# Real Analysis [GATE (Graduate Aptitude Test in Engineering) Mathematics]: Questions 9 - 16 of 29

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## Question 9

Real Analysis
Riemann Integration

Appeared in Year: 2008

### Question

MCQ▾

For the real values of , the minimum value of the function is

### Choices

Choice (4)Response

a.

0

b.

1

c.

2

d.

0.5

## Question 10

Real Analysis

Appeared in Year: 2005

### Question

MCQ▾

For the function , the maximum occurs when x is equal to

### Choices

Choice (4)Response

a.

-1

b.

0

c.

2

d.

1

## Question 11

Real Analysis

Appeared in Year: 1995

### Question

MCQ▾

The function f (x) = has

### Choices

Choice (4)Response

a.

A maxima at x = 1, but not minima

b.

No maxima, but a minima at x = 3

c.

A maxima at x = 1 and a minima at x = 3

d.

A maxima at x = 3 and a minima at x = 1

## Question 12

Real Analysis

### Question

MCQ▾

In the interval , the function is

### Choices

Choice (4)Response

a.

Maximum at x = 2

b.

Maximum at x = 1

c.

Monotonically decreasing

d.

Maximum at x = 1.5

## Question 13

Real Analysis
Riemann Integration

### Question

MCQ▾

A function is given as

Find the optimal value of f (x, y) .

### Choices

Choice (4)Response

a.

3

b.

10

c.

d.

## Question 14

Real Analysis

MCQ▾

The function

### Choices

Choice (4)Response

a.

Has its maximum value at

b.

Has its maximum value at

c.

Is increasing on the interval

d.

Is increasing on the interval

## Question 15

Real Analysis

Appeared in Year: 2004

### Question

MCQ▾

The function has its maxima at

### Choices

Choice (4)Response

a.

Both

b.

2 only

c.

Only

d.

## Question 16

Real Analysis

Appeared in Year: 2004

### Question

MCQ▾

A point on a curve is said to be an extreme if it is a local minimum or a local maximum. The number of distinct extrema for the curve is

### Choices

Choice (4)Response

a.

2

b.

1

c.

3

d.

0

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