# NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 68 - 79 of 101

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## Question number: 68

» Definite Integral as Limit of a Sum

Appeared in Year: 2007

### Describe in Detail

Evaluate

### Explanation

… (36 more words) …

## Question number: 69

» Limits

Appeared in Year: 2005

### Write in Short

Evaluate:

## Question number: 70

» Cauchy 2nd Theorem on Limits

Appeared in Year: 2017

### Describe in Detail

Evaluate

### Explanation

Let us consider the sequence as follows

…………eq. (1)

… (273 more words) …

## Question number: 71

» Leibniz Rule for Differentiation under Integral Sign

Appeared in Year: 2005

### Write in Short

Differentiate

## Question number: 72

» Taylor Series Expansion (Complex)

Appeared in Year: 2009

### Describe in Detail

Write down the coefficient of in the Taylor series expansion of the function about the origin.

### Explanation

Taylor series expansion about the origin is given by

Now coefficient of is

… (638 more words) …

## Question number: 73

» Square Root of a Complex Plane

Appeared in Year: 2012

### Describe in Detail

Find all the square Roots of the complex number .

### Explanation

The square roots of are

And

Here let

Comparing

The square roots of are

Thus all

… (13 more words) …

## Question number: 74

» Definite Integral as Limit of a Sum

Appeared in Year: 2015

### Write in Short

Evaluate

## Question number: 75

Appeared in Year: 2015

### Describe in Detail

Let . Evaluate the determinant

### Explanation

Let

Applying , then

Taking common from , we get

Applying

… (69 more words) …

## Question number: 76

» Definite Integral as Limit of a Sum

Appeared in Year: 2005

### Describe in Detail

Evaluate

### Explanation

………. eq. (A)

Replace by by the sign of .

Lower limit

Upper limit

becomes

… (88 more words) …

## Question number: 77

Appeared in Year: 2015

### Describe in Detail

Evaluate

### Explanation

This is exponential form form

Using the result

If

Then

… (36 more words) …

## Question number: 78

Appeared in Year: 2011

### Describe in Detail

Find the cube Roots of

### Explanation

Let

… (288 more words) …

## Question number: 79

» Differentiability in Complex Plane

Appeared in Year: 2007

### Question

Which of the following function are differentiable at ?

### Choices

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

a. |
| |

b. |
| |

c. |
| |

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