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 .
EditExplanation
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
EditQuestion 95
Appeared in Year: 2013
Describe in Detail Subjective▾
In each of the following find the points of continuity of f.
a)
b)
EditExplanation
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) ________
EditExplanation
(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 |
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
Explanation
Let
… (112 more equations) …
Question 100
Appeared in Year: 2012
Question True-False▾
Statements
If … eq. (1)
Where , then the polynomial has a root in the interval .
If is continuous and differentiable in , where and if
Then there exists such that
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. |