# NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 35 - 43 of 101

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## Question number: 35

Appeared in Year: 2012

### Question

Let be a sequence of functions defined on . Determine . For each the following.

### Choices

Choice (4) | Response | |
---|---|---|

a. |
| |

b. |
| |

c. |
| |

d. | All a. , b. and c. are correct |

## Question number: 36

Appeared in Year: 2013

### Describe in Detail

Find the area of the polygon whose vertices are represented in the complex plane by the eighth roots of unity.

### Explanation

In triangle OAB

area of triangle

Area of polygon whose vertices are represented in the complex plane by the eighth roots of unity

… (15 more words) …

## Question number: 37

Appeared in Year: 2011

### Describe in Detail

Evaluate

### Explanation

And

This is exponential form

Using the Result:

If

Then

Now

… (141 more words) …

## Question number: 38

Appeared in Year: 2007

### Describe in Detail

Find the Minimum value of the function:

### Explanation

Here

**Step I:**

**Step II:** Let us solve

i. e

and

we get

is the only critical point

**Step III:**

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## Question number: 39

Appeared in Year: 2005

### Describe in Detail

Let denote the seventh roots of unity. Evaluate

### Explanation

Let x be nth root of unity. Then

(Where k is an integer)

Let . Then nth roots of unity

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## Question number: 40

Appeared in Year: 2006

### Describe in Detail

What is the relation between the height and radius of a right circular cylinder of fixed volume and Minimal Total surface area?

### Explanation

Here given that is the radius of the base of right circular cylinder and its height. is the volume and Let be the total surface area.

Also

Now

… (92 more words) …

## Question number: 41

Appeared in Year: 2012

### Describe in Detail

Find the area of the pentagon whose vertices are the fifth root of unity in the complex plane.

### Explanation

To find fifth root of unity.

Let

Putting we get

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## Question number: 42

Appeared in Year: 2015

### Describe in Detail

Does the integral exist? If it exists give its value.

### Explanation

Yes, its value is…

Note that is not defined for . Here we can write;

(Integration by parts)

………eq. (A)

Now

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## Question number: 43

» Convergence of Positive Series Test

Appeared in Year: 2014

### Describe in Detail

Which of the following series are convergent?

a)

b)

c) , Where

### Explanation

Option (a) The given series is where

Take

Which is finite and non –zero

By comparison test

behave alike

But is divergent by p –test

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