NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 18 - 25 of 231

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Question 18

Appeared in Year: 2015

Write in Short Short Answer▾

Find the Radius of Convergence of the series

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Question 19

Appeared in Year: 2015

Describe in Detail Subjective▾

Let be the polygon in the complex plane with vertices situated at the nth Roots of unity. Let be the area and let be its perimeter. Evaluate

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Explanation

The points represented by nth roots of unity are located at the vertices of a regular polygon of n sides, inscribed in a unit circle having center at the origin, one vertex being on the positive real axis (in figure below)

The Positive Real Axis

But when n approaches to infinity, the n sided polygon will approach to circle of unit radius.

… (13 more equations, 5 figures) …

Question 20

Appeared in Year: 2008

Describe in Detail Subjective▾

Determine if each of the following series is absolutely convergent, conditionally convergent or divergent:

a)

b)

c)

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Explanation

Option (a) The given series is

Here

… (776 more equations) …

Question 21

Appeared in Year: 2005

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Let n be a positive integer. Let and let . For what value of n will f be twice differentiable but its second derivative discontinuous at ?

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Explanation

Let

… (351 more equations) …

Question 22

Appeared in Year: 2007

Question MCQ▾

Let . Which of the following function are analytic in the entire complex plane?

Choices

Choice (4)Response

a.

b.

c.

d.

Question does not provide sufficient data or is vague

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Question 23

Appeared in Year: 2015

Describe in Detail Subjective▾

Find the sum of the following series upto n terms.

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Explanation

Let be the rth term of the given series. Then

… (108 more equations) …

Question 24

Appeared in Year: 2014

Describe in Detail Subjective▾

Let . Evaluate

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Explanation

applying

Applying

… (89 more equations) …

Question 25

Appeared in Year: 2007

Write in Short Short Answer▾

Evaluate:

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