Agricultural Engineering Gate Yearwise 



Agricultural Engineering Gate 2024 Questions with Answer

Ques 1 GATE 2024

If two distinct non-zero real variables x and y are such that (x+y) is proportional to (x-y) then the value of x/y

A

depends on xy

B

depends only on x and not on y

C

depends only on y and not on x

D

is a constant


(d) is the correct answer.

Ques 2 GATE 2024

Consider the following sample of numbers:
9, 18, 11, 14, 15, 17, 10, 69, 11, 13
The median of the sample is

A

13.5

B

14

C

11

D

18.7


(a) is the correct answer.

Ques 3 GATE 2024

The number of coins of ₹1, 25, and 10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in 25 coins is _______.

A

21%

B

14(2/7)%

C

10%

D

30%


(b) is the correct answer.

Ques 4 GATE 2024

For positive non-zero real variables p and q, if log(p² + q²) = log p + log q + 2 log 3, then, the value of (p⁴+q⁴)/(p²q²) is _______.

A

79

B

81

C

9

D

83


(a) is the correct answer.

Ques 5 GATE 2024

A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken.
Then, the ratio of the volume of the cylindrical tube to the volume of the cube is _______.

A

1/π

B

2/π

C

3/π

D

4/π


(a) is the correct answer.

Ques 6 GATE 2024

A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is _______.

A

18

B

24

C

20

D

21


(c) is the correct answer.

Ques 7 GATE 2024

The divergence of the curl of a twice continuously differentiable vector function is _______.

A

0

B

1

C

2

D

8


(a) is the correct answer.

Ques 8 GATE 2024

Laplace transform of a function f(t) = t⁴ as a function of 's' is _______.

A

120/s⁵

B

24/s⁵

C

120/s⁴

D

24/s⁴


(a) is the correct answer.

Ques 9 GATE 2024

A continuously differentiable function y = f(x) satisfies one or more of the following conditions at its point of inflection:

A

d²y/dx² ≠ 0

B

d²y/dx² = 0

C

d³y/dx³ = 0

D

d³y/dx³ ≠ 0


(b, d) is the correct answer.

Ques 10 GATE 2024

The mean and variance of a dataset are 16 and 25, respectively. The coefficient of variation of the dataset, in %, is _______. (Rounded off to 2 decimal places)


(31.25) is the correct answer.

Ques 11 GATE 2024

The chances for passing an endurance test for three threshers P, Q and R are 1/6, 1/4 and 1/2, respectively. The probability of passing the endurance test by at least one thresher, in fraction, is _______. (Rounded off to 2 decimal places)


(0.58) is the correct answer.

Ques 12 GATE 2024

are two matrices. The matrix [P]T[Q] is

A

B

C

D


(b) is the correct answer.

Ques 13 GATE 2024

The complete solution for the differential equation d²y/dx² + 2dy/dx - 3y = 0 for y(0) = 0 and dy/dx(0) = 8 is _______.

A

2(ex - e3x)

B

2(ex - e⁻³x)

C

2(e⁻³x - ex)

D

2(ex + e⁻³x)


(b) is the correct answer.

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