Electrical Engineering Gate Yearwise 




Electrical Engineering Gate 2024 Questions with Answer

Ques 14 GATE 2024

A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in dB) of the difference amplifier is _______. (rounded off to 2 decimal places)


(40.83) is the correct answer.

Ques 15 GATE 2024

Which one of the following matrices has an inverse?

A

B

C

D


(c) is the correct answer.

Ques 16 GATE 2024

Let X be a discrete random variable that is uniformly distributed over the set {-10,-9,...,0,...,9,10}. Which of the following random variables is/are uniformly distributed?

A

X2

B

X3

C

(X-5)2

D

(X+10)2


(a) x2, d) (x+10)2) is the correct answer.

Ques 17 GATE 2024

Which of the following complex functions is/are analytic on the complex plane?

A

f(z)=jRe(z)

B

f(z)=Im(z)

C

f(z)=e|z|

D

f(z)=z2-z


(c) f(z)=z*, d) f(z)=z2-z) is the correct answer.

Ques 18 GATE 2024

Consider the complex function f(z)=cos z+e(z2). The coefficient of z5 in the Taylor series expansion of f(z) about the origin is _______. (rounded off to 1 decimal place)


(0.2) is the correct answer.

Ques 19 GATE 2024

The sum of the eigenvalues of the matrix

is _______. (rounded off to the nearest integer)


(25) is the correct answer.

Ques 20 GATE 2024

Let X(ω) be the Fourier transform of the signal x(t)=e(-t4)cos t.
The value of the derivative of X(ω) at ω=0 is _______. (rounded off to 1 decimal place)


(1.0) is the correct answer.

Ques 21 GATE 2024

Consider a vector u̅=2x̂+ŷ+2ẑ, where x̂, ŷ, and ẑ represent unit vectors along the coordinate axes x, y, and z, respectively. The directional derivative of the function f(x,y,z)=2 ln(xy)+ln(yz)+3 ln(xz) at the point (x,y,z)=(1,1,1) in the direction of u̅ is _______.

A

0

B

7/(5√2)

C

7

D

21


(c) 7) is the correct answer.

Ques 22 GATE 2024

Let f(t) be a real-valued function whose second derivative is positive for -∞<t<∞. Which of the following statements is/are always true?

A

f(t) has at least one local minimum.

B

f(t) cannot have two distinct local minima.

C

f(t) has at least one local maximum.

D

The minimum value of f(t) cannot be negative.


(b) f(t) cannot have two distinct local minima.) is the correct answer.

Ques 23 GATE 2024

Consider the function f(t)=(max(0,t))2 for -∞<t<∞, where max(a,b) denotes the maximum of a and b. Which of the following statements is/are true?

A

f(t) is not differentiable.

B

f(t) is differentiable and its derivative is continuous.

C

f(t) is differentiable but its derivative is not continuous.

D

f(t) and its derivative are differentiable.


(b) is the correct answer.

Ques 24 GATE 2024

Which of the following differential equations is/are nonlinear?

A

B

C

D


(b) is the correct answer.

Ques 25 GATE 2024

For a coordinate transformation where Vp and Vq are to be expressed in terms of Vα and Vβ as [[Vp],[Vq]]=S[[Vα],[Vβ]], the possible option(s) for matrix S is/are _______.

A

B

C

D


(a) is the correct answer.

Ques 26 GATE 2024

If '→' denotes increasing order of intensity, then the meaning of the words '[talk → shout → scream]' is analogous to '[please → _______ → pander]'.
Which one of the given options is appropriate to fill the blank?

A

flatter

B

flutter

C

fritter

D

frizzle


(a) is the correct answer.

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