Metallurgical Engineering Gate Yearwise 



Metallurgical Engineering Gate 2024 Questions with Answer

Ques 1 GATE 2024

If X1 and X2 are independent normally distributed random variables with means μ1 and μ2, and variances ρ1 and ρ2, respectively, then the combination X = X1 + X2 has mean μ and variance ρ such that _______.

A

μ = μ1 + μ2 and ρ = ρ1 + ρ2

B

μ2 = μ12 + μ22 and ρ = ρ1 + ρ2

C

μ = μ1 + μ2 and ρ2 = ρ12 + ρ22

D

μ2 = μ12 + μ22 and ρ2 = ρ12 + ρ22



Ques 2 GATE 2024

Which one of the following represents the first three terms of the Taylor series of ln(1+x/1-x) about the origin for |x| < 1?

A

x - x2/2 + x3/3

B

x + x2/2 + x3/3 +...

C

x + x3/3 + x5/5 +...

D

2(x + x3/3 + x5/5 +...)



Ques 3 GATE 2024

Consider the normal (Gaussian) distributions a, b, c shown in the figure.

σp and μp are the standard deviation and mean of a distribution p, respectively, and the means are positive. Which one of the following deductions is correct?

A

σa < σb < σc

B

σa > σb > σc

C

μa = μb = μc

D

μa > μb > μc



Ques 4 GATE 2024

Which of the following statements is/are correct for a square matrix A with real number entries?
AT denotes the transpose of A and A-1 denotes the inverse of A.

A

A is symmetric if AT = -A.

B

A is skew-symmetric if AT = -A.

C

If A is orthogonal, then AT = A-1.

D

If A is orthogonal, then its determinant is zero.



Ques 5 GATE 2024

The divergence of the vector field
V→ = x2y î + y3z ĵ + z4 k̂
at the point (1,1,1) is _______. (Round off to the nearest integer)


7 is the correct answer.


Ques 6 GATE 2024

where x, y are not identically zero, then the values of λ are _______.

A

5,-3

B

4,-4

C

3,-5

D

5,-4



Ques 7 GATE 2024

If dy/dx = 4xy, y(0) = 1, then _______.

A

y = 2x2+1

B

y = 2e2x2 - 1

C

y = 2ex2 - 1

D

y = e2x2



Ques 8 GATE 2024

The following data is obtained from an experiment:

If the data is fit using the straight line
y = mx + c (where m and c are constants)
using the least-squares method, then the value of m is _______. (Round off to one decimal place).


5.2 is the correct answer.


Ques 9 GATE 2024

The integral ∫01xe-xdx evaluates to _______. (Round off to two decimal places)


0.26 is the correct answer.


Ques 10 GATE 2024

If '→' denotes increasing order of intensity, then the meaning of the words [dry → arid → parched] is analogous to [diet → fast → _______]. Which one of the given options is appropriate to fill the blank?

A

starve

B

reject

C

feast

D

deny



Ques 11 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 is _______.

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



Ques 12 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



Ques 13 GATE 2024

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

A

14 2/7 %

B

15 %

C

30 %

D

40 %



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