correct answer.

Ques 33 GATE 2023

The rate of increase of a scalar field f(x, y, z) = xyz in the direction v = (2, 1, 2) at a point (0, 2, 1) is

A

$\frac{2}{3}$

B

$\frac{4}{3}$

C

2

D

4


(C) is the correct answer.

Ques 34 GATE 2023

Let ω4 = 16j. Which of the following cannot be a value of ω?

A

2ej2π/8

B

2ejπ/8

C

2ej5π/8

D

2ej9π/8


(B) is the correct answer.

Ques 35 GATE 2023

The value of the contour integral, ∮C(z+2/z2+2z+2)dz, where the contour C is {z: |z + 1 - 3/2 j| = 1}, taken in the counter clockwise direction, is

A

-π(1 + j)

B

π(1 + j)

C

π(1 - j)

D

-π(1 - j)


(A) is the correct answer.

Ques 36 GATE 2023

Let the sets of eigenvalues and eigenvectors of a matrix B be {λk|1 ≤ k ≤ n} and {vk|1 ≤ k ≤ n}, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where B = P-1AP, respectively, are

A

{λk det(A)|1 ≤ k ≤ n} and {Pvk|1 ≤ k ≤ n}

B

{λk|1 ≤ k ≤ n} and {vk|1 ≤ k ≤ n}

C

{λk|1 ≤ k ≤ n} and {Pvk|1 ≤ k ≤ n}

D

{λk|1 ≤ k ≤ n} and {P-1vk|1 ≤ k ≤ n}


(C) is the correct answer.

Ques 37 GATE 2023

A random variable X, distributed normally as N(0, 1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is (In the options given below, a, b, c are non-zero constants and g(y) is piece-wise continuous function.)

A

aδ(y - 1) + bδ(y + 1) + g(y)

B

aδ(y + 1) + bδ(y) + cδ(y - 1) + g(y)

C

aδ(y + 2) + bδ(y) + cδ(y - 2) + g(y)

D

aδ(y + 2) + bδ(y - 2) + g(y)


(d) is the correct answer.

Ques 38 GATE 2023

The value of the line integral ∫QP(z2dx + 3y2dy + 2xz dz) along the straight line joining the points P(1, 1, 2) and Q(2, 3, 1) is

A

20

B

24

C

29

D

-5


(d) is the correct answer.

Ques 39 GATE 2023

Let x be an n × 1 real column vector with length l = √xTx. The trace of the matrix P = xxT is

A

l2

B

l2/4

C

1

D

l2/2


(a) is the correct answer.

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