Engineering Mathematics [GATE (Graduate Aptitude Test in Engineering) Electronics]: Questions 7 - 11 of 71

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Question 7

Engineering Mathematics
Divergence and Curl, Gauss's, Green's and Stoke's Theorems

Appeared in Year: 2019

Question

MCQ▾

Consider the line integral

The integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region shown in the figure below. The region R is the area enclosed by the union of a rectangle and a semi-circle of radius . The line integral evaluates to

Counterclockwise Direction

Choices

Choice (4)Response

a.

b.

c.

d.

Question 8

Engineering Mathematics
Linear Dependence and Independence

Appeared in Year: 2010

Question

MCQ▾

Given f (t) = L-1 . If , then the value of k is

Choices

Choice (4)Response

a.

3

b.

4

c.

1

d.

2

Question 9

Engineering Mathematics
First Order Equations

Appeared in Year: 2019

Question

MCQ▾

The families of curves represented by the solution of the equation

For n = – 1 and n =+ 1, respectively, are

(Carry One Mark Each)

Choices

Choice (4)Response

a.

Hyperbolas and Parabolas

b.

Parabolas and Circles

c.

Circles and Hyperbolas

d.

Hyperbolas and Circles

Question 10

Engineering Mathematics
Eigen Values and Eigen Vectors

Appeared in Year: 2010

Question

MCQ▾

The Eigen values of a skew-symmetric matrix are (One Mark)

Choices

Choice (4)Response

a.

Always pure imaginary

b.

Either zero or pure imaginary

c.

Always zero

d.

Always real

Question 11

Engineering Mathematics
Mean Value Theorems

Appeared in Year: 2015

Question

MCQ▾

A function is defined in the closed interval . The value of x, in the open interval for which the mean value theorem is satisfied, is

Choices

Choice (4)Response

a.

b.

c.

d.

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