Metallurgical Engineering Gate 2026 Questions with Answer

Ques 1 GATE 2026

Which of the following elements, when present in iron, enhance(s) its corrosion resistance?

Ques 2 GATE 2026

Given a scalar field φ(x, y, z) = x² − yz
Magnitude of a vector in the direction of the most rapid increase of φ at a point P (3,4,1), rounded-off to two decimal places, is _______________

Ques 3 GATE 2026

Given a function f(t) = e^−at, where a is a constant. The Laplace transform of the function is L[f(t)] = F(s). Which one of the following options is correct?

Ques 4 GATE 2026

Select the correct pair of eigen vectors for the following symmetric matrix.
[1 2; 2 4]

Ques 5 GATE 2026

Choose one correct option.
Given w = f(ax+by) where a and b are constants.
The value of (b ∂w/∂x − a ∂w/∂y) is:

Ques 6 GATE 2026

Value of scalar triple product a.(b × c) is (answer in integer) _____________.
a = 2i − 3j + 4k
b = i + 2j − 3k
c = 3i + 4j − k
Here, i, j and k are mutually orthogonal unit vectors.

Ques 7 GATE 2026

A box contains 20 thermometers, 3 of which are defective. One person randomly draws 2 thermometers from the box, one-by-one, without replacement. The probability in percent (rounded-off to two decimal places) that none of these TWO thermometers is defective, is ________________ %.

Ques 8 GATE 2026

Consider a distribution with the following probability density function
f(x) = 0.5, 0 < x < 2
f(x) = 0.0, Otherwise
Given that the mean of the above probability distribution is 1, the variance (rounded off to two decimal places) is _______________.

Ques 9 GATE 2026

Taking number of intervals n = 3, the value of the integral ∫₀^0.3 e^−x2 dx using Trapezoidal method, is ________________ (rounded off to two decimal places).

Ques 10 GATE 2026

Solution of the differential equation 10x² d²y/dx² − 20x dy/dx + 22.4y = 0 is y = c₁x^m1 + c₂x^m2 where m₁ ≠ m₂.
The value of m₁ + m₂ (answer in integer) is _____________

Ques 11 GATE 2026

A copper ore contains 30 wt.% chalcopyrite (CuFeS₂) and remaining gangue material. Assuming no copper in gangue material, the amount of copper in the ore (rounded off to one decimal place) is ______________ wt.%.
Given: Atomic weights of Fe, Cu and S are 56, 63.5, and 32 g/mol, respectively.

Ques 12 GATE 2026

A blast furnace produces hot metal with the following composition:
4 wt.% C, 1.5 wt.% Si, and rest Fe.
Only input of iron is through iron ore containing 85 wt.% Fe₂O₃ and 15 wt.% gangue consisting of SiO₂ and Al₂O₃.
2% of all iron (by weight) is lost in slag.
The amount of ore used to produce 1000 kg of hot metal (rounded off to one decimal place) is _________________ kg.
Given: Atomic weights of Fe and O are 56 g/mol and 16 g/mol, respectively.

Ques 13 GATE 2026

Al₂O₃ can be electrolyzed with an inert anode or a carbon anode.
Overall reactions are as follows:
Reaction I: For inert anode,
(2/3) Al₂O₃ (s) → (4/3) Al (l) + O₂ (g); ΔG° (in Joules) = 1124800 − 218 T
Reaction II: For carbon anode,
(2/3) Al₂O₃ (s) + C (s) → (4/3) Al (l) + CO₂ (g); ΔG° (in Joules) = 730700 − 218 T
T denotes temperature in Kelvin
Given: Faraday constant = 96500 Coulomb
If inert anode is replaced by carbon anode during electrolysis of Al₂O₃ at temperature 1300 K, the decrease in the magnitude of decomposition potential between the two reactions (rounded off to two decimal places) is _________________ Volts.