Dear Students in this post we are providing you MTH202 Solved Grand Quiz Spring 2021. We have provided all Past MTH202 Grand Quiz with 100% correct Solution. You can also visit our website vulmshelp.com for the solution of MTH202 Mid Term past paper and Final Term Past paper.

^{SOC101 SOLVED MCQs}

**Range of function /[f(x)=(e^x)/] is ___________**

**Set of positive real numbers**

**Composite relation symbolically written as _______**

**SoR={(a,c)aeA, ceC, 3eB, (a,b)eR and (b,c)eS}**

**If x=17(mod 5) which of the following integers are valid solution for x ?**

**12**

**Range of the relation {(0,1),(3,22),(90,34)}**

**{1,22,34}**

**Let A= {0,1,2} and R = {(0,2),(1,1),(2,0)} be a relation on A. The which of the following ordered pairs are needed to make it transitive?**

**(0,0) and (2,2)**

**Operation of subtraction is a binary operation on the set of __________**

**Integers**

**Let S=R and define the ‘square’ relation R= {(x,y)Ix ^{2}=y^{2}}. The square relation is an _________ relation**

**Equivalence relation**

**The logic gate NOT is a uniary operation on {0,1}.**

**True**

**Let A= {1,2}, then P(A)=__________**

**{{},{1},{2},{1,2}}**

**If a relation R is reflexive, anti symmetric and transitive then which of the following is not true for the inverse relation.**

**Inverse relation will be irreflexive.**

**Let R be a binary relation on a set A,R is anti-symmetric iff ___________**

**a,beA if (a,b)eR and (b,a)eR then a=b**

**“-“ is a binary operation on the set of integers Z.**

**True**

**The inverse relation R^(-1) from B to A is defined as ____________**

**R^(-1) = {(b,a) e B*A I (a,b)eR}**

**Which of the following is always true for the matrix representation of a symmetric relation?**

**Matrix is equal to its transpose**

**Let A= {1,2,3,4} and let R and S be transitive binary relations on A defined as; R= {(1,2), (1,3), (2,2), (3,3), (4,2), (4,3) and S={(2,1), (2,4), (3,3)} then RuS= {(1,2), (1,3), (2,1), (2,2), (2,4), (3,3), (4,2), (4,3)}**

**R union S is transitive**

**Let S=R and define the ‘ square’ relation R = {(x,y)Ix ^{2}=y^{2}}. The square is an _________ relation.**

**Equivalance relation**

**If x=-10(mod 15). Which of the following integers are valid solution for x?**

**5**

**Let R be a binary relation on a set A. If R is anti symmetric then ______________**

**Inverse of R is anti symmetric**

** If A={1,2,3} is a set and R = {(1,2),(2,2),(2,1)} is a relation on A, R is**

**Symmetric**

**Let A={0,1} and B=(1). Let R and S be two binary relations on Cartesian product of A and B such that R={(0,1)} and S= {(1,1)}. Then R intersection S=_________________**

**Empty**

**A relation R is said to be ______ iff it is reflexive, antisymmetric and transitive.**

**Partial order Relation**

**Let X={1,2,3} and Y={7,8,9} and let f be function defined from X to Y such that f is onto then which of the following statement about f is true?**

**Co-domain of f must contain 1 element**

**The function fog and gof are always equal**

**False**

**If a relation R={(1,2),(2,3),(3,4)(4,1)(2,2) is given then which of the following is true about this relation.**

**R is reflexive**

**A set is called countable if , and only if, it is____________**

**finite**

**Let f(x) = x ^{2}-1 define function f from R to R and c=2 be any scalar, then c,f(x) is __________**

**2x**^{2}+2

**The set Z of all integers is ___________**

**Countable**

**Let R be a binary relation on a set A. If R is anti symmetric then _______**

**Inverse of R is symmetric**

**For (2x-3, 4y+2) = (1,10). What will be the value of x and y ?**

**(2,2)**

**Let f and g be the two functions from R to R defined by f(x) = IxI and g(x)= square root of x ^{2} for all xeR. Then______**

**F(x) is not equal to g(x)**

**If a set A has 15 elements then P(A) (power set of A) has ___________ elements.**

**2^15**

**For the relation below to be a function, x cannot be what values {(12,14),(13,5),(-2,7),(x,13)}?**

**X cannot be 12, 13, or -2**

**Let the set A = {1,2,3,4}. Then the relation {(2,4),(4,2)} is ____________**

**Symmetric**

**For the following relation to be a function, x can not be what values? R={(2,4),(x,1), (4,2),(5,6)}.**

**x cannot be 2,4 and 5**

**Vertical line test is used to determine that whether the graph of a relation is a function or not.**

**True**

**The properties of being symmetric and being anti symmetric are ____________**

**Not negative of each other**

**The number of elements in AxB are ___________ if A is a set with ‘5’ elements and B is a set with ‘4’ elements.**

**20**

**R={(a,1)(b,2)(c,3)(d,4)} then the inverse of this relation is _____________**

**{(1,a)(2,b)(3,c)(4,d)}**

**Logic gate NOT does not define a binary operation on (0,1) because ____________**

**It takes a single input and gives a single output**

** How many real numbers exist between 1 and 5**

**3**

**The number pi is**

**Irrational**

**The number square root 2 is**

**Irrational**

**Range the relation {(0,1)(3,22),(90,34)}**

**{0,3,90}**

**Supherical coordinate 0 is related to the cylindrical coordinate as_____________**

**@=@**

**Operation of subtraction is a binary operation on the set________**

**Integers**

** Let A {1,2,3,4} and R={(1,2),(2,3),(3,3),(3,4)} be a relation on A. Then which one of the following ordered pair has made R not an irreflexive relation?**

**(3,3)**

**Input values of the function are called the ____________**

**Domain**

**Range of function f(x)=IxI will be**

**Set of positive real numbers**

**Which of the following is not a binary operation on the set of integers?**

**Division**

**In the matrix representation of an irreflexive relation all the entries in the main diagonal are __________**

**0**

**If the partition set of A is {A _{1},A_{2}} then**

**A**_{1}nA_{2}= not empty set

**Let A= {a,b} then P(A) =**

**{Non empty set, {a},{b},{a,b}}**

**Which relations below are not functions?**

**{(13,14),(13,5),(16,7),(18,13)}**

**In the directed graph of an antisymmetric relation there is _________ pair of arrows between two distinct elements of the set.**

**No**

**If a relation R= (1,1),(2,1)(2,2) is given then which of the following is not true about this relation**

**R is irreflexive**

**Let R and S be transitive relations on a set A then ________________**

**Neither R union S is transitive nor R intersection S is transitive**

**Let R={(1,2)(3,4)(5,6)(7,8)}. Domain of the inverse of the relation is _____________**

**{2,4,6,8}**

**Let A={1,2,3,4,5} and B={4,9,,16,17,25}. Then the relation R={(2,4),(3,9),(4,16),93,17)} The inverse of R is’**

**{(4,2),(9,3),(16,4),(17,3)}**

** Let R be a relation on a set A. If R is symmetric then its compliment is __________ **

- Irreflexive

**Which is not a binary operation on the set of natural numbers N?**

**Subtraction**

**If a relation R={(1,1)(2,1)(1,2)(2,2)} is given then which of the following is not true about this relation.**

**R is irreflexive**

**R={(a,1)(b,2)(c,3)(d,4)} then the inverse of this relation is ______________**

**{(1,a)(2,b)(3,c)(4,d)}**

**For any set A, the Cartesian product of A and A is known as ____________**

**Universal relation**

**Let A={p,q,r,s} and define a relation R on A by R={(p,p),(p,r),(q,r),(q,s),(r,s)} Then which one of the following is the correct statement about R:**

**R is not reflexive**

**A={1,2} B={3,4}, R={(1,3)(2,4)}. Then the complement of R is __________.**

**{(1,4)(2,3)}**

**Domain of a relation symbolically written as____________.**

**Dom(R)={aeAI(a,b)eR}**

**Let X={2,4,5} and Y={1,2,4} and R be a relation from X to Y defined by R={(2,4)(4,1)(a,2)}. For what value of ‘a’ the relation R is a function?**

**5**

**Let A={1,2,3,4,5,6,7,8,9}, then which of the following sets represent the partition of the set A?**

**A={1,3,5,7,9}, B={2,4,6}, C={8}**

**Let A={1,2,3} and B={2,4} then number of binary relations from A to B are _____________.**

**64**

**A relation R is said to be ________iff it is reflexive, antisymmetric and transitivde.**

**Partial order Relation**

**Let f be a function from X={2,4,5} to Y={1,2,4,6} defined as:f={(2,6),(4,2),(5,1)} . The range of f is _________**

**{1,2,6}**

**Let A={0,1,2} and R={(0,2),(1,1),(2,0)} be a relation on A. Then which of the following statement about R is true?**

**R is symmetric**

**Let A={2,3,4} and B={2,6,8} and let R be the “divides” relation from A to B i.e for all (a,b) belong to (Cartesian product of A and B), a,R b iff a I b (a divides b). Then**

**R={(2,2),(2,6),(2,8),(3,6),(4,8)}**

**Let A={1,2,3,…,50} and B={2,4,6,8,10}. Then the Cartesian product of A and B has ___________ elements.**

**250**

**In the matrix representation of an reflexive relation all the entries in the main diagonal are ___________**

**1**

**Which of the following is not a type of a relation?**

**Permutation**

**Let X={2,4,5} and Y={1,2,4} and R be a relation from X to Y defined by R={(2,4),(4,1),(a,2)}. For what value of ‘a’ the relation R is a function ?**

**5**

**Which of the following is not a representation of a relation?**

**Venn diagram**

**Let A={1,2,3,4} and define the following relations on A. Then R={(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)} is _________**

**R is irreflexive**

**The range of f:X-> Y is also called the image of**

**True**

**Complementary Relation symbolically written as _________**

**R=A*B- R={(a,b)eA*BI (a,b)not belong to R}**

**Let A={1,2,3,4} and R=(1,1)(2,2),(3,3),(4,4) then R is**

**All options**

**If a relation R={(1,1),(2,1),(1,2),(2,2)} is given then which of the following is not true about this relation.**

**R is irreflexive**

**Which of the following logical connective is not a binary operation ?**

**Implication**

** A set may be dividend up into its disjoint subsets, such division is called_______**

**Partition**

**If A=(1,2,3)&B=(4,5,6) and R ={(1,4)(2,5)(3,6)(3,4)} The complementary relation is _________**

**A*B(difference or – ) R**

**In matrix representation of a__________ relation, the diagonal entries are always 1.**

**Reflexive**

**R is not symmetric iff there are elements a and b in A such that ___________**

**(a,b) belongs to R but (b,a) does not belong to R**

**Which relations below are functions?**

**R1={(3,4),(4,5),(6,7),(8,9)}**

**R2={(3,4),(4,5),(6,7),(3,9)}**

**R3={(-3,4),(4,-5),(0,0),(8,9)}**

**R4={(8,11),(34,5),(6,17),(8,19)}**

**R1 and R3 are functions**

**The logic gate OR and AND are uniary operation on {0,1}**

**False**

**There is atleast one loop in the graph of an irreflexive relation**

**False**

**There is atleast one loop in the graph of an reflexive relation**

**True**

**A contains 3 elements and B contains 2 elements, then number of subsets of A*B are _________**

**64**

**Let A={1,2,3} and B={0,1,2} and C={a,b} R={(1,0),(1,2),(3,1),(3,2)} S={(0,b),(1,a),(2,b)} composite of R and S=______________**

**{(1,b),(1,a),(3,a),(3,b)}**

**If R is transitive then the inverse relation will be transitive**

**True**

**The number of elements in the power set of P(not empty set) denoted by P(P(not empty set) is**

**2**

**The function defined from Z to Z as f(x)= 1/(x+2)(x-2) is not well defined because __________**

**Function is not defined at x=2 and x=-2**

**Rang of relation {(0,1),(3,22),(90,34)} is ___________**

**{1, 22, 34}**

**The number of elements in the power set of P(not empty set) denoted by P(not empty set) is**

**1**

**Let R={(1,2),(3,4),(5,6),(7,8)}. Domain of inverse of the relation is _________**

**{2,4,6,8}**

**The relation ‘divides’ on the set of integers is _________**

**A symmetric relation**

**Operation of subtraction is a binary operation on the set of__________**

**Integers**

**If R is transitive then the inverse relation will be transitive.**

**True**

**Let A={1,2,3,4} and define the relation R on A by R={(1,2),(2,3),(3,3),(3,4)}. Then__________**

**R is both reflexive and irreflexive**

**A set may be divided up into its disjoints subsets,such division is called**

**Partition**

**If a set A contains is elements then the number of elements in its power set P(A) is ________**

**2**^{n}

**Range of a relation symbolically written as _______.**

**Ran R = {b****∈****B I (a, b)****∈****R }**

**Let R be a binary relation on a set A. IF R is anti symmetric then _________.**

**Inverse of R is anti symmetric**

**Let A be a set with m elements and B be a set with n elements then the number of elements in A*B are _________**

**m.n**

** Let A{1,2,3,4} and define the following relation on A. Then R={(1,3),(2,2),(2,4),(3,1),(4,2)} Is __________**

**R is symmetric**

**If A={1,2,3}& B={4,5,6} and R={1,4},{2,5},{3,6},{3,4}. The complementary relation is ________**

**A*B (difference or -) R**

**Let R be a relation on a set A. If R is reflexive then its compliment is __________**

**Irreflexive**

**25=1(mod 3) means that 3 divides _______**

**25-1**

**Let R be the universal relation on a set A then which one of the following statement about R is true ?**

**R is reflexive, symmetric and transitive**

**Domain of a relation symbolically written as ______**

**Dom(R)= {aeR I (a,b) e R}**

**Let R be a relation on a set A. R is transitive if and only if for all a,b,ceA then**

**(a,b)eR and (b,c)eR then (a,c)eR**

**Let A be a non-empty set and P(A) the power set of A Deifne the ‘ subset’ relation , c as follows for all X,Y e P(A), XcY <-> for all x, iff xeX then xeY . Then c is _________**

__c__**is partial order relation**

**Define a relation R={(1,1),(2,2),(3,3),(1,3) the relation is**

**R is reflexive and transitive**

** Let R be a relation on a set A. R is transitive if and only if for all a,b,ceA then.**

**(a,b)eR and (b,c)eR then (a,c)eR**

**Let R and S be reflexive relations on a set A then R intersection S is reflexive**

**True**

**A function whose range consists of only one element is called________**

**One to one function**

**The set Z of all integers is ___________**

**Countable**

**One-to-one correspondence means the condition of _______**

**Both (a) and (c)**

**Let X={1,5,9} and Y={3,4,7}, Define a function f from X to Y such that f(1)=7,f(5)=3,f(9)=_________. Which is true f(9) to make it a one-to-one (injective) function?**

**4**

**What will be the fourth term of the following sequence 1/2,2/3,3/4 ______?**

**4/5**

**The value of 6!=**

**720**

**A constant function is one to one iff its ________ is a singleton.**

**Domain**

**A constant function is onto iff its ___________ is a singleton.**

**Co-domain**

**Number of one to one functions from X={a,b} to Y={u,v} are equal to ______-**

**2**

**If f is defined recursively by f(0) = -1 and f(n+1)=f(n)+3, then f(2)=_________.**

**5**

**A function whose inverse function exists is called a/an__________**

**Invertible function**

**Let f(2)=3, g(2)=3, f(4)=1 and g(4)=2 then the value of fog(4) is……**

**3**

**Let A={1,2,3,4} and B={7} then the constant function from A to B is ________.**

**Onto**

**Composition of a function is a commutative operation.**

**False**

**Composition of a function is not a commutative operation**

**True**

**The sum of first five whole number is __________.**

**10**

**If f and g are two one-to-one functions, then their composition that is gof is one-to-one.**

**True**

**Inverse of a surjective function is always a function.**

**False**

**Inverse of a surjective function may not be a function**

**True**

**Let X={1,2,3,4} and Y={7,8,9} and let f be function defined from X to Y such that f is onto then which of the following statement about f is true?**

**Co-domain of f must contain 3 elements**

**If f; X->Y and g; Y->Z are both onto functions. Then gof; X->Z is _________**

**onto**

**If f and g are two one-to-one functions, then their composition gof is_________**

**One-to-one**

**If f: W →X, g:X →Y, and h:Y →Z are functions, then___________**

**(hog)of = ho(gof)**

**Cardinality of positive prime numbers less than 20 is __________.**

**8**

**IF f(x)=sin ^{-1}(x) and g(x)=sin x then gof(x) is _________.**

**X**

**0!=_________.**

**1**

**An important data type in computer programming consists of __________.**

**Finite sequences**

**Let f(x)=2x and g(x)=x+2 define functions f and g from R to R, then (f-g)(x) is __________.**

**x-2**

**The total number of terms in an arithmetic series 0+5+10+15+….50 are _________.**

**11**

**9!/6!=________**

**504**

**Let f(x)=3x and g(x)=3x-2 define functions f and g from R to R, THEN (F+G)(X) is ___________**

**6x-2**

**If f is a bijective function then (f ^{-1}f(x)) is equal to**

**X**

**A sequence whose terms alternate in sign is called an_________**

**Alternating sequence**

**Common ration in the sequence “4, 16, 64, 256,…” is…..12.**

**4**

**0.8181818181 is a infinite geometric series.**

**True**

**The word ‘algorithm’ refers to a step-by-step method for performing some action.**

**True**

**A predicate become ______ when its variables are given specific values**

**Sentence**

**The sum of two irrational numbers must be an irrational number.**

**False**

**The sum of two irrational numbers need not be irrational number**

**True**

**The division by zero is allowed in mathematics.**

**Fasle**

**The product of any two consecutive positive integers is divisible by 2**

**True**

**If ‘n’ is an odd integer then n^3+n is ________.**

**Even**

**For integers a,b,c, If divides b and a divides c, then a divides (a+b).**

**False**

**Quotient remainder theorem states that for any positive integer d, there exist unique integer q and r such that ________ and 0< r<d**

**N=d.q+r**

**A rule that assigns a numerical value to each outcome in a simple space is called**

**Random variable**

**If A and B are two disjoint (mutually exclusive) events then P(AB)=**

**P(A) + P(B)**

**How many ways are there to select five players from a 10 member tennis team to make a trip to a match to another school?**

**C(10,5)**

**The expectation of x is equal to**

**Sum xf(x)**

**If P(A intersection B) = P(A) P(B) THEN THE events A and B are called**

**Independent**

**A walk that starts and ends at the same vertex is called.**

**None optins**

**How many integers from 1 through 1000 are neither multiple of 3 nor multiple of 5**

**497**

**What is the probability of getting a number greater than 4 when a die is thrown?**

**3/5**

**Eater formula for graphs is___________.**

**F=e-v+2**

**X+a,x+3a,x+5a…..is an____________**

**Arithmetic sequence**

**Composition of a function is a commutative operation.**

**False**

**Real valued function is a function that assigns _____ to each member of its domain.**

**Only a real number**

**Let X={1,2,3,4} and a function ‘f’ defined on X f(1)=1,f(2)=2,f(3)=3,f(4)=4 then ________**

**F is an identity function**

**A constant function is surjective if and only if ____________**

**The co-domain consists of a single element**

**Cardinality means the total number of elements in a set.**

**True**

**If f(x)=2x and g(x)=x then g(f(x)) is _________.**

**2x**^{2}^{}

** Let f:R->R is one to one function then c,f, c is not equal 0 is also one to one function.**

**True**

**Let X={1,2,3,4} and a function ‘f’ defined from X to X by f(1)=1, f(2)=1, f(3)=1, f(4)=1 then which of the following is true?**

**F is a constant function**

**If f and g are two one-to-one functions, then their composition that is gof is one-to-one.**

**True**

**Which of the following is not correct for a ‘sequence’?**

**A sequence is a relation whose domain is the set of natural numbers**

**F(x)=x ^{2} is not one to one function from R to R^{+}**

- True

**Let f: R->R is one to one function then c,f c is not equal to is also one to one function.**

**True**

**Let f(x)=x+2 then f ^{-1}(x) is________**

**x-2**

**Let f(x)=x ^{2}+1 define functions f from R to R and c=2 be any scalar, then c,f(x) is __________.**

**2x**^{2}-1

**One to one correspondence means the condition of __________.**

**Both (a)and (c)**

^{ }**A function F: R-> R defined by f(x) = square root x is a real valued function.**

**False**

**If g:R->R defined by g(x)=e ^{2} is a real valued function of a real variable.**

**True**

**A function F:R-> R defined by f(x) = log x is a real valued function**

**True**

**½, then 3 ^{rd} term of sequence is __________.**

**1/2**

**The process of defining an object in terms of smaller versions of itself is called recursion.**

**True**

**Which of the following is not correct for a ‘sequence’?**

**A sequence is a relation whose domain is the set of natural numbers**

**A set is called countable if, and only if, it is ____________.**

**Finite and countable infinite…..both**

**A set that is not countable is called ___________.**

**Uncountable**

**A sequence whose terms alternate in sign is called an _______.**

**Alternating sequence**

**Let f: R->R is one to one function then c,f is also one to one function for _______.**

**C is not equal 0**

**Let f(x) = x+3 then f ^{-1}(x) is __________-**

**x-3**

**Let f and g be two functions defined by f(x) = x+2 and g(x)= 2x+1. Then the composition of f and g is__________.**

**2x+3**

**Number of one to one functions form X={a,b} to Y={u,v} are equal to ______**

**2**

**The flbonacci sequence is deined as F _{0}=1_{,}F_{ 1}=1_{,} F_{k}=F_{k-1}+F_{k-2} for all integers k> 2 then which of the following is true for F_{2}**

**F**_{2}-F_{1}= 2+1=3

**x+a, x+3a, x+5a,…… is a/an______.**

**Arithmetic sequence**

**Inverse of a function may not be a function.**

**True**

**In the following sequence a _{k}=K/(k+1), for k=1, a_{1} will be __________.**

**½**

**If f(x)=x and g(x)= -x are both one to one function then (f+g)(x) is also one to one function.**

**False**

**If f(x)=x and g(x)= -x are both one to one function then (f+g)(x) is not one to one function.**

**True**

**The function ‘f’ and ‘g’ are inverse of each other if and only if their composition gives_______.**

**Identity function**

**Which of the following set is the domain of a sequence?**

**Set of real numbers**

**Let C is defined as the set of all countries in the world then C is a _________.**

**Finite set**

**A constant function is surjective if and only if________.**

**The co domain consists of a single element**

**The sum of the series a _{1} + a_{2} +a_{3} + …….. can be written as ___________.**

**Inverse of a function may not be a function.**

**True**

**3**

**Let X={1,2,3,4} and a function ‘f’ defined from X to X by f(1)=1, f(2)=1, f(3)=1, f(4)=1 then which of the following is true?**

**F is a constant function**

**The composition of function is always**

**Associative**

**A set is countably infinite if, and only if, it has the same cardinality as the set of**

**Positive integers**

**Two functions ‘f’ and ‘g’ from ‘X’ to ‘Y’ are said to be equal if and only if ______.**

**F(x)=g(x) for all ‘x’ belongs to X**

**Y=x ^{3 }is a graph of bijective function from R to R.**

**True**

**Domain and range are same for___________.**

**Identity funtion**

**Let X={1,2,3,4} and a function ‘f’ defined on X by f(1)=1,f(2)=2,f(3)=3**

**F is an identity function**

**Composition of a function is a commutative operation.**

**True**

**Inverse of a surjective function is always a function.**

**False**

**A function whose inverse function exists is called a/an________.**

**Invertible**

**Given a set X define a function I from X to X by i(x)=x from all x belonging to X . Then_________.**

**I is both injective and surjective**

**Let f: R->R is a one to one function then c,f is also one to one function for.**

**C is not equal 0**

**Let X={1,5,9} and Y={3,4,7}. Define a function f from X to Y such that f(1)=7, f(5)=3, f(9)=______. Which is true for f(9) to make it a one-to-one (injective) function?**

**4**

**Which of the following is not a predecessors of ak?**

**A**_{k}+1

**Two functions ‘f’ and ‘g’ from X to Y are said to be equal if and only if_________.**

**F(x)=g(x) for all ‘x’ belongs to x**

**The two functions ‘f’ and ‘g’ are equal if _______.**

**F(x) =3x and g(x)= 6x**^{2}+3x/2x^{2}+1 for all xeR

**If first term of a geometric sequence is 2 and common ratio is ½, then 3 ^{rd} ter, of sequence.**

**¼**

**Y= squre root x is an __________function form R ^{+ }to R**

**One to one function**

**Y= x ^{2} is an __________function form R to R^{+}**

**NOT ONE TO ONE FUNTION**

**If a function (gof)(x) : X->Z is defined as (gof)(x)=g(f(x)) for all xeX, Then the function__________—.**

**(gof)**

**If 0 is the first term and -2 be the common difference of an arithmetic series, then the sum of first five terms of series is _________.**

**-20**

**If f(x)=sin ^{-1}(x) and g(x) = sin x then gof(x) is ___________.**

**X**

**F: X->Y that is both one to one and onto is called a _________.**

**Bijective function**

**What does ‘y’ denotes in a geometric sequence?**

**Common ratio**

**Let g be a function defined by g(x)=x+1. Then the composition of (gog).**

**X+2**

**A graph of a function f is one to one iff every horizontal line intersects the graph in at most one point.**

**True**

**Which of the following is true for the following sequence?**

**If n is even, then Cn=2 and if n is odd, then Cn = 0**

**The function ‘f’ and ‘g’ are inverse of each other if and only if their composition gives__________.**

**Identity function**

**N! is defined to be ___________.**

**The product of the integers from 1 to n**

**Let A = {1,2,3,4} and B={7} then the constant function from A to B**

**Both one to one and onto**

**A set is called countable if, and only if, it is ___________.**

**Countably infinite and finite**

**If f(x) = x and g(x) = -x are both one to one functions then (f+g)(x) is also one to one function.**

**False**

**If a is the 1st term and d be the common difference of an arithmetic sequence then the sequence is a, a+d, a+2d, a+3d….**

**True**

**x+a, x+3a, x+5…… is a/an_________.**

**Arithmetic sequence**

**inverse of an injective function may not be a function.**

**True**

y=x^{3}** is a graph of bijective function form R to R**

**False**

**Two functions ‘f’ and ‘g’ from x to y are said to be equal if and only if _____.**

**F(x)=g(x) for all ‘x’ belongs to x**

**Common ration in sequence ’36, 12, 4 , 4/3, …..’ is ……**

**1/3**

**A set is called finite if, and only if, is the _______ or there is ———.**

**Empty set or one-to-one**

**Let f(X)=x ^{2}-1 and g(x)=x+1 define functions f and g from R to R, then (f/g)x**

**x-1**

**A graph of a function f is one to one iff every horizontal line intersects the graph in at most one point.**

**True**

**Let g be a function defined by g(x) = x+1. Then the composition of (gog).**

**X+2**

**F:X->Y that is both one to one and onto is called a ___________.**

**Bijective function**

**What does ‘I’ denotes in a geometric sequence?**

**Common ratio**

**Let A={1,2,3,4} and B={7} then the constant function from A to B is ______.**

**Both one to one and onto**

**N! is defined to be ________.**

**The product of the integers from 1 to n**

**A set is called countable if, and only if, it is _________.**

**Both b and c**

**Which of the following is the example of an alternating sequence?**

**C**_{n}=n/n+1 for n__>__0

**X+a, x+3a, x+5a….. is an________**

**Arithmetic sequence**

**0, -5, -10, -15, … is an __________.**

**Arithemetic sequence**

**5, 9, 13, 17, … is an __________.**

**Arithemetic sequence**

**An important data type in computer programming consists of ____________.**

**Finite sequence**

**One-to-one correspondence means the condition of _________.**

**One-one and onto ….both**

**Cardinality means the total number of elements in a set.**

**True**

**Inverse of a function may not be a function.**

**True**

** The functions ‘f’ and ‘g’ are inverse of each other if and only if their composition gives ____________.**

**Identity function**

**A set is called finite if , and only if, it is the _________ or there is ________.**

**Empty set or one-to-one**

**Let f and g be the two functions from R to R defined by f(x) = IXI and g(x) = square root x ^{2} for all xeR, then __________.**

**F(x) is not equal to g(x)**

**If f ^{-1}(x) = 6-x/2 then f^{-1 }(2) is __________.**

**2**

**Let f(2)=3, g(2)=3, f(4)=1 and g(4)=2 then the value of fog(4) is _______.**

**3**

**An important date type in computer programming consists of _——.**

**Finite sequence**

**Let f(x)=x+3 then f ^{-1}(x) is _________.**

**X-3**

**If f:X->Y amd g:Y->Z are both onto function. Then gof : X->Z is _______.**

**One-to-one function**

**The functions ‘f’ and ‘g’ are inverse of each other if and only if their composition gives**

**Identity function**

**The two function ‘f’ and ‘g’ are equal if _____________.**

**F(x) = 3x and g(x) = 6x**^{2}+3x/2x+1 for all xeR

**Two functions ‘f’ and ‘g’ from X To Y are said to be equal if and only if——.**

**F(x) and g(x) for all ‘x’ belongs to X**

**Which of the following set is the domain of a sequence?**

**Set of natural numbers**

**If 1 ^{st} term of a geometric sequence is 2 and common ratio is 1/2 , then 3^{rd} term of sequence is __________.**

**1/2**

**Composition of a function is a commutative operation.**

**True**

**If a function (gof)(x): X-> Z is defined as (gof)(x)=g(f(x)) for all xeX. Then the function _________ is known as composition of f and g.**

**(g o f)**

**A set is countably infinite if and only if and only if, it has the same cardinality as the set of _________.**

**Positive integers**

** The 3 ^{rd} term of the sequence b_{n}=5^{n} is _______.**

**125**

**If f is a bijective function then (f ^{-1}(f(x)) Is equal to _____.**

**X**

**Let f(x) = x and g(x) = -x for all xeR, then (f+g)(x) is ____.**

** 0**

** An infinite sequence may have only a finite number of values.**

**True**

**The functions fog and gof are always equal .**

**False**

**If f and g are two one-to-one functions, then their composition that is gof is one-to-one.**

**True**

**A function whose range consists of only one element is called ___________.**

**Constant function**

**Let X ={1,5,9} and Y={3,4,7}. Define a function f from X to Y such that f(1)=7, f(5)=3, f(9)=4 then which of the following statement about ‘f’ is true?**

**F is both one-to-one and onto**

**Y=x ^{3} is a graph of bijective function from R to R.**

**True**

**A function whose inverse function exists is called a/an______.**

**Invertible**

**Let F and g be two functions defined by f(x)= x+2 and g(x)= 2x+1. Then the composition of f and g is _____.**

**2x + 5**

**If r is a positive real number, then the value of r in 3, r,r=-27r is **

**-9**

**The _____ of the terms of a sequence forms a series.**

**Sum**

**The sum of first five whole number is _________.**

**10**

**If f _{k}=f_{k}-1+f_{k}-2then f_{0}=1_{ , }f_{1}=2, then f_{2}= __________.**

**3**

**Let f(x) = 3x and g(x) = x + 2 define functions f and g from R to R, then (f.g)(x) is _____.**

- 3x
^{2}+ 6x

**Let R be a relation on a set A. If R is reflexive then its compliment is ________ .**

- Irreflexive

**If A = Set of students of virtual university then A has been written in the _________.**

**Descriptive form**

**If a function (g o f)(x):X→Z is defined as (g o f)(x) = g(f(x)) for all x ****∈**** X. Then the function ________ is known as composition of f and g.**

**(g o f)**

**If X and Y are independent random variables and a and b are constants, then Var(aX + bY)is equal to**

**aVar(X) + bVar(Y)**

**Let A = {1, 2, 3} and B = {2, 4} then number of functions from A to B are _________.**

**8**

**p is equivalent to q’ means ________.**

**p is necessary and sufficient for q.**

**Let A and B be subsets of U with n(A) = 12, n(B) = 15, n(A’) = 17, and n(A intersection B) = 8, then n(U)=______ .**

**29**

**For the following relation to be a function, x can not be what values?R = {(2,4), (x,1), (4,2), (5,6)}**

**x cannot be 2, 4 or 5**

**Find the number of the word that can be formed of the letters of the word “ELEVEN”.**

**120**

**There are three bus lines between A and B, and two bus lines between B and C. Find the number of ways a person can travel round trip by bus from A to C by way of B?**

- 6

**Among 20 people, 15 either swim or jog or both. If 5 swim and 6 swim and jog, how many jog?**

**16**

**A predicate becomes _________ when its variables are given specific values.**

**statement**

**Find the number of distinct permutations that can be formed using the letters of the word ”BENZENE”**

**420**

**Suppose there are 8 different tea flavors and 5 different biscuit brands. A guest wants to take one tea and one brand of biscuit. How many choices are there for this guest?**

**40**

**In how many ways a student can choose one of each of the courses when he is offered 3 mathematics courses, 4 literature courses and 2 history courses.**

**24**

**If p ↔ q is True, then ________.**

**p and q both are True**.

**If A and B be events with P(A) = 1/3, P(B) = 1/4 and P(A ∩ B) = 1/6, then P(A ****∪**** B) = ________ .**

**5/12**

**an integer n is a perfect square if and only if ________ for some integer k.**

**n = k^2**

**If A and B are disjoint finite sets then n(A ****∪**** B) = ______.**

- n(A) + n(B)

**Let X = {2, 4, 5} and Y= {1, 2, 4} and R be a relation from X to Y defined by R = {(2,4), (4,1), (a,2)}. For what value of ‘a‘ the relation R is a function ?**

**5**

**∼****(P → q) is logically equivalent to _________.**

**p****∧****∼****q**

**A tree is normally constructed from ________.**

**left to right**

**A Random variable is also called a _________.**

**Chance Variable**

**The conjunction p ****∧**** q is True when _________.**

**p is True, q is True**

**The logical statement p ****∧**** q means ________.**

**p AND q**

**Which of the followings is the factorial form of 5 . 4?**

**5!/3!**

**What is the minimum number of students in a class to be sure that two of them are born in the same month?**

**13**

**If p is false and q is true, then ****∼****p ↔ q is ________.**

**True**

**If f and g are two one-to-one functions, then their composition that is gof is one-to-one.**

**TRUE**

**( p ****∨**** ****∼****p ) is the ________.**

**Tautology**

**(-2)! = _________ ?**

**Undefined**

**If p = It is raining, q = She will go to college“It is raining and she will not go to college”will be denoted by**

**p****∧****∼****q**

**Let X = {1, 2, 3}, then 2-combinations of the 3 elements of the set X are _________?**

**{1, 2}, {1, 3} and {2, 3}**

**Let f(x) = x ^{2} + 1 define functions f from R to R and c = 2 be any scalar, then c.f(x) is ______.**

**2x**^{2}+ 2

**The disjunction of p and q is written as ________.**

**p****∨****q**

**If X and Y are independent random variables, then E(XY) is equal to**

**E(x)E(y)**

**How many possible outcomes are there when a fair coin is tossed four times?**

**16**

**Which of the followings is the product set A * B * C ? where A = {a}, B = {b}, and C = {c, d}.**

**{(a, b, c), (a, b, d)}**

**The number of the words that can be formed from the letters of the word,“COMMITTEE” are**

**9! / (2!2!2!)**

**One-to-One correspondence means the condition of ______.**

**One-One and onto**

**The functions f o g and g o f are always equal.**

**FALSE**

**If order matters and repetition is allowed, then which counting method should be used in order to select ‘k’ elements from a total of ‘n’ elements?**

**K-Sample**

** Determine values of x and y, where (2x, x + y) = (8, 6).**

**x = 4 and y = 2**

**Let g be a function defined by g(x) = x + 1. Then the composition of (g o g)(x)is ______.**

**x + 2**

**What is the truth value of the sentence?**

‘It rains if and only if there are clouds.’

**False**

**Reductio and absurdum’ is another name of _________.**

**Proof by contradiction**

**X belongs to A or x belongs to B, therefore x belongs to ________.**

**A union B**

**Which of the followings is the product set A * B * C? Where A = {a}, B = {b}, and C = {c, d}.**

**{(a, b, c), (a, b, d)}**

**Real valued function is a function that assigns _______ to each member of its domain.**

**Only a real number**

**The negation of “Today is Friday” is**

**Today is not Friday**

** A non-zero integer d divides an integer n if and only if there exists an integer k such that _________.**

**n = d k**

**The statement p → q is logically equivalent to ****∼****q → ****∼****p**

**True**

**Let R be the universal relation on a set A then which one of the following statement about R is true?**

**R is reflexive, symmetric and transitive.**

**Let f(x)=3x and g(x) = 3x − 2 define functions f and g from R to R. Then (f+g)(x) = ________.**

**6x − 2**

**The switches in parallel act just like ________.**

**OR gate**

**The converse of the conditional statement p → q is**

**q → p**

**If X and Y are random variables, then E(aX) is equal to**

**aE(X)**

**Which of the following statements is true according to the Division Algorithm?**

**17 = 5 x 3 + 2**

**Let p → q be a conditional statement, then the statement q → p is called ________.**

**Converse**

**The disjunction p ****∨**** q is False when ________.**

**P is False, q is False.**

**A student can choose a computer project from one of the two lists. The two lists contain 12 and 18 possible projects, respectively. How many possible projects are there to choose from?**

**30**

**The converse of the conditional statement ‘If I live in Quetta, then I live in Pakistan’ is ________.**

**If I live in Pakistan, then I live in Quetta**.

**The functions ‘f’ and ‘g’ are inverse of each other if and only if their composition gives _______.**

**Identity function**

**P (0, 0)=______?**

**1**

**Let p1, p2, p3 be True premises in a given Truth Table. If the conjunctions of the Conclusion with each of p1, p2, p3 are True, then the argument is ________.**

**Valid**

**If p is false and q is false, then ****∼****p implies q is ________.**

**False**

**A box contains 5 different colored light bulbs. Which of the followings is the number of ordered samples of size 3 with replacement?**

**125**

**Let A = {2, 3, 5, 7}, B = {2, 3, 5, 7, 2}, C = Set of first five prime numbers. Then from the following which statement is true ?**

**A = B**

**The set of prime numbers is _________.**

**Infinite set**

**The contrapositive of the conditional statement ‘If it is Sunday, then I go for shopping’ is ________.**

**I do Not go for shopping, then it is Not Sunday.**

**Let p be True and q be True, then ( ****∼****p ****∧**** q ) is ________.**

**False**

**In how many ways a student can choose a course from 2 science courses,3 literature courses and 5 art courses.**

**30**

**The method of loop invariants is used to prove __________ of a loop with respect to certain pre and post-conditions.**

**correctness**

**A student is to answer five out of nine questions on exams. Find the number of ways that can choose the five questions**

**126**

**If A and B are any two sets, then A − B = B – A**

**False**

**There are 5 girls students and 20 boys students in a class. How many students are there in total?**

**25**

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