Electrical Engineering GATE 2023 Questions with Answer

Ques 14 Engineering Mathematics

For a given vector w=[1 2 3]^T, the vector normal to the plane defined by w^TX=1 is _______.

[-2 -2 2]^T

[3 0 -1]^T

[3 2 1]^T

[1 2 3]^T

Ques 15 Engineering Mathematics

In the figure, the vectors u and v are related as: Au=v by a transformation matrix A. The correct choice of A is _______.

Ques 16 Engineering Mathematics

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation σ_o.
The σ_o is estimated by randomly drawing out 10,000 numbers of samples (x_n). The estimates σ̂₁, σ̂₂ are computed in the following two ways.

Which of the following statements is true?

E(σ̂₂²)=σ_o²

E(σ̂₂)=σ_o

E(σ̂₁²)=σ_o²

E(σ̂₁)=E(σ̂₂)

Ques 17 Engineering Mathematics

In the following differential equation, the numerically obtained value of y(t), at t=1, is _______. (Round off to 2 decimal places).

0.25 is the correct answer.

Ques 18 Engineering Mathematics

Three points in the x-y plane are (-1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is _______. (Round off to 2 decimal places).

1.00 is the correct answer.

Ques 19 Engineering Mathematics

Consider the following equation in a 2-D real-space.
|x₁|^p+|x₂|^p=1 for p>0
Which of the following statement(s) is/are true?

When p=2, the area enclosed by the curve is π.

When p tends to ∞, the area enclosed by the curve tends to 4.

When p tends to 0, the area enclosed by the curve is 1.

When p=1, the area enclosed by the curve is 2.

Ques 20 Engineering Mathematics

The expected number of trials for the first occurrence of a "head" in a biased coin is known to be 4. The probability of the first occurrence of a "head" in the second trial is _______. (Round off to 3 decimal places).

0.188 is the correct answer.

Ques 21 Engineering Mathematics

The closed curve shown in the figure is described by r=1+cos θ, where r=√(x²+y²); x=r cos θ, y=r sin θ.
The magnitude of the line integral of the vector field F=-yî+xĵ around the closed curve is _______. (Round off to 2 decimal places). *

6.28 is the correct answer.

Ques 22 Engineering Mathematics

A quadratic function of two variables is given as
f(x₁,x₂)=x₁²+2x₂²+3x₁+3x₂+x₁x₂+1.
The magnitude of the maximum rate of change of the function at the point (1,1) is _______. (Round off to the nearest integer).

8 is the correct answer.

Ques 23 General Aptitude

Rafi told Mary, "I am thinking of watching a film this weekend."
The following reports the above statement in indirect speech:
Rafi told Mary that he _______ of watching a film that weekend.

thought

is thinking

am thinking

was thinking

Ques 24 General Aptitude

Permit: _______:: Enforce: Relax
(By word meaning)

Allow

Forbid

License

Reinforce

Ques 25 General Aptitude

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?

1/36

1/6

5/6

1/3

Ques 26 General Aptitude

A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco.
The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco. Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

Approximately 30% of tobacco users successfully stopped consuming tobacco.

Approximately 65% of tobacco users successfully stopped consuming tobacco.

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Electrical Engineering GATE 2023 Questions with Answer