Electronics and Communication GATE 2025 Questions with Answer

Ques 40 Electronic Devices and Circuits

An ideal p-n junction germanium diode has a reverse saturation current of 10 μA at 300 K.
The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias current of 100 mA at 300 K is
(Consider the Boltzmann constant k_B=1.38×10^-23 J/K and the charge of an electron e=1.6×10^-19 C.)

Ques 41 Engineering Mathematics

Consider the matrix A below:

For which of the following combinations of α, β, and γ, is the rank of A at least three?

Only (i), (iii), and (iv)

Only (iv)

Only (ii)

Only (i) and (iii)

Ques 42 Engineering Mathematics

Consider the following series:
(i) Σ_n=1^∞ 1/√n
(ii) Σ_n=1^∞ 1/(n(n+1))
(iii) Σ_n=1^∞ 1/n!
Choose the correct option.

Only (ii) converges

Only (ii) and (iii) converge

Only (iii) converges

All three converge

Ques 43 Engineering Mathematics

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.
What is the probability that the two balls drawn have different colours?

2/3

1/3

1/2

Ques 44 Engineering Mathematics

Consider the function f:R→R defined as f(x)=2x³-3x²-12x+1.
Which of the following statements is/are correct? (Here, R is the set of real numbers.)

f has no global maximizer

f has no global minimizer

x=-1 is a local minimizer of f

x=2 is a local maximizer of f

Ques 45 Engineering Mathematics

The function y(t) satisfies t²y'(t)-2ty'(t)+2y(t)=0, where y'(t) and y'(t) denote the first and second derivatives of y(t), respectively.
Given y'(0)=1 and y'(1)=-1, the maximum value of y(t) over [0,1] is ______ (rounded off to two decimal places).

Ques 46 Engineering Mathematics

Consider a non-negative function f(x) which is continuous and bounded over the interval [2, 8]. Let M and m denote, respectively, the maximum and the minimum values of f(x) over the interval.
Among the combinations of α and β given below, choose the one(s) for which the inequality β ≤ ∫₂⁸ f(x)dx ≤ α is guaranteed to hold.

β=5m, α=7M

β=6m, α=5M

β=7m, α=6M

β=7m, α=5M

Ques 47 Engineering Mathematics

Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle C in the complex plane is/are TRUE?

∮_Ce^zdz=0

∮_Czⁿdz=0, where n is an even integer

∮_Ccos z dz≠0

∮_Csec z dz≠0

Ques 48 Engineering Mathematics

Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled.
Let the random variable X denote the sum of the outcomes obtained.
The expectation of X is ______ (rounded off to two decimal places).

Ques 49 Engineering Mathematics

Consider the vectors

For real-valued scalar variable X, the value of min_x ||ax-b||₂ is ______ (rounded off to two decimal places).
||⋅||₂ denotes the Euclidean norm, i.e., for y=[(y₁); (y₂)], ||y||₂=√(y₁²+y₂²).

Ques 50 General Aptitude

Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Group-I: Abuse → Insult → Ridicule
Group-II: ______ → Praise → Appreciate
Select the most appropriate option to complete the above sentence.

Extol

Prize

Appropriate

Espouse

Ques 51 General Aptitude

Had I learnt acting as a child, I ______ a famous film star.
Select the most appropriate option to complete the above sentence.

can be

will be

am going to be

could have been

Ques 52 General Aptitude

The 12 musical notes are given as C, C^#, D, D^#, E, F, F^#, G, G^#, A, A^#, and B.
Frequency of each note is ¹√2 times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F^# and C is:

&sup6;√2

√2

&sup4;√2

1 2 3 4 5

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Electronics and Communication GATE 2025 Questions with Answer