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
Appeared in Year: 2007
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
Appeared in Year: 2007
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
Appeared in Year: 2011
Describe in Detail
Evaluate
Explanation
Let …………. eq. (1)
………. eq. (2)
Subtracting eq. (2) from (1)
If
… (230 more words) …
Question number: 100
Appeared in Year: 2012
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. | |
Question number: 101
Appeared in Year: 2005
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 | |