# 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

### 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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