Mining Engineering Gate Yearwise 


Mining Engineering Gate 2023 Questions with Answer

Ques 1 GATE 2023

In how many ways can cells in a 3x3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.

A

2

B

9

C

3

D

6



Ques 2 GATE 2023

There are 4 red, 5 green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the smallest value of N that guarantees there will be at least two balls of the same colour?
One cannot see the colour of the balls until they are picked.

A

4

B

15

C

5

D

2



Ques 3 GATE 2023

Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?

A

16

B

4

C

120

D

720



Ques 4 GATE 2023

If x satisfies the equation 48x=256, then x is equal to

A

1/2

B

log168

C

2/3

D

log48



Ques 5 GATE 2023

Given two vectors 𝑨 βƒ—βƒ— =3π’Š+2𝒋 and 𝑩 βƒ—βƒ— =π’Š+𝒋, the magnitude of projection of 𝑨 βƒ—βƒ— along 𝑩 βƒ—βƒ— is

A

5/√2

B

5/√13

C

5/√26

D

5



Ques 6 GATE 2023

Given two random variables X and Y, the expected value E(3X-5Y) is

A

3E(X)-5E(Y)

B

3E(X)+5E(Y)

C

3E(X)-5E(Y)-15E(XY)

D

E(X)-E(Y)-E(XY)



Ques 7 GATE 2023

A linear programming problem is given as:
Maximize Z=4x1+2x2
Subject to:
2x1-2x2≤20
4x1≤80
x1≥0, x2≥0
The problem has

A

Unbounded solution.

B

Infeasible solution.

C

Multiple optimal solutions.

D

Unique optimal solution.



Ques 8 GATE 2023

x and y are functions of independent variables r and as given below
x=r cos θ, y=r sin θ
The Jacobian of x, y is

A

tan θ

B

r2sin θ cos θ

C

r2

D

r



Ques 9 GATE 2023

Matrix A is negative definite. Which one of the following is NOT the correct statement about the matrix?

A

It is symmetric.

B

Determinant of A is always less than zero.

C

All the eigen values are less than zero.

D

Trace of A is always less than zero.



Ques 10 GATE 2023

The evaluation of the integral

A

ln(ex+xe)

B

1/e ln(ex-χe)

C

1/e ln(ex+xe)

D

ln(ex-xe)



Ques 11 GATE 2023

Given the function f(x)=|x|+|x-1|,
For all the real values of x, which one of the following statements is CORRECT?

A

The function is continuous and not differentiable at one point.

B

The function is continuous but not differentiable at two points.

C

The function is discontinuous.

D

The function is continuous and differentiable.



Ques 12 GATE 2023

The slope and intercept values of three linear equations are

The above system of equations has

A

Trivial solution.

B

A single solution.

C

Multiple solutions.

D

No Solution.



Ques 13 GATE 2023

A regression line is constructed between shovel production rate and shovel swing angle for 50 observations as shown below.

t-values corresponding to level of significance (P) and degree of freedom (DF)
If residuals are normally distributed and significance tests of the parameters are conducted at 0.05 significance level, the true statement is

A

Both intercept and slope are significant.

B

Intercept is significant but slope is not significant.

C

Intercept is not significant but slope is significant.

D

Both intercept and slope are not significant.



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