What topics are covered on Page 1 of GATE 2026 Mining Engineering questions?

Page 1 contains Questions 1 to 13. Engineering Mathematics topics include the Cayley-Hamilton theorem, divergence, differential equations, probability distributions, Fourier series, Hessian matrices, Newton divided-difference interpolation, simultaneous equations and linear regression. Engineering Mechanics topics include beams, rotational motion, belt friction and truss analysis.

What polynomial satisfies the Cayley-Hamilton theorem in GATE 2026 Mining Engineering?

For the matrix P = [[2,1],[0,3]], the characteristic polynomial is λ² - 5λ + 6. Therefore, according to the Cayley-Hamilton theorem, P² - 5P + 6I = 0.

What is the coefficient of determination in the GATE 2026 Mining regression question?

For the given dataset and best-fit line y = 2.2x + 2.3, the coefficient of determination r² is 0.48.

How many rotations does the motor shaft make while slowing down?

The motor shaft decreases uniformly from 50 revolutions per second to 20 revolutions per second over 15 seconds. It completes 525 rotations during this period.

What is the force in member PR of the truss in GATE 2026 Mining Engineering?

For the truss carrying a 10 kN vertical load at Q, the force in member PR is 4.33 kN.

Mining Engineering Gate 2026 Questions with Answer

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Ques 1 GATE 2026

If I is an identity matrix, the polynomial equation that satisfies the Cayley-Hamilton theorem for the matrix P = [[2, 1], [0, 3]] is

P² - 5P + 6I = 0

P² - 5P + 5I = 0

P² - 6P + 5I = 0

P² - 4P + 3I = 0

(a) is the correct answer.

Ques 2 GATE 2026

Let î and ĵ are the unit vectors in the x and y direction, respectively. The divergence (∇.F) of F = x²y î + y³x ĵ at the point (3,2) is

(d) is the correct answer.

Ques 3 GATE 2026

Which one of the following is a non-linear, second-order, and first-degree differential equation?

d²y/dx² + cos x (dy/dx) + e^xy = 0

d²y/dx² + cos y = 0

d²y/dx² + sin x = 0

(dy/dx)² + 3y = 0

(b) is the correct answer.

Ques 4 GATE 2026

Match the distribution with its corresponding probability density/mass function.
Distribution type: (P) Binomial Distribution, (Q) Poisson Distribution, (R) Normal Distribution, (S) Exponential Distribution
Probability density/mass function:
(1) f(x) = (1/(σ√2π)) exp(-(1/2)((x-μ)/σ)²), σ > 0
(2) f(x) = (n choose x) p^x(1-p)^n-x, x = 0,1,2,...,n
(3) f(x) = (μ^x/x!) exp(-μ), x = 0,1,2,...
(4) f(x) = λ exp(-λx), x > 0

P→2, Q→3, R→1, S→4

P→1, Q→3, R→2, S→4

P→3, Q→2, R→1, S→4

P→2, Q→4, R→3, S→1

(a) is the correct answer.

Ques 5 GATE 2026

Which of the following statements about Fourier series is/are correct?

The Fourier series of an even function contains only cosine terms

The Fourier series of an odd function contains only cosine terms

The Fourier series of an odd function contains only sine terms

The Fourier series of an even function contains only sine terms

(a,c) is the correct answer.

Ques 6 GATE 2026

The value of the determinant of the Hessian of f(x,y) = x² + y² + xy - 8x - 7y at its stationary point is

(b) is the correct answer.

Ques 7 GATE 2026

Given the data in the following Table, Newton’s divided difference interpolation polynomial is
y = b₀ + b₁(x-2) + b₂(x-2)(x-2.5).
If the values of b₀ and b₁ are 3 and 1, respectively, then the value of b₂ is
x: 2.0, 2.5, 3.0
y: 3.0, 3.5, 5.0

(a) is the correct answer.

Ques 8 GATE 2026

Given and Px = b.
If Py = d with , the value of y₂ is

(a) is the correct answer.

Ques 9 GATE 2026

Using linear regression (least squares), the best-fit line for the given dataset is y = 2.2x + 2.3. Given the residual sum of squares is 25.8, the coefficient of determination (r²), is _______________. (rounded off to two decimal places)

x	y
2	8
3	9
4	7
5	16

(0.48) is the correct answer.

Ques 10 GATE 2026

A simply supported beam PQRS is shown.

The location at which the zero shear force is acting on the beam is

(d) is the correct answer.

Ques 11 GATE 2026

The shaft of a motor rotating at 50 rev s^-1 is uniformly retarded to 20 rev s^-1 in 15 s. The number of complete rotations the shaft makes in the given time is _______________. (answer in integer)

(525) is the correct answer.

Ques 12 GATE 2026

A belt is wrapped around a pulley as shown. The coefficient of friction between the belt and pulley is 0.3. If there is no slippage between the belt and pulley, the angle of wrap (θ), in degrees, is _______________. (rounded off to two decimal places)

(132.38) is the correct answer.

Ques 13 GATE 2026

A truss PQR carries vertical load of 10 kN at Q as shown. P is a pinned support and R is a roller support, with PR = 5 m (horizontal), angle QPR = 60°, and angle QRP = 30°. The force in member PR, in kN, is _______________. (rounded off to two decimal places)

(4.33) is the correct answer.

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