NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 1 - 9 of 101

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Question number: 1

» Sequences and Series (Convergence)

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Appeared in Year: 2006

Short Answer Question▾

Write in Short

For what value of p does the following series converge?

Question number: 2

» Continuity and Differentiability

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Appeared in Year: 2005

Essay Question▾

Describe in Detail

Let is a differentiable function such that for all . For what value of will be the function be necessarily one-to-one?

Explanation

Let

Then

if ………. . eq. (A)

If

Then [By LMVT]

[From (A) ]

then the function is not injective i. e o

… (34 more words) …

Question number: 3

» Line Integral in Complex Plane

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Appeared in Year: 2009

Essay Question▾

Describe in Detail

Let and let f be defined by

If C is the straight-line segment joining ; compute

Explanation

Let P be the point in which represents the complex number .

Graph of the straight-line segment

Graph of the Straight-Line Segment

is the line from

On so that

… (84 more words) …

Question number: 4

» Continuity

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Appeared in Year: 2006

MCQ▾

Question

Pick out the function which are continous atleast at one point in the real line.

Choices

Choice (4)Response

a.

b.

c.

d.

Both b. and c. are correct

Question number: 5

» Nth Roots of Unity

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Appeared in Year: 2008

Short Answer Question▾

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Write down an equation of degree four satisfied by all the complex fifth roots of unity.

Question number: 6

» Indeterminate Forms

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Appeared in Year: 2008

Essay Question▾

Describe in Detail

Evaluate:

Explanation

This is exponential form form

Using the Result

If

Then

… (70 more words) …

Question number: 7

» Exponential Series

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

Find the sum of the following infinite series.

Explanation

… (76 more words) …

Question number: 8

» Exponential Series

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Appeared in Year: 2013

Essay Question▾

Describe in Detail

Let . Find the sum of the infinite series.

Explanation

Let

Put

…………… eq. (A)

Now we know the exponential series

…………. . eq. (1)

Replacing by in (1)

…………. . eq. (2)

Adding eq

… (92 more words) …

Question number: 9

» Cauchy-Riemann Equation

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Appeared in Year: 2005

Short Answer Question▾

Write in Short

Let be two twice continuously differentiable functions on satisfying the Cauchy –Riemann equation. Let . Define . Express the complex derivative of i. e. in terms of the partial derivatives of .

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