Agricultural Engineering Gate 2020 Questions with Answer

Ques 1 GATE 2020

The function f(x) = x² - 4x³ + 6x² - 4x + 1 has a

Ques 2 GATE 2020

A linear system of equations has n unknowns. The ranks of the coefficient matrix and the augmented matrix of the linear system of equations are r₁ and r₂, respectively. The condition for the equations to be consistent with a unique solution is

Ques 3 GATE 2020

General solution to the ordinary differential equation,
d³y/dx³ + 6 d²y/dx² + 11 dy/dx + 6 y = 0 is

Ques 4 GATE 2020

If one of the two Eigenvalues of a matrix [3 2; 2 1] is 4.236, then the other Eigenvalue (round off to 3 decimal places) is _______.

Ques 5 GATE 2020

lim_x→0 (e^x - e^-x - 2x) / (x - sin x) is _______.

Ques 6 GATE 2020

A particle moves along the curve R = (2t³ + 4t²) i + (3t² - 5t) j + (7t² + 6t) k, where t is the time. The velocity component of the particle in the direction 3i + 2j + k at time t = 2 is

Ques 7 GATE 2020

Let a function f(t) = 4 cos 2t + 6 e^-8t. The Laplace transform of the given function f(t), L{f(t)} = F(s) = ∫₀^∞ f(t) e^{-s t} dt is

Ques 8 GATE 2020

Taking six intervals, each of π/12 and using Simpson's one-third rule, the value of the definite integral ∫₀^π √cos θ dθ (round off to 3 decimal places) is _______.

Ques 9 GATE 2020

Two playing cards are drawn at random, but in succession from a pack of red cards (26 in number) without replacement. The probability of drawing a king first, followed by drawing a queen is P×10⁻³. The value of P (round off to 3 decimal places) is _______.

Ques 10 GATE 2020

In a tractor steering system, the angle made by the kingpin axis projected on the longitudinal plane of the tractor with the vertical axis is known as

Ques 11 GATE 2020

A tractor operated 9-row precision planter has 16 cells on the metering plates. The speed ratio of the metering plates to the ground drive wheel is 1:2 and the rolling diameter of the ground drive wheel is 40 cm. Assuming no skid, the plant to plant spacing in rows in mm is

Ques 12 GATE 2020

A towed pneumatic wheel with an unloaded radius of 330 mm covers a distance of 9.9 m in 5 revolutions without any skid. Assuming the rolling radius to be same as the static loaded radius of the wheel, the deflection of the wheel in mm (round off to 1 decimal place) is _______.

Ques 13 GATE 2020

The grain to straw ratio of 500 kg feed material is 3:2. The blown grain loss, separation loss and cleaning efficiency of the thresher are 0.05%, 0.5% and 99.1%, respectively. Considering 100% threshing efficiency, grain recovery at the main grain outlet in kg (round off to 2 decimal places) is _______.