NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 80 - 88 of 101

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Question number: 80

» Definite Integral

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Appeared in Year: 2014

MCQ▾

Question

Which of the following statements are true?

Choices

Choice (4)Response

a.

If , then is rational when n is even

b.

If , then is rational when n is odd

c.

If , then is Irrational when n is even

d.

Question does not provide sufficient data or is vague

Question number: 81

» Inequalities Using LMVT

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Appeared in Year: 2014

MCQ▾

Question

Let . Which of the following statements are true?

Choices

Choice (4)Response

a.

b.

c.

d.

All a. , b. and c. are correct

Question number: 82

» Maxima and Minima

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Appeared in Year: 2009

Essay Question▾

Describe in Detail

Let

Examine whether admits a local maximum or minimum at ?

Explanation

Here

Now

At

So n

… (100 more words) …

Question number: 83

» Binomial Series

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Appeared in Year: 2010

Essay Question▾

Describe in Detail

Find the sum of the infinite series:

Explanation

Let

Consider the series

……. . eq. (A)

Comparing eq. (A) with the standard form i. e.

… (258 more words) …

Question number: 84

» Convergence of Positive Series Test

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Appeared in Year: 2011

Essay Question▾

Describe in Detail

Test the following series for convergence.

a)

b)

Explanation

Option (a) The given series is

Take

which is non –zero and finite

… (328 more words) …

Question number: 85

» Interval of Convergence

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Appeared in Year: 2006

Essay Question▾

Describe in Detail

Find the interval of convergence of the series

Explanation

The given series is

Put

The given power series

Let

By Cauchy second theorem on limits, we have

… (138 more words) …

Question number: 86

» Definite Integral

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Appeared in Year: 2013

Essay Question▾

Describe in Detail

Evaluate

Explanation

Graph of the evaluate

Graph of the Evaluate

Question number: 87

» Definite Integral as Limit of a Sum

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Appeared in Year: 2008

Essay Question▾

Describe in Detail

Evaluate

Explanation

Replacing by the sign of

Upper limit

Lower limit

Question number: 88

» Definite Integral

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Appeared in Year: 2016

MCQ▾

Question

Let Which of the following statements are true?

Choices

Choice (4)Response

a.

is rational for all

b.

is Irrational for all

c.

is rational if

d.

All of the above

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