# MCQs or Short Questions

On this page, MCQs or short questions with out answers are given. Students need to find the answer them self. This page will be updated occasionally and new MCQs or short question will be posted here.

1. A number which is neither even nor odd is
• (A) 0
• (B) 2
• (C) $2n$ such that $n \in \mathbb{Z}$
• (D) $2\pi$
2. A number which is neither positive nor negative is
• (A) 0
• (B) 1
• (C) $\pi$
• (D) None of these
3. Concept of the divisibility only exists in set of …………..
• (A) natural numbers
• (B) integers
• (C) rational numbers
• (D) real numbers
4. If a real number is not rational then it is ……………
• (A) integer
• (B) algebraic number
• (C) irrational number
• (D) complex numbers
5. Which of the following numbers is not irrational.
• (A) $\pi$
• (B) $\sqrt{2}$
• (C) $\sqrt{3}$
• (D) 7
6. Is there a rational number exists between any two rational numbers.
7. Is there a real number exists between any two real numbers.
8. Is the set of rational numbers is countable?
9. Is the set of real numbers is countable?
10. A set $A$ is said to be countable if there exists a function $f:A\to \mathbb{N}$ such that
• (A) $f$ is bijective
• (B) $f$ is surjective
• (C) $f$ is identity map
• (D) None of these
11. Let $A=\{x| x\in \mathbb{N} \wedge x^2 \leq 7 \}$. Then supremum of $A$ is
• (A) 7
• (B) 3
• (C) does not exist
• (D) 0
12. A convergent sequence has only ……………. limit(s).
• (A) one
• (B) two
• (C) three
• (D) None of these
13. A sequence $\{s_n\}$ is said to be bounded if
• (A) there exists number $\lambda$ such that $|s_n|<\lambda$ for all $n\in\mathbb{Z}$.
• (B) there exists real number $p$ such that $|s_n|<p$ for all $n\in\mathbb{Z}$.
• (C) there exists positive real number $s$ such that $|s_n|<s$ for all $n\in\mathbb{Z}$.
• (D) the term of the sequence lies in a vertical strip of finite width.
14. If the sequence is convergent then
• (A) it has two limits.
• (B) it is bounded.
• (C) it is bounded above but may not be bounded below.
• (D) it is bounded below but may not be bounded above.
15. A sequence $\{(-1)^n\}$ is
• (A) convergent.
• (B) unbounded.
• (C) divergent.
• (D) bounded.
16. A sequence $\{\frac{1}{n} \}$ is
• (A) bounded.
• (B) unbounded.
• (C) divergent.
• (D) None of these.
17. A sequence $\{s_n\}$ is said be Cauchy if for $\epsilon>0$, there exists positive integer $n_0$ such that
• (A) $|s_n-s_m|<\epsilon$ for all $n,m>0$.
• (B) $|s_n-s_m|<n_0$ for all $n,m>\epsilon$.
• (C) $|s_n-s_m|<\epsilon$ for all $n,m>n_0$.
• (D) $|s_n-s_m|<\epsilon$ for all $n,m<n_0$.
18. Every Cauchy sequence has a ……………
• (A) convergent subsequence.
• (B) increasing subsequence.
• (C) decreasing subsequence.
• (D) positive subsequence.
19. A sequence of real number is Cauchy iff
• (A) it is bounded
• (B) it is convergent
• (C) it is positive term sequence
• (D) it is convergent but not bounded.
20. Let $\{s_n\}$ be a convergent sequence. $If$\lim_{n\to\infty}s_n=s$, then • (A)$\lim_{n\to\infty}s_{n+1}=s+1$• (B)$\lim_{n\to\infty}s_{n+1}=s$• (C)$\lim_{n\to\infty}s_{n+1}=s+s_1$• (D)$\lim_{n\to\infty}s_{n+1}=s^2\$.
21. Every convergent sequence has …………….. one limit.
• (A) at least
• (B) at most
• (C) exactly
• (D) none of these
22. If the sequence is decreasing, then it …………….
• (A) converges to its infimum.
• (B) diverges.
• (C) may converges to its infimum
• (D) is bounded.
23. If the sequence is increasing, then it …………….
• (A) converges to its supremum.
• (B) diverges.
• (C) may converges to its supremum.
• (D) is bounded.
24. Give an example of sequence, which is bounded but not convergent.
25. Is every bounded sequence is convergent?
26. Is product of two convergent sequences is convergent?
• atiq/sp15-mth321/mcqs