GATE CE area:engineering-mathematics PYQs & Answers — Page 9

Questions 81–90 of 174. Imported answers require independent review unless marked reviewed.

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive

-axis are

Your answerChoose one option.

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Consider the polynomial

on the domain

given by

. The first and second derivatives are

and

Consider the following statements:

I. The given polynomial is zero at the boundary points

and

II. There exists one local maxima of

within the domain

III. The second derivative

throughout the domain

IV. There exists one local minima of

within the domain

The correct option is:

Your answerChoose one option.

Only statements I, II and III are correct.

Only statements I, II and IV are correct.

Only statements I and IV are correct.

Only statements II and IV are correct.

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Let

denote the maximum of two real numbers

and

. Which of the following statement(s) is/are TRUE about the function

Your answerSelect all correct options. You can choose more than one.

It is continuous on its domain.

It has a local minimum at

It has a local maximum at

It is differentiable on its domain.

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Let

be a non-zero vector of size

. Which of the following statement(s) is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is a symmetric matrix.

is an eigenvalue of

has a rank of 2022.

is invertible.

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Consider the differential equation

For the initial condition

, the value of

obtained using Euler’s method with a step-size of 0.2 is ________. (round off to one decimal place)

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The concentration

of pollutants in a one-dimensional reservoir at position

and time

satisfies the diffusion equation

on the domain

, where

is the diffusion coefficient of the pollutants. The initial condition

is defined by the step-function shown in the figure.

The boundary conditions of the problem are given by

at the boundary points

and

at all times. Consider

, and

. The steady-state concentration

at the center

of the reservoir (in

) is ________. (in integer)

Diagram for Civil Engineering question 48

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A set of observations of independent variable (

) and the corresponding dependent variable (

) is given below.

	5	2	4	3
	16	10	13	12

Based on the data, the coefficient

of the linear regression model

is estimated as 6.1.

The coefficient

is ______________. (round off to one decimal place)

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A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is ______. (round off to three decimal places)

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At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is ______. (round off to two decimal places)

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Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

Your answerChoose one option.

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GATE CE area:engineering-mathematics PYQs

Question 36

Question 36

Question 45

Question 45

Question 48

Question 48

Question 49

Question 49

Question 63

Question 3