What topics are covered on Page 3 of GATE 2026 Electrical Engineering questions?

Page 3 contains Questions 27 to 39. The first questions cover Engineering Mathematics including orthogonal matrices, matrix rank, complex-variable contour integration, random variables and definite integration. The remaining questions cover General Aptitude such as grammar, visual reasoning, geometry, logical inference, synonyms and numerical patterns.

What properties of an orthogonal matrix are correct in GATE 2026 Electrical Engineering?

For a real orthogonal matrix, its determinant is either +1 or -1, its eigenvalues have modulus 1, and it preserves both Euclidean norms and inner products. Therefore, the correct options are A, B and D.

What is the magnitude of the contour integral in GATE 2026 Electrical Engineering?

For the given complex contour integral over the circle centered at 2+i with radius 3/2, the magnitude evaluates to approximately 19.10.

What value of alpha minimizes the expected squared error in GATE 2026 Electrical?

For the given random variables X and Y, the value of alpha that minimizes E((X-alpha Y)^2) is 0.1.

Electrical Engineering Gate 2026 Questions with Answer

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Ques 27 GATE 2026

Consider an n × n orthogonal matrix A with real entries and each column having unit Euclidean norm.
Which of the following statements is/are correct?

The value of the determinant of A is either +1 or −1

The eigenvalues of A have modulus 1

∥Ax∥ = ∥x∥, for all x∈Rⁿ, and (Ax)^T(Ay) ≠ x^Ty, for all distinct x,y∈Rⁿ

∥Ax∥ = ∥x∥, for all x∈Rⁿ, and (Ax)^T(Ay) = x^Ty, for all x,y∈Rⁿ

(a,b,d) is the correct answer.

Ques 28 GATE 2026

Consider the system of linear equations: Ax = b, where A is an n × n matrix, and x and b are n-dimensional column vectors.
Suppose this system of equations has a unique solution. Which of the following statements is/are correct?

A⁻¹ exists

The system of equations A^mx = b also has a unique solution for m = 1, 2, 3,...

rank(A) = rank(A^m), for m = 1, 2, 3,...

rank(A) < rank([A|b]), where [A|b] denotes the augmented matrix.

(a,c) is the correct answer.

Ques 29 GATE 2026

The magnitude of the contour integral
∮_C ((z+1)²/((z−i)(z−2))) dz
over the contour C: |z − 2 − i| = 3/2 is ______
(Round off to two decimal places)
Note: z is a complex variable and i = √−1

(19.10) is the correct answer.

Ques 30 GATE 2026

Let X and Y be two real-valued random variables with E(X) = 1, E(Y) = 2, E(X²) = 4, E(Y²) = 9, and E(XY) = 0.9, where E denotes the expectation operator.
The value of α that minimizes E((X−αY)²) is __________
(Round off to one decimal place)

(0.1) is the correct answer.

Ques 31 GATE 2026

The integral
(1/π) ∫₀^∞ x²⁰²⁶/((1+x²⁰²⁶)(1+x²)) dx
evaluates to _________
(Round off to two decimal places)

(0.25) is the correct answer.

Ques 32 GATE 2026

‘The shopkeeper sells lemons.’
In this sentence, the word ‘lemons’ is the ________.

object

subject

predicate

verb

(a) is the correct answer.

Ques 33 GATE 2026

The figure below is supposed to show three non-overlapping shapes – one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by ‘?’ and completes the oval and the two triangles?

(d) is the correct answer.

Ques 34 GATE 2026

At how many points will the curves y = x² and y = −x² − 2x − 1 intersect in the real (x, y) plane?

(b) is the correct answer.

Ques 35 GATE 2026

‘If Anish had scored hundred runs in today’s match, he would have been made the captain of his team. He would have then become the youngest captain in his team’s history. Unfortunately, he got out without scoring any runs. Hence, there won’t be any change in the captaincy for now.’
Based on the paragraph above, which one of the following statements is true?

Anish made hundred runs but was denied captaincy.

Anish was the captain of his team before the game today.

The current captain is older than Anish.

Anish is the youngest player in his team.

(b) is the correct answer.

Ques 36 GATE 2026

Which one of the following figures P, Q, R, or S, correctly shows the 45° clockwise-rotated version of figure (I)?

(b) is the correct answer.

Ques 37 GATE 2026

Match the words in Column I with their synonyms in Column II.

Column I	Column II
(i) Lonely	(p) Verbatim
(ii) Literal	(q) Solitary
(iii) Lousy	(r) Deadly
(iv) Lethal	(s) Terrible

(i)-(q); (ii)-(p); (iii)-(s); (iv)-(r)

(i)-(q); (ii)-(s); (iii)-(r); (iv)-(p)

(i)-(s); (ii)-(p); (iii)-(q); (iv)-(r)

(i)-(r); (ii)-(s); (iii)-(p); (iv)-(q)

(a) is the correct answer.

Ques 38 GATE 2026

In the given figure, PQ is the diameter of a circle with center O. Two points R and S are chosen on the circle such that ∠ROS = 80°. When PR and QS are extended, they meet at T. The value of ∠RTS is _________________

40°

50°

60°

80°

(a) is the correct answer.

Ques 39 GATE 2026

Based on the relationship between each polygon and the number inside it, the value of ‘X’ is ______
(Triangle: 6, Rectangle: 24, Pentagon: 120, Hexagon: X)

720

596

240

(a) is the correct answer.

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