Question QMC1 :

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Question QMC2 : If f is a continuously differentiable real-valued function defined on the open interval (1, -4) such that f(3) = 5 and f

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Question QMC3 :

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Question QMC4 : A real-valued function f defined on R has the following property. For every positive number ϵ, there exist a positive number δ. This property is equivalent to which of the following statement about f?

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Question QMC5 : Which of these functions is not uniformly continuous on (0,1)?

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Question QMC6 : Let Sn be a sequence of real numbers on a bounded set S, where Lin inf Sn ± lin sup Sn. Which of the following is not necessarily true?

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Question QMC7 : Which of the following is true about a uniformly continuous function, f on [a,b]?

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Question QMC8 :

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Question QMC9 : Which of the following is true

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Question QMC10 : Rational numbers can be expressed as ratio of true integers with repeated or terminations decimals. On the other hand, irrational numbers refer to any real numbers that are not rational. So, is I a rational number or an irrational number

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Question QMC11 : Given a non-empty subset S of R on the interval [0,5]. Then, any number greater than 5 is an upper bound of S, Since it is greater than ll of the numbers contained in S. Therefore, we can say that 5.01, 5.1, 6 and 7 are all upper bound of S. Among all these upper bound, the one with the smallest value is known as the ________ of S.

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Question QMC12 : The absolute value of a real non-zero number r, denoted by |r| is always

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Question QMC13 :

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Question QMC14 : By Lagrange’s means value theorem, f(x) can also be written as:

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Question QMC15 : What is the first derivative of the function f(x) = x

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Question QMC16 : A monotonic sequence is said to be

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Question QMC17 : $\underset{n\to \infty}{\mathrm{lim}}\frac{1}{n}$ Converges to?

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Question QMC18 : $\underset{n\to \infty}{\mathrm{lim}}\frac{1}{{n}^{2}+1}$ Converges to?

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Question QMC19 :

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Question QMC20 : Every nonempty set of real numbers of that has an upper bound, also has a supremum in R. This is the ____________

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Question QMC21 : Two sets A and B are equal if every $x\u03f5A$ belongs to B and every $y\u03f5B$ belongs to A. This is called …

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Question QMC22 : Which word is the odd one out in set notation

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Question QMC23 : Which of the following, concisely defines the union of A and B?

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Question QMC24 : A $\cap $ B is read as…

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Question QMC25 : Which of the following is not true in set operations

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Question QMC26 : The difference of A and B may also be defined concisely by A – B = …

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Question QMC27 : Let R be the set of real numbers and let Q be the set of rational numbers. Then R – Q consist of the…

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Question QMC28 : $N\cup R=\dots ?$

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Question QMC29 : The set – theoretic product of A and B is denoted by …

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Question QMC30 : The notation A/B or A $~$ B represents …

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Question QMC31 : Let the universal set be $N=\left\{1,2,3,...\right\},$ find$A\text{'}$ if A = {8, 9, 10, …}

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Question QMC32 : Let the universal set be the set of positive integers and let A be the set of the positive even numbers. Find $A\text{'}$

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Question QMC33 : Given that A = {0, 1} and B = {1, 2, 3}. Find A $\cup $ B

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Question QMC34 : Find A $\cap $ B if A = {0, 1} and B = {1, 2, 3}.

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Question QMC35 : Find A – B if A = {0, 1} and B = {1, 2, 3}

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Question QMC36 : Find A $\cap \varnothing $ if A = {0, 1}

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Question QMC37 : Concept of the divisibility only exists in set of__________

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Question QMC38 : Find A $\cup A\text{'}$ if the universal set is {1, 2, 3, 4} and A = {2, 3}.

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Question QMC39 : The number of elements in the Power set P(S) of the set S={[$\varnothing $], 1, [2,3]} is

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Question QMC40 : If A and B are sets and A $\cup $ B =A $\cap $ B, then

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Question QMC41 : The union of the sets {1,2,5} and {1,2,6} is the set ................

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Question QMC42 : The intersection of the sets {1,2,5} and {1,2,6} is the set ……………

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Question QMC43 : Two sets are called disjoint if their ………….. is empty set.

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Question QMC44 : Which of the following two sets are disjoint?

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Question QMC45 : The complement of the set A is ………..

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Question QMC46 : Individual objects in a set are called …………..

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Question QMC47 : Set {x: x is an odd number between 10 and 18}

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Question QMC48 : Let A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find A $\cup $ C

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Question QMC49 : Find the equation of the circle centre (2, - 3) and radius 4

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Question QMC50 : Find the distance between the points Z

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Question QFB1 : If ${I}_{n}=[0,\frac{1}{n}]$ for $n\in N$, then ${I}_{n}\supseteq {I}_{n+1}$ for each $n\in N$ so that this sequence of intervals is __________

Answer: Nested

Question QFB2 : A positive real number is rational if and only if its decimal representation is _____________

Answer: Periodic

Question QFB3 : The unit interval [0, 1] = $\{x\in R:0\le x\le 1\}$ is ________

Answer: Not countable

Question QFB4 : If C is an infinite set and B is a finite set, then C\B is an ________

Answer: infinite set

Question QFB5 : If $\left({x}_{n}\right)$ is an unbounded increasing sequence, then $lim\left({x}_{n}\right)$ is ____

Answer: Infinite

Question QFB6 : . Let $\left({x}_{n}\right)$ and $\left({y}_{n}\right)$ be two sequences of positive real numbers and suppose that for $L\in R,$ $L>0$ we have $lim\left(\frac{{x}_{n}}{{y}_{n}}\right)=L$.Then $lim\left({x}_{n}\right)=$ +$\infty $ if and only if $lim\left({y}_{n}\right)$ is an ________

Answer: Infinite

Question QFB7 : Consider the series generated by ${\left\{{(-1)}^{n}\right\}}_{n=0}^{\infty}$ that is the series $\sum _{n=0}^{\infty}{(-1)}^{n}=$(+1) + (-1) + (+1) +… This series is a ________

Answer: Divergent

Question QFB8 : A function meant a definite formula such as $f\left(x\right)={x}^{2}+3x+5$ which associates to each real number $x$ another number $f\left(x\right)$ then $f(-4)$ is ____

Answer: 9

Question QFB9 : A function which is both one-one and onto is known as __________

Answer: Bijective

Question QFB10 : The limit of the sequence $\frac{1}{{n}^{2}+1}$ is _______

Answer: 1

Question QFB11 : The limit of the sequence $\frac{2n}{{n}^{2}+1}$ is _______

Answer: 2

Question QFB12 : The Bolzano-Weierstrass theorem say that a bounded sequence of real numbers has a ________

Answer: divergent subsequence

Question QFB13 : . A monotone sequence of real number is properly divergent if and only if it is an ________

Answer: Unbounded

Question QFB14 : Consider the series $\sum _{n=1}^{\infty}\frac{1}{n(n+1)}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\dots $ this series converges to _________

Answer: 0

Question QFB15 : The limit $\underset{x\to \infty}{\mathrm{lim}}{x}^{n}$ is _______

Answer: Infinite

Question QFB16 : The limit $\underset{x\to 0}{\mathrm{lim}}\frac{1}{{1+e}^{\frac{1}{x}}}$ is _______

Answer: 1

Question QFB17 : The limit $\underset{x\to -2}{\mathrm{lim}}{x}^{3}$

Answer: -8

Question QFB18 : Let f be the rational function defined by $f\left(x\right)=\frac{{2x}^{7}-{9x}^{6}+{11x}^{2}-2}{{4x}^{9}-{10x}^{8}-6x+7}$ ,$\underset{x\to -1}{\mathrm{lim}}f\left(x\right)$ is ___________

Answer: 2

Question QFB19 :

Answer: 7

Question QFB20 :

Answer: 3

Question QFB21 : The $\underset{w\to -2}{\mathrm{lim}}\sqrt{{3w}^{3}+{7w}^{2}}$ is _______

Answer: 2

Question QFB22 : " + " is ___________ operation on $$\mathbb{R}$$

Answer: binary operation

Question QFB23 : If a real number is not rational then it is an _______

Answer: Integer

Question QFB24 : If a real number is not rational then it is an __________ number

Answer: Irrational

Question QFB25 : A number which is neither positive nor negative is

Answer: 0

Question QFB26 : The supremum is also called the ____ upper bound

Answer: Least

Question QFB27 : The harmonic series ___

Answer: Diverges

Question QFB28 : A monotone sequence of real numbers is properly divergent if and only if it is _______

Answer: Unbounded

Question QFB29 : $\pi $is an example of ___________ numbers

Answer: Irrational

Question QFB30 : Concept of the divisibility only exists in set of __________

Answer: Integers

Question QFB32 : A convergent sequence has only ______________ limit(s)

Answer: 1

Question QFB33 : Every convergent sequence has ___________one limit

Answer: 7

Question QFB34 : Give the next 3 terms of the sequence 0,1,1,2,3,5,8,………,____

Answer: 13, 21, 34

Question QFB35 : Two Sets A and B are said to be _______ if and only if they have the same elements but possibly with different listings.

Answer: Equal

Question QFB36 :

Answer: 4

Question QFB37 : List the first 3 terms of the inductively defined sequence x

Answer: 1,4,13

Question QFB38 : A set is said to be _______ if the process of counting the element in the set terminates.

Answer: Finite

Question QFB39 : A set is said to be __________ if its either empty or it has n elements for some

Answer: Finite

Question QFB40 : The property of a natural numbers which states that every nonempty subset of a natural number has a least element is termed well _____ principle

Answer: Ordering

Question QFB41 : Abounded sequence of real numbers has a ____ subsequence

Answer: Convergent

Question QFB42 : A function $f:A\to R$ is said to be ____ on A if there exists a constant M > 0 such that $f\left(x\right)\le M$ for all x in A

Answer: Bounded

Question QFB43 : The theorem that a sequence in $R$ can have at most one limit is the ____.

Answer: Uniqueness

Question QFB44 : A sequence that has no limit is said to be ____

Answer: Divergent

Question QFB45 : For x and y an element of a natural number N, (-x)(-y) equal____

Answer: Xy

Question QFB46 : A set N is called a subset of a set M if every _______ of N is a member of M.

Answer: Element

Question QFB47 : The set B of second elements of a function $f$ is called the ____ of the function.

Answer: Range

Question QFB48 : The set A of first elements of a function $f$ is called the ____of the function.

Answer: Domain

Question QFB49 : Let A and B be two non- empty sets then $A\cap B=\varnothing $ shows that A and B are____ sets

Answer: Disjoint

Question QFB50 : A set is said to be ______ if it contains no element.

Answer: Null

Question QFB31 : Find the lim of 3x6+5x-8 as x tends to zero

Answer: 8