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msc:mcqs_short_questions:real_analysis [2023/04/01 18:39] – [Edit - Panel] Administrator | msc:mcqs_short_questions:real_analysis [2023/04/03 04:06] (current) – [Series of Numbers] Administrator | ||
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* (C) Additive identity | * (C) Additive identity | ||
* (D) Additive inverse of zero \\ <btn type=" | * (D) Additive inverse of zero \\ <btn type=" | ||
- | </ | + | </ |
+ | < | ||
2. Which one of them is not interval. | 2. Which one of them is not interval. | ||
* (A) $(1,2)$ | * (A) $(1,2)$ | ||
* (B) $\left(\frac{1}{2}, | * (B) $\left(\frac{1}{2}, | ||
* (C) $[3. \pi]$ | * (C) $[3. \pi]$ | ||
- | * (D) $(2\pi, | + | * (D) $(2\pi, |
- | </ | + | </ |
+ | < | ||
3. A number which is neither even nor odd is | 3. A number which is neither even nor odd is | ||
* (A) 0 | * (A) 0 | ||
* (B) 2 | * (B) 2 | ||
* (C) $2n$ such that $n \in \mathbb{Z}$ | * (C) $2n$ such that $n \in \mathbb{Z}$ | ||
- | * (D) $2\pi$ \\ <btn type=" | + | * (D) $2\pi$ \\ <btn type=" |
- | </ | + | </ |
+ | < | ||
4. A number which is neither positive nor negative is | 4. A number which is neither positive nor negative is | ||
* (A) 0 | * (A) 0 | ||
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* (D) does not exist \\ <btn type=" | * (D) does not exist \\ <btn type=" | ||
</ | </ | ||
- | ==== Sequence of Numbers ==== | + | ==== Sequence of Numbers ==== |
< | < | ||
1. A convergent sequence has only ................ limit(s). | 1. A convergent sequence has only ................ limit(s). | ||
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* (C) is convergent. | * (C) is convergent. | ||
* (D) is divergent. \\ <btn type=" | * (D) is divergent. \\ <btn type=" | ||
- | </ | ||
- | - A series $\sum a_n$ is convergent if and only if ..................... is convergent | ||
- | * (A) $\{\sum_{k=1}^{\infty}a_k \}$ | ||
- | * (B) $\{\sum_{k=1}^{n}a_k \}$ | ||
- | * (C) $\{\sum_{n=1}^{\infty}a_k \}$ | ||
- | * (D) $\{ a_n \}$ \\ <btn type=" | ||
</ | </ | ||
- | ==== Series of Numbers ==== | + | ==== Series of Numbers ==== |
< | < | ||
1. A series $\sum_{n=1}^\infty a_n$ is said to be convergent if the sequence $\{ s_n \}$, where .................. | 1. A series $\sum_{n=1}^\infty a_n$ is said to be convergent if the sequence $\{ s_n \}$, where .................. | ||
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* (C) $\sum |a_n|$ is convergent. | * (C) $\sum |a_n|$ is convergent. | ||
* (D) $\sum |a_n|$ is divergent but $\sum a_n$ is convergent. \\ <btn type=" | * (D) $\sum |a_n|$ is divergent but $\sum a_n$ is convergent. \\ <btn type=" | ||
+ | </ | ||
+ | 11. A series $\sum a_n$ is convergent if and only if ..................... is convergent | ||
+ | * (A) $\{\sum_{k=1}^{\infty}a_k \}$ | ||
+ | * (B) $\{\sum_{k=1}^{n}a_k \}$ | ||
+ | * (C) $\{\sum_{n=1}^{\infty}a_k \}$ | ||
+ | * (D) $\{ a_n \}$ \\ <btn type=" | ||
</ | </ | ||
==== Limit of functions ==== | ==== Limit of functions ==== | ||
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* (C) $3.8$ | * (C) $3.8$ | ||
* (D) $0.1$ \\ <btn type=" | * (D) $0.1$ \\ <btn type=" | ||
- | < | + | </panel> |