NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 18 - 25 of 231
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Question 18
Question 19
Appeared in Year: 2015
Describe in Detail Subjective▾
Let be the polygon in the complex plane with vertices situated at the nth Roots of unity. Let be the area and let be its perimeter. Evaluate
EditExplanation
The points represented by nth roots of unity are located at the vertices of a regular polygon of n sides, inscribed in a unit circle having center at the origin, one vertex being on the positive real axis (in figure below)
But when n approaches to infinity, the n sided polygon will approach to circle of unit radius.
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Question 20
Appeared in Year: 2008
Describe in Detail Subjective▾
Determine if each of the following series is absolutely convergent, conditionally convergent or divergent:
a)
b)
c)
EditExplanation
Option (a) The given series is
Here
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Question 21
Appeared in Year: 2005
Describe in Detail Subjective▾
Let n be a positive integer. Let and let . For what value of n will f be twice differentiable but its second derivative discontinuous at ?
EditExplanation
Let
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Question 22
Appeared in Year: 2007
Question MCQ▾
Let . Which of the following function are analytic in the entire complex plane?
Choices
Choice (4) | Response | |
---|---|---|
a. | ||
b. | ||
c. | ||
d. | Question does not provide sufficient data or is vague |
Question 23
Appeared in Year: 2015
Describe in Detail Subjective▾
Find the sum of the following series upto n terms.
Edit
Explanation
Let be the rth term of the given series. Then
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Question 24
Explanation
applying
Applying
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