Agricultural Engineering Gate Yearwise 



Agricultural Engineering Gate 2026 Questions with Answer

Ques 1 GATE 2026

Identify the following partial differential equations in the given order based on their generic form where c is a constant, and u1 and u2 are functions of (x,t) and (x,y), respectively:
(i) ∂²u1/∂t² = c² ∂²u1/∂x²
(ii) ∂u1/∂t = c² ∂²u1/∂x²
(iii) ∂²u2/∂x² + ∂²u2/∂y² = 0

A

(i) Wave equation (ii) Heat equation (iii) Laplace equation

B

(i) Heat equation (ii) Laplace equation (iii) Wave equation

C

(i) Laplace equation (ii) Wave equation (iii) Heat equation

D

(i) Heat equation (ii) Wave equation (iii) Laplace equation


(a) is the correct answer.

Ques 2 GATE 2026

A box contains one red ball and two blue balls. One ball is drawn at random, its colour is noted and the ball is returned to the box. The process is repeated. In the first two draws, blue ball appears each time. The probability of drawing blue ball again in the third draw is

A

2/3

B

1/3

C

1/2

D

1


(b) is the correct answer.

Ques 3 GATE 2026

The general solution to the ordinary differential equation d²y/dx² = cos 2x is

A

y = −(cos 2x)/4 + C1x + C2, where C1 and C2 are constants

B

y = (sin 2x)/2 + C1, where C1 is a constant

C

y = (cos 2x)/4 + C1x + C2, where C1 and C2 are constants

D

y = −(sin 2x)/2 + C1, where C1 is a constant


(a) is the correct answer.

Ques 4 GATE 2026

Two square matrices A and B of the same order are such that, det[A · B] = −80 and det[A] = 5. Here, A · B is the product of A and B. The value of det[BT] is

A

−16

B

−1/16

C

−400

D

28


(a) is the correct answer.

Ques 5 GATE 2026

Consider the simultaneous equations
2x + 4y = −7; 3x + 5y = 1
While solving using Gauss elimination without pivoting, after the forward elimination, the diagonal elements of the coefficient matrix are

A

2 and −1

B

3 and 2

C

5 and −2

D

3 and 4


(c) is the correct answer.

Ques 6 GATE 2026

The value of the integral I = ∫₀¹ ∫₀¹ x cos(xy) dxdy is

A

1 − cos(1)

B

1 + cos(1)

C

1 − sin(1)

D

1 + sin(1)


(c) is the correct answer.

Ques 7 GATE 2026

The determinant of a 2 × 2 square matrix is 1.6. If the sum of the eigen values is −2.8, the eigen values are

A

−2 and −0.8

B

−1.8 and −1

C

−3 and 0.2

D

−1.2 and −1.6


(a) is the correct answer.

Ques 8 GATE 2026

The following two vectors are adjacent sides of a parallelogram:
A⃗ = 2î + 3ĵ − k̂ and B⃗ = 5î − 4k̂
The magnitude of area of the parallelogram is ________ (Rounded off to two decimal places)


(18.79) is the correct answer.

Ques 9 GATE 2026

While solving an equation e−x − x = 0 for x, using Newton-Raphson method with initial guess x0 = 2, the solution after first iteration (x1) is ________ (Rounded off to two decimal places)


(1.48) is the correct answer.

Ques 10 GATE 2026

A plough attachment, which is a miniature plough bottom that cuts a narrow, shallow furrow ahead of the shin and moves trash and roots toward the main furrow so that they are completely covered by the mouldboard, is called as

A

Jointer

B

Coulter

C

Subsoiler

D

Weed hook


(a) is the correct answer.

Ques 11 GATE 2026

A flat belt of negligible mass and thickness drives an output pulley of 0.6 m diameter, constantly rotating at 500 rpm without slip. The arc of contact is 190° for this pulley, while it is 170° for the smaller input pulley. The coefficient of friction between the belt and pulleys is 0.30. The measured slack-side tension is 250 N. Neglecting other losses, the power transmitted by the belt drive, in kW, is nearest to
(Take π = 3.14)

A

4.8

B

5.6

C

6.5

D

7.3


(c) is the correct answer.

Ques 12 GATE 2026

A tractor PTO runs at a constant speed of 540 rpm to drive a rotary tiller via flange coupling having a shear pin parallel to the shaft. The shear pin axis is located at 60 mm from the PTO shaft axis. The allowable shear stress of the pin material is 200 MPa. For overload safety, it must fail at 150% of the rated torque to protect the gearbox. The tiller requires 40 kW under normal load at rated PTO speed. Neglecting bending, stress concentration effects, and other losses, the pin diameter, in mm, is nearest to
(Take π = 3.14)

A

7.5

B

10.6

C

6.1

D

8.6


(a) is the correct answer.

Ques 13 GATE 2026

A tractor-mounted boom sprayer carries a horizontal row of 12 identical flat-fan nozzles (spray angle 110°). To achieve uniform coverage, the required lateral overlap between adjacent nozzle footprints at the target plane is 30% of single nozzle footprint. Boom height is 0.60 m above the target plane.
The tractor is set to travel at a theoretical forward speed of 8 km.h−1. Wheel slip is 8% and the field efficiency is 75%. All other losses are neglected. The total time (in minutes) required to spray 25 ha field is ________. (Rounded off to the nearest integer)


(138) is the correct answer.

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