NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 60 - 67 of 101

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Question number: 60

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Appeared in Year: 2005

Essay Question▾

Describe in Detail

Find the sum of the series

Question number: 61

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Appeared in Year: 2009

Essay Question▾

Describe in Detail

Test the following series for convergence.

a)

b)

Where is a convergent series of positive terms.

Explanation

Option (a) The given series is

Here

By Cauchy’s Root test the given series is convergent.

option (a) is correct

Option (b) Using Result

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Question number: 62

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Appeared in Year: 2013

Evaluate

Question number: 63

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

Find the sum of the following infinite series

Explanation

………. eq. (A) [ Rearranging the terms]

Now we know that

Put

………. . eq. (1)

Also

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Question number: 64

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Appeared in Year: 2012

MCQ▾

Question

Determine if the following claim is true or false:

Choices

Choice (4)Response

a.

b.

c.

d.

Question does not provide sufficient data or is vague

Question number: 65

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Appeared in Year: 2009

Essay Question▾

Evaluate

Let

Question number: 66

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Appeared in Year: 2016

Essay Question▾

Describe in Detail

Let be an arbitrary positive real number define

Which of the following statements are true?

a) For all , we have

b) The sequence is monotonic

c) The sequence convergent

Explanation

…………eq. (1)

That point (By Induction)

Result is true for

Assume that the result is true for

Result is true for

But res

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Question number: 67

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Appeared in Year: 2006

MCQ▾

Question

Let denote the set of all continuously differentiable real valued function defined on the real line. Define

where denotes the derivative of the function f. Pick out the true statements.

Choices

Choice (4)Response

a.

A is an Infinite set.

b.

A is Empty set

c.

A is a finite and non-empty set

d.

All of the above

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