GATE IN area:engineering-mathematics PYQs & Answers — Page 6

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Questions 51–60 of 73. Imported answers require independent review unless marked reviewed.

Topic practice 73 questionsPage 6 of 8

The unit vectors along the mutually perpendicular

and

axes are

and

respectively. Consider the plane

and two vectors

and

on that plane such that

for any scalar

. A vector perpendicular to both

and

is ____.

Your answerChoose one option.

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Consider the recursive equation

, with initial condition

and

being a very small valued scalar. This recursion numerically solves the ordinary differential equation _____.

Your answerChoose one option.

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A set of linear equations is given in the form

, where

is a

matrix with real number entries and

. Will it be possible to solve for

and obtain a unique solution by multiplying both left and right sides of the equation by

(the super script

denotes the transpose) and inverting the matrix

? Answer is ____.

Your answerChoose one option.

Yes, it is always possible to get a unique solution for any

matrix $A.

No, it is not possible to get a unique solution for any

matrix $A.

Yes, can obtain a unique solution provided the matrix

is well conditioned

Yes, can obtain a unique solution provided the matrix

is well conditioned

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Let

. The value of the integral

over a circle

with center

and radius

evaluated in the anti-clockwise direction is ____.

Your answerChoose one option.

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Consider the matrix

. One of the eigenvectors of

Your answerChoose one option.

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Consider the differential equation

, with the initial condition

. The solution to this ordinary differential equation is ____

Your answerChoose one option.

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Consider the function

. The minimum value the function attains on the line

(rounded off to one decimal place) is ____

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are three orthogonal vectors. Given that

and

, the vector

is parallel to

Your answerChoose one option.

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A 3 × 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is ______.

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The curve

is such that the tangent to the curve at every point

has a Y-axis intercept

, given by

. Then,

is proportional to

Your answerChoose one option.

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GATE IN area:engineering-mathematics PYQs

Question 1

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Question 15

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Question 27

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Question 1

Question 16

Question 26