NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 18 - 25 of 101

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Question number: 18

» Radius of Convergence

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Appeared in Year: 2015

Short Answer Question▾

Write in Short

Find the Radius of Convergence of the series

Question number: 19

» Geometry in Complex Plane

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

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 .

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

The Positive Real Axis

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

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Question number: 20

» Tests of Convergence

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Appeared in Year: 2008

Essay Question▾

Describe in Detail

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

a)

b)

c)

Explanation

Option (a) The given series is

Here

Take

By comparison test behave alike

They converge or diverge together

converges by p –test

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Question number: 21

» Continuity and Differentiability

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Appeared in Year: 2005

Essay Question▾

Describe in Detail

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 ?

Explanation

Let

i. e

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Question number: 22

» Analyticity in C

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Appeared in Year: 2007

MCQ▾

Question

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

Question number: 23

» Summation of Series

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

Find the sum of the following series upto n terms.

Explanation

Let be the rth term of the given series. Then

Where

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Question number: 24

» Determinant

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

Let . Evaluate

Explanation

applying

Applying

Taking common from

By

Applying

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Question number: 25

» Indeterminate Forms

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Appeared in Year: 2007

Short Answer Question▾

Write in Short

Evaluate:

Developed by: