# GATE (Graduate Aptitude Test in Engineering) Mathematics: Questions 26 - 32 of 34

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## Question 26

Riemann Integration

Appeared in Year: 2008

### Question

MCQ▾

Consider a function where x is a real number. Then the function has

### Choices

Choice (4)Response

a.

Three maxima

b.

Only one minimum

c.

Only two minima

d.

Three minima

## Question 27

### Question

MCQ▾

The local maxima or local minima and corresponding maximum or minimum value of the function

### Choices

Choice (4)Response

a.

Local minima at

b.

Local maxima at

c.

Local maxima at

d.

Local minima at

## Question 28

Linear Second Order Ordinary Differential Equations with Variable Coefficients

### Write in Short

The function satisfy the equation The value of ‘t’ is ________.

## Question 29

Riemann Integration

Appeared in Year: 2009

### Question

MCQ▾

The distance between the origin and the point nearest to it on the surface is?

### Choices

Choice (4)Response

a.

0

b.

2

c.

1

d.

4

## Question 30

Appeared in Year: 2004

### Question

MCQ▾

The function has a

### Choices

Choice (4)Response

a.

Maximum at

b.

Minimum at

c.

Maximum at

d.

Minimum at

## Question 31

Riemann Integration

### Question

MCQ▾

The numbers, whose sum is 16 and the sum of whose cubes is minimum, are

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 32

Riemann Integration

Appeared in Year: 2009

### Question

MCQ▾

A cubic polynomial with real coefficients?

### Choices

Choice (4)Response

a.

May have up to three extrema and up to 2 zero crossings

b.

Cannot have more than two extrema and more than three zero crossings

c.

Can possibly no extrema and no zero crossings?

d.

Will always have an equal number of extrema and zero crossings

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