NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 97 - 101 of 101

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Question number: 97

» Convergence of Positive Series Test

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Appeared in Year: 2007

MCQ▾

Question

Which of the following series are convergent?

Choices

Choice (4)Response

a.

b.

c.

d.

Both b. and c. are correct

Question number: 98

» Interval of Convergence

Edit

Appeared in Year: 2007

Essay Question▾

Describe in Detail

Find the interval of convergence of the series

Explanation

The given series is

Put

So the given series is

(By Cauchy’s second theorem on limits)

… (243 more words) …

Question number: 99

» G.P Series

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Appeared in Year: 2011

Essay Question▾

Describe in Detail

Evaluate

Explanation

Let …………. eq. (1)

………. eq. (2)

Subtracting eq. (2) from (1)

If

… (230 more words) …

Question number: 100

» Rolle's Theorem and IVT

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Appeared in Year: 2012

True-False▾

Statements

  1. If …………. eq. (1)

    Where , then the polynomial has a root in the interval .

  2. If is continuous and differentiable in , where and if

    Then there exists such that

  3. The polynomial has only one real root.

Choices

Choice (4)Response

a.

None of the statements is correct.

b.

Both statement Ⅰ & statement Ⅱ are true.

c.

All the statements are correct.

d.

Only statement Ⅱ is true.

Question number: 101

» Taylor's Theorem

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Appeared in Year: 2005

MCQ▾

Question

Let

Pick out the true statements:

Choices

Choice (4)Response

a.

b.

is a decreasing function on the entire real line

c.

None of the above

d.

Question does not provide sufficient data or is vague

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