NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 72 - 80 of 101

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Question number: 72

» Taylor Series Expansion (Complex)

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Appeared in Year: 2009

Essay Question▾

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

… (104 more words) …

Question number: 73

» Square Root of a Complex Plane

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

Find all the square Roots of the complex number .

Explanation

The square roots of are

And

Here let

Comparing

… (92 more words) …

Question number: 74

» Definite Integral as Limit of a Sum

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Appeared in Year: 2015

Short Answer Question▾

Write in Short

Evaluate

Question number: 75

» Determinant

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let . Evaluate the determinant

Explanation

Let

Applying , then

Taking

… (99 more words) …

Question number: 76

» Definite Integral as Limit of a Sum

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Appeared in Year: 2005

Essay Question▾

Describe in Detail

Evaluate

Explanation

………. eq. (A)

Replace by by the sign of .

Lower lim

… (92 more words) …

Question number: 77

» Indeterminate Forms

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

Evaluate

Explanation

This is exponential form form

Using the result

If

Then

… (121 more words) …

Question number: 78

» Nth Roots of Unity

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Appeared in Year: 2011

Essay Question▾

Describe in Detail

Find the cube Roots of

Explanation

Let

… (144 more words) …

Question number: 79

» Differentiability in Complex Plane

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Appeared in Year: 2007

MCQ▾

Question

Which of the following function are differentiable at ?

Choices

Choice (4) Response

a.

b.

c.

d.

All a. , b. and c. are correct

Question number: 80

» Definite Integral

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Appeared in Year: 2014

MCQ▾

Question

Which of the following statements are true?

Choices

Choice (4) Response

a.

If , then is rational when n is even

b.

If , then is rational when n is odd

c.

If , then is Irrational when n is even

d.

Question does not provide sufficient data or is vague