Chemical Engineering Gate 2026 Questions with Answer

Ques 14 GATE 2026

Which one of the following is the value of lim_x→0 (e^x−x−1)/(cos x−1)?

Ques 15 GATE 2026

Which one of the following is the pair of eigenvalues of the matrix [[−3,4],[4,3]]?

Ques 16 GATE 2026

An experiment is performed by rolling an unbiased die once. Events A and B are defined as follows:
Event A: The outcome of the rolled die is a prime number.
Event B: The outcome of the rolled die is an odd number less than 4.
The conditional probability of A given B, denoted by P(A|B), is ______ (rounded off to one decimal place).

Ques 17 GATE 2026

Using single step trapezoidal rule, the value of ∫₀^0.5 (1 + 16x − 20x²) dx is ______ (rounded off to two decimal places).

Ques 18 GATE 2026

Consider the following complex numbers
z₁ = r₁(cos θ₁ + i sin θ₁)
z₂ = r₂(cos θ₂ + i sin θ₂)
where r₁, r₂ are real numbers, 0 ≤ θ₁ ≤ π/2, 0 ≤ θ₂ ≤ π/2, and i = √−1
If |z₁ + z₂| = |z₁| + |z₂|, which one of the following conditions is necessarily CORRECT?

Ques 19 GATE 2026

Consider the following curve in polar coordinates.
r = 2 − 2 sin θ
Which one of the following is the area enclosed by the curve for 0 ≤ θ ≤ 2π?

Ques 20 GATE 2026

When a cylindrical capillary glass tube, open at both ends, is vertically inserted in a pool of water, the water level in the tube rises to 7 cm relative to the water level outside the tube. Consider that the surface tension of water is 0.07 N m⁻¹ and that the contact angle of water on glass is 0°. The density of water is 1000 kg m⁻³, and the local acceleration due to gravity is 10 m s⁻². The diameter of the capillary tube (in µm) is __________ (rounded off to the nearest integer).

Ques 21 GATE 2026

Consider a two-dimensional, steady, laminar flow of an incompressible fluid with zero pressure gradient, over a thin horizontal flat plate of length 2 m. The free stream velocity is 1 m s⁻¹. A boundary layer thickness of 1 mm is observed at a distance of 0.25 m from the leading edge of the plate. At 1 m from the leading edge, the boundary layer thickness (in mm) is _________ (rounded off to the nearest integer).

Ques 22 GATE 2026

The velocity profile for a fully developed laminar flow of an incompressible Newtonian fluid, at steady state, through a horizontal infinitely wide and long slit of gap 0.01 m is given by the following equation.
u(y) = 7.5 − 3 × 10⁵y²
where y is the vertical distance measured from the center of the slit. The average velocity of the fluid (in m s⁻¹) is ____________ (rounded off to the nearest integer).

Ques 23 GATE 2026

In which of the following condition(s), Bernoulli's equation is applicable?

Ques 24 GATE 2026

Water is discharged from vertical side of a tank through a circular orifice of diameter 2 cm under laminar flow conditions. The water surface in the tank is maintained at constant level above the center of the orifice. If the fluid jet has a diameter of 1.6 cm at its vena contracta, then the coefficient of contraction is ________________ (rounded off to two decimal places).

Ques 25 GATE 2026

Consider a flow with the following velocity field
V⃗ = (x + y)î + (y + z)ĵ + (z + x)k̂
where î, ĵ and k̂ are the unit vectors in the x, y and z directions, respectively. Which one of the following is CORRECT?

Ques 26 GATE 2026

"He often _____ the numbers. False claims are not going to help. Honesty _____ trust", said the manager. Choose the option with the correct order of words to fill the blanks.