GATE MN area:engineering-mathematics PYQs & Answers — Page 3

Questions 21–30 of 89. Imported answers require independent review unless marked reviewed.

Vectors

and

represent the two adjacent sides of a triangle. The magnitude of the area of the triangle and the unit vector perpendicular to both a and b respectively, are

Your answerChoose one option.

28.93 and 0.58i − 0.76j − 0.27k

28.93 and 17.0i − 22.0j − 8.0k

14.46 and 0.58i − 0.76j − 0.27k

14.46 and 17.0i − 22.0j − 8.0k

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A thermal power plant has an agreement with three mines M1, M2 and M3 to receive ‘Grade 1’ coal, in the proportion of 60%, 25% and 15%, respectively. The probabilities that a wagon supplied coal to the plant containing below ‘Grade 1’ from mines M1, M2 and M3 are 0.02, 0.03 and 0.04, respectively. On a random check, a sample wagon is found to carry below ‘Grade 1’ coal. The probability that the wagon belongs to mine M1, is _____. (round off up to 2 decimals)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The root of the function,

in the interval [0, 1] using bisection method after two iterations, is _____. (round off up to 2 decimals)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

Your answerChoose one option.

3E(X) − 5E(Y)

3E(X)+5E(Y)

3E(X) − 5E(Y) − 15E(XY)

E(X) − E(Y) − E(XY)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

x and y are functions of independent variables

and

as given below

The Jacobian of x, y is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

Your answerChoose one option.

It is symmetric.

Determinant of A is always less than zero.

All the eigen values are less than zero.

Trace of A is always less than zero.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The evaluation of the integral

yields

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Given the function

For all the real values of x, which one of the following statements is CORRECT ?

Your answerChoose one option.

The function is continuous and not differentiable at one point.

The function is continuous but not differentiable at two points.

The function is discontinuous.

The function is continuous and differentiable.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The slope and intercept values of three linear equations are

Equation no.	Slope	Intercept
1	2.0	3.0
2	4.0	5.0
3	6.0	2.0

The above system of equations has

Your answerChoose one option.

Trivial solution.

A single solution.

Multiple solutions.

No Solution.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

	Estimated parameter	Standard error
Intercept	29.6	13.45
Slope	2.5	1.32

t-values corresponding to level of significance (P) and degree of freedom (DF)

DF	one-tail 0.1	0.05	0.025	0.01	0.005	0.001	0.0005
30	1.31	1.697	2.042	2.457	2.75	3.385	3.646
60	1.296	1.671	2	2.39	2.66	3.232	3.46

If residuals are normally distributed and significance tests of the parameters are conducted at 0.05 significance level, the true statement is ____

Your answerChoose one option.

Both intercept and slope are significant.

Intercept is significant but slope is not significant.

Intercept is not significant but slope is significant.

Both intercept and slope are not significant.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE MN area:engineering-mathematics PYQs

Question 43

Question 45

Question 52

Question 16

Question 21

Question 27

Question 39

Question 40

Question 41

Question 42