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

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Appeared in Year: 2007

Essay Question▾

Describe in Detail

Evaluate

Explanation

… (36 more words) …

Question number: 69

» Limits

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Appeared in Year: 2005

Short Answer Question▾

Write in Short

Evaluate:

Question number: 70

» Cauchy 2nd Theorem on Limits

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Appeared in Year: 2017

Essay Question▾

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

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Appeared in Year: 2005

Short Answer Question▾

Write in Short

Differentiate

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

… (638 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

The square roots of are

Thus all

… (13 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 common from , we get

Applying

… (69 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 limit

Upper limit

becomes

… (88 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

… (36 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

… (288 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

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