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

Home
GATE
Chemical Engineering
Topics
area:engineering-mathematics

Questions 21–30 of 93. Imported answers require independent review unless marked reviewed.

Topic practice 93 questionsPage 3 of 10

Consider a linear homogeneous system of equations

, where

is an

matrix,

is an

vector and

is an

null vector. Let

be the rank of A. For a non-trivial solution to exist, which of the following conditions are/is satisfied?

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

Determinant of A = 0

Determinant of A ≠ 0

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

Consider a matrix

, where

is a constant. If the eigenvalues of

are

and

, then the value of

, rounded off to the nearest integer, is __________

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

Let

and

be the polar coordinates defined by

and

. The area of the cardioid

, is

Diagram for Chemical Engineering question 47

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

The Newton-Raphson method is used to solve

, where

. If the initial guess

, the value of the next iterate,

, rounded off to 2 decimal places, is ______

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

Consider the line integral

, with

, where

and

are unit vectors in the

Cartesian coordinate system. The path C is given by

, where

. The value of the integral, rounded off to 2 decimal places, is ________

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

Consider the ordinary differential equation

, with the boundary conditions

and

. The solution

, rounded off to 2 decimal places, is ________

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

Consider the function

. The directional derivative of the function at the point

along

, where

and

are unit vectors in the x and y directions, respectively, rounded off to 2 decimal places, is ______

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

Which one of the following is the CORRECT value of

, as defined by the expression given below?

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

The vector

is defined as

Which one of the following is the CORRECT value of divergence of

, evaluated at the point

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 that

where

and

with

, which one of the following options is CORRECT?

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

GATE CH area:engineering-mathematics PYQs

Question 26

Question 30

Question 47

Question 50

Question 51

Question 52

Question 53

Question 11

Question 12

Question 13