NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 93 - 100 of 231

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Question 93

Appeared in Year: 2012

Describe in Detail Subjective▾

Let be the Boundary of the square in the complex plane with vertices at the points which is described in the anticlockwise direction. Evaluate .

Edit

Explanation

The Boundary of the Square

Along OA

… (731 more equations, 36 figures) …

Question 94

Appeared in Year: 2008

Write in Short Short Answer▾

Let be a simple closed contour in the complex plane described in the positive sense. Evaluate.

When

a) lies inside and

b) lies outside

Edit

Question 95

Appeared in Year: 2013

Describe in Detail Subjective▾

In each of the following find the points of continuity of f.

a)

b)

Edit

Explanation

Option (a) is discontinuous for all values of x on real line

Points of continuity

Option (b) is continous when

… (500 more equations) …

Question 96

Appeared in Year: 2012

Describe in Detail Subjective▾

Let . Fill in the blanks with the correct sign :

a) ________

b) ________

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Explanation

(a) Let

Then satisfies the conditions of LMVT in consequently there exists some satisfying

… (433 more equations) …

Question 97

Appeared in Year: 2007

Question MCQ▾

Which of the following series are convergent?

Choices

Choice (4)Response

a.

b.

c.

d.

Both b. and c. are correct

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Question 98

Appeared in Year: 2007

Describe in Detail Subjective▾

Find the interval of convergence of the series

Edit

Explanation

The given series is

Put

So the given series is

… (236 more equations) …

Question 99

Appeared in Year: 2011

Describe in Detail Subjective▾

Evaluate

Edit

Explanation

Let

… (112 more equations) …

Question 100

Appeared in Year: 2012

Question 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.

Edit