Chemical Engineering Gate 2024 Questions with Answer

Ques 27 GATE 2024

During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Earth-Moon distances is closest to

Ques 28 GATE 2024

The first non-zero term in the Taylor series expansion of (1 − x) − e^−x about x = 0 is

Ques 29 GATE 2024

Consider the normal probability distribution function f(x) = 4 / √(2π) e^−8(x+3)2 If μ and σ are the mean and standard deviation of f(x) respectively, then the ordered pair (μ, σ) is

Ques 30 GATE 2024

If z₁ = −1 + i and z₂ = 2i, where i = √(−1), then Arg(z₁ / z₂) is

Ques 31 GATE 2024

Consider a linear homogeneous system of equations Ax = 0, where A is an 𝑛 × 𝑛 matrix, x is an 𝑛 × 1 vector and 0 is an 𝑛 × 1 null vector. Let 𝑟 be the rank of A. For a non-trivial solution to exist, which of the following conditions is/are satisfied?

Ques 32 GATE 2024

Consider a matrix A = [
−5   a
−2   −2
], where a is a constant. If the eigenvalues of A are −1 and −6, then the value of a, rounded off to the nearest integer, is ___________

Ques 33 GATE 2024

Let 𝑟 and 𝜃 be the polar coordinates defined by 𝑥 = 𝑟 𝑐𝑜𝑠 𝜃 and 𝑦 = 𝑟 𝑠𝑖𝑛 𝜃. The area of the cardioid 𝑟 = 𝑎 (1 − 𝑐𝑜𝑠 𝜃),0≤𝜃≤2𝜋, is

Ques 34 GATE 2024

Consider the line integral ∫_C F(r) · dr, with F(r) = x î + y ĵ + z &kcirc;, where î, ĵ, and &kcirc; are unit vectors in the (x, y, z) Cartesian coordinate system.
The path C is given by r(t) = cos(t) î + sin(t) ĵ + t &kcirc;, where 0 ≤ t ≤ π.
The value of the integral, rounded off to 2 decimal places, is _________

Ques 35 GATE 2024

Consider the ordinary differential equation x² (d²y / dx²) − x (dy / dx) − 3y = 0,
with the boundary conditions y(x = 1) = 2 and y(x = 2) = 17/2.
The solution y(x) at x = 3/2, rounded off to 2 decimal places, is ___________

Ques 36 GATE 2024

Consider the function 𝑓(𝑥,𝑦,𝑧)=𝑥⁴+2 𝑦³+𝑧². The directional derivative of the function at the point 𝑃 (−1,1,−1) along (𝒊̂+𝒋̂), where 𝒊̂ and 𝒋̂ are unit vectors in the x and y directions, respectively, rounded off to 2 decimal places, is _______

Ques 37 GATE 2024

Consider the process in the figure for manufacturing B.
The feed to the process is 90 mol% A and a close-boiling inert component I.
At a particular steady-state:
• B product rate is 100 kmol h⁻¹
• Single-pass conversion of A in the reactor is 50%
• Recycle-to-purge stream flow ratio is 10
The flow rate of A in the purge stream, in kmol h⁻¹, rounded off to 1 decimal place, is _____

Ques 38 GATE 2024

An infinitely long cylindrical water filament of radius R is surrounded by air. Assume water and air to be static. The pressure outside the filament is P_out and the pressure inside is P_in. If γ is the surface tension of the water-air interface, then P_in − P_out is

Ques 39 GATE 2024

The velocity field in an incompressible flow is v = αxy î + v_y ĵ + β k̂, where î, ĵ and k̂ are unit-vectors in the (x, y, z) Cartesian coordinate system. Given that α and β are constants, and v_y = 0 at y = 0, the correct expression for v_y is