Metallurgical Engineering Gate 2023 Questions with Answer

Ques 1 GATE 2023

Order (O) and degree (D) of the differential equation (dy/dx)³ = √(d²y/dx² + 10) are _______.

Ques 2 GATE 2023

The value of lim_x→1 (7x⁷ - 20x⁵ + 13x)/(3x³ + x - 4) is _______.

Ques 3 GATE 2023

The sum of eigen values of the matrix

Ques 4 GATE 2023

The probability of setting an easy exam paper by three setters are 1/2, 1/3 and 1/4. If all three are setting one paper each, then the probability that at least one of the papers will be easy is _______ (round off to 2 decimal places).

Ques 5 GATE 2023

The maximum value of function f(x) = 4x³ - 24x² + 36 in the domain [-1,5] is _______ (round off to nearest integer).

Ques 6 GATE 2023

A fluid flow field is given by the velocity vector V→ = e^xyz(x î + z k̂). The curl of velocity at (1, 2, 3) is _______.

Ques 7 GATE 2023

Given, φ̅ = xy î + yz ĵ + xz k̂. S is a surface bounded by the planes x = 0, y = 0, z = 0, x = 3, y = 2, and z = 1. If n̂ is the unit vector normal to S, then ∫∫_S φ̅⋅n̂ dS is _______.

Ques 8 GATE 2023

Match the plots in Section I with the corresponding functions in Section II.

Ques 9 GATE 2023

For the equation

Ques 10 GATE 2023

"You are delaying the completion of the task. Send _______ contributions at the earliest."

Ques 11 GATE 2023

References : ______ : : Guidelines : Implement
(By word meaning)

Ques 12 GATE 2023

In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

Ques 13 GATE 2023

In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.
When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads.
He dropped out of college. Based only on the above information, which one of the following statements can be logically inferred with certainty?