MTH202 Solved Grand Quiz Spring 2021

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MTH202  Solved Grand Quiz Spring 2021

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)Ix2=y2}. 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)Ix2=y2}. 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) = x2-1 define function f from R to R and c=2 be any scalar, then c,f(x) is __________

  • 2x2+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 x2 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 {A1,A2} then

  • A1nA2= 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 ________

  • 2n

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 ,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-1f(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 _________.

  • 2x2

 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)=x2 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)=x2+1 define functions f from R to R and c=2 be any scalar, then c,f(x) is __________.

  • 2x2-1

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)=e2 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 3rd 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 F0=1,F 1=1, Fk=Fk-1+Fk-2  for all integers k> 2 then which of the following is true for F2

  • F2-F1= 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 ak=K/(k+1), for k=1, a1 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 a1 + a2 +a3 + …….. 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=xis 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?

  • Ak+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)= 6x2+3x/2x2+1 for all xeR

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

  • ¼

Y= squre root x is an __________function form R+ to R

  • One to one function

Y= x2 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=x3 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)=x2-1 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?

  • Cn=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 x2 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) = 6x2+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 1st term of a geometric sequence is 2 and common ratio is 1/2 , then 3rd 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 3rd term of the sequence bn=5n 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=x3 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 fk=fk-1+fk-2then f0=1 , f1=2, then f2= __________.

  • 3

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

  • 3x2 + 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) = x2 + 1 define functions f from R to R and c = 2 be any scalar, then c.f(x) is ______.

  • 2x2 + 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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