1. What is not true about number zero.
2. Which one of them is not interval.
3. A number which is neither even nor odd is
4. A number which is neither positive nor negative is
5. Concept of the divisibility only exists in set of …………..
6. If a real number is not rational then it is ……………
7. Which of the following numbers is not irrational.
8. A set $A$ is said to be countable if there exists a function $f:A\to \mathbb{N}$ such that
9. Let $A=\{x| x\in \mathbb{N} \wedge x^2 \leq 7 \} \subset \mathbb{N}$. Then supremum of $A$ is
1. A convergent sequence has only ……………. limit(s).
2. A sequence $\{s_n\}$ is said to be bounded if
3. If the sequence is convergent then
4. A sequence $\{(-1)^n\}$ is
5. A sequence $\left\{\dfrac{1}{n} \right\}$ is
6. A sequence $\{s_n\}$ is said be Cauchy if for $\epsilon>0$, there exists positive integer $n_0$ such that
7. Every Cauchy sequence has a ……………
8. A sequence of real number is Cauchy iff
9. Let $\{s_n\}$ be a convergent sequence. If $\lim_{n\to\infty}s_n=s$, then
10. Every convergent sequence has …………….. one limit.
11. If the sequence is decreasing, then it …………….
12. If the sequence is increasing, then it …………….
13. If a sequence converges to $s$, then ………….. of its sub-sequences converges to $s$.
14. If two sub-sequences of a sequence converge to two different limits, then a sequence ……………
1. A series $\sum_{n=1}^\infty a_n$ is said to be convergent if the sequence $\{ s_n \}$, where ………………
2. If $\sum_{n=1}^\infty a_n$ converges then ………………………
3. If $\lim_{n\to \infty} a_n \neq 0$, then $\sum_{n=1}^\infty a_n$ ………………………
4. A series $\sum_{n=1}^\infty \left( 1+\frac{1}{n} \right)$ is ………………..
5. Let $\sum a_n$ be a series of non-negative terms. Then it is convergent if its sequence of partial sum ……………
6. If $\lim_{n\to\infty} a_n=0$, then $\sum a_n$ …………….
7. A series $\sum \frac{1}{n^p}$ is convergent if
8- If a sequence $\{a_n\}$ is convergent then the series $\sum a_n$ …………….
9. An alternating series $\sum (-1)^n a_n$, where $a_n\geq 0$ for all $n$, is convergent if
10. An series $\sum a_n$ is said to be absolutely convergent if
11. A series $\sum a_n$ is convergent if and only if ………………… is convergent
1. A number $L$ is called limit of the function $f$ when $x$ approaches to $c$ if for all $\varepsilon>0$, there exist $\delta>0$ such that ……… whenever $0<|x-c|<\delta$.
2. If $\lim_{x \to c}f(x)=L$, then ………….. sequence $\{x_n\}$ such that $x_n \to c$, when $n\to \infty$, one has $\lim_{n \to \infty}f(x_n)=L$.
3. Let $f(x)=\frac{x^2-5x+6}{x-3}$, then $\lim_{x\to 3}f(x)=$………..
1. Which one is not partition of interval $[1,5]$.
2. What is norm of partition $\{0,3,3.1,3.2,7,10 \}$ of interval $[0,10]$.