## Objective Questions

*Question*

The conjunction p ∧ q is True when _________.

- p is True, q is False
- p is False, q is True
- p is True, q is True
- p is False, q is False

Answer: 3 | Chapter No. 1 |

*Question*

The disjunction of p and q is written as ________.

- p ∨ q
- p ∧ q
- p XOR q
- None of the given

Answer: 1 | Chapter No. 1 |

*Question*

The logical statement p ∧ q means ________.

- p OR q
- p NOT q
- p AND q
- p XOR q

Answer: 3 | Chapter No. 1 |

*Question*

The disjunction p ∨ q is False when ________.

- p is False, q is True.
- p is True, q is False.
- p is True, q is True.
- p is False, q is False.

Answer: 4 | Chapter No. 1 |

*Question*

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
- p ∧ q
- ∼(p ∧ q)
- ∼p ∧ q

Answer: 1 | Chapter No. 1 |

*Question*

The negation of “Today is Friday” is

- Today is Saturday
- Today is not Friday
- Today is Thursday
- None of the given

Answer: 2 | Chapter No. 1 |

*Question*

( p ∨ ∼p ) is the ________.

- Contradiction
- Conjunction
- Tautology
- Contingency

Answer: 3 | Chapter No. 2 |

*Question*

The converse of the conditional statement p → q is

- q → p
- ∼q → ∼p
- ∼p → ∼q
- None of the given

Answer: 1 | Chapter No. 3 |

*Question*

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

Answer: 1 | Chapter No. 3 |

*Question*

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

- t ( where t is tautology. )
- c ( where c is contradiction. )
- True
- False

Answer: 4 | Chapter No. 3 |

*Question*

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

- True
- False

Answer: 1 | Chapter No. 3 |

*Question*

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

- Inverse
- Converse
- Contrapositive
- Double conditional

Answer: 2 | Chapter No. 3 |

*Question*

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

- True
- False

Answer: 2 | Chapter No. 3 |

*Question*

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.
- If I live in Pakistan, then I do Not live in Quetta.
- If I do Not live in Quetta, then I do Not live in Pakistan
- If I do Not live in Quetta, then I live in Pakistan

Answer: 1 | Chapter No. 3 |

*Question*

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

- p ∧ ∼q
- p ∨ ∼q
- ∼p ∧ q
- ∼p ∨ q

Answer: 1 | Chapter No. 3 |

*Question*

If p ↔ q is True, then ________.

- Only p is True.
- Only q is True.
- p and q both are True.
- None of the given.

Answer: 3 | Chapter No. 4 |

*Question*

What is the truth value of the sentence?

**'It rains if and only if there are clouds.'**

- True
- False

Answer: 2 | Chapter No. 4 |

*Question*

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

- True
- False

Answer: 1 | Chapter No. 4 |

*Question*

'p is equivalent to q' means ________.

- p is not necessary but p is sufficient for q.
- p is neither necessary nor sufficient for q.
- p is necessary and sufficient for q.
- p is necessary but not sufficient for q.

Answer: 3 | Chapter No. 4 |

*Question*

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 ________.

- False
- True
- Invalid
- Valid

Answer: 4 | Chapter No. 5 |

*Question*

The switches in parallel act just like ________.

- NOT gate
- AND gate
- OR gate
- XOR gate

Answer: 3 | Chapter No. 5 |

*Question*

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
- A = C
- B = C
- All the three sets are equal.

Answer: 1 | Chapter No. 7 |

*Question*

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

- Tabular form
- Set builder form
- Descriptive form
- A is not a set

Answer: 3 | Chapter No. 7 |

*Question*

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

- True
- False

Answer: 2 | Chapter No. 8 |

*Question*

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

- A intersection B
- A union B
- A difference B
- A symmetric difference B

Answer: 2 | Chapter No. 8 |

*Question*

Range of the relation {(0,1), (3,22), (90,34)} is __________ .

- {0, 3, 90}
- {1, 22, 34}
- {0, 1, 3}
- {0, 1, 3, 22, 90, 34}

Answer: 2 | Chapter No. 11 |

*Question*

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

Answer: 1 | Chapter No. 11 |

*Question*

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

- x = 3 and y = 5
- x = 4 and y = 2
- x = 6 and y = 12
- x = 4 and y = 12

Answer: 2 | Chapter No. 11 |

*Question*

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

- R is not symmetric
- R is not reflexive
- R is not transitive
- R is reflexive, symmetric and transitive.

Answer: 4 | Chapter No. 12 |

*Question*

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

- Reflexive
- Irreflexive
- Symmetric
- Antisymmetric

Answer: 2 | Chapter No. 14 |

*Question*

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

- Reflexive
- Irreflexive
- Symmetric
- Antisymmetric

Answer: 2 | Chapter No. 14 |

*Question*

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

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

Answer: 2 | Chapter No. 14 |

*Question*

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

- Reflexive
- Irreflexive
- Symmetric
- Antisymmetric

Answer: 2 | Chapter No. 14 |

*Question*

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
- R1 and R2 are functions
- R2 and R4 are functions
- R3 and R2 are functions

Answer: 1 | Chapter No. 15 |

*Question*

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
- x cannot be 4, 1 or 6
- x cannot be 2, 4 or 6
- x cannot be 1, 2 or 6

Answer: 1 | Chapter No. 15 |

*Question*

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 ?

- 1
- 2
- 4
- 5

Answer: 4 | Chapter No. 15 |

*Question*

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

- 6
- 8
- 16
- 64

Answer: 2 | Chapter No. 15 |

*Question*

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

- Onto
- One to one
- Both one to one and onto
- Neither one to one nor onto

Answer: 1 | Chapter No. 16 |

*Question*

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

- one-One
- identity
- onto
- one-One and onto

Answer: 4 | Chapter No. 16 |

*Question*

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.

- (f o g)
- f
^{-1}(g(x)) - (g o f)
- g
^{-1}(f(x))

Answer: 3 | Chapter No. 17 |

*Question*

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

- x
- x + 1
- x + 2
- x
^{2}+ 2x + 1

Answer: 3 | Chapter No. 17 |

*Question*

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

- constant function
- identity function
- bijective function
- injective function

Answer: 2 | Chapter No. 17 |

*Question*

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

- TRUE
- FALSE

Answer: 2 | Chapter No. 17 |

*Question*

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

- empty set, onto
- empty set, one-to-one
- one-to-one, onto
- empty set, bijective

Answer: 2 | Chapter No. 18 |

*Question*

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

- TRUE
- FALSE

Answer: 1 | Chapter No. 18 |

*Question*

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

- 2
- x
^{2}+ 1 - 2x
^{2}- 1 - 2x
^{2}+ 2

Answer: 4 | Chapter No. 18 |

*Question*

The set Z of all integers is _____.

- uncountable
- countable

Answer: 2 | Chapter No. 18 |

*Question*

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

- 2x − 2
- 3x + 2
- 4x + 2
- 3x
^{2}+ 6x

Answer: 4 | Chapter No. 18 |

*Question*

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

- negative real number
- positive real number
- only a real number
- any arbitrary real number

Answer: 3 | Chapter No. 18 |

*Question*

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

- −2
- 6x + 2
- 6x − 2
- 6x.x − 2

Answer: 3 | Chapter No. 18 |

*Question*

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

- 9
- 10
- 11
- infinite

Answer: 3 | Chapter No. 20 |

*Question*

If r is a positive real number, then the value of r in 3.r.r = −27r is ________.

- −9
- +9
- 0
- None of the given

Answer: 1 | Chapter No. 25 |

*Question*

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

- n = 2k
- n = k^2
- n = square-root of k
- n = k^3

Answer: 2 | Chapter No. 25 |

*Question*

Reductio and absurdum' is another name of _________.

- Direct Method of proof
- proof by contradiction
- proof by contapositive
- None of the given

Answer: 2 | Chapter No. 26 |

*Question*

The set of prime numbers is _________.

- finite set
- infinite set
- continuous set
- None of the given

Answer: 2 | Chapter No. 26 |

*Question*

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

- sentence
- statement
- algorithm
- iteration

Answer: 2 | Chapter No. 27 |

*Question*

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

- 17 = 5 x 1 + 12
- 17 = 5 x 3 + 2
- 17 = 5 x 4 - 3
- 17 = 5 x 5 - 8

Answer: 2 | Chapter No. 27 |

*Question*

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

- n = d / k
- n = d k
- n = d + k
- n = d - k

Answer: 2 | Chapter No. 27 |

*Question*

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

- falseness
- correctness

Answer: 2 | Chapter No. 27 |

*Question*

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?

- 5
- 6
- 10
- 36

Answer: 2 | Chapter No. 29 |

*Question*

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?

- 12
- 18
- 30
- 216

Answer: 3 | Chapter No. 29 |

*Question*

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?

- 5
- 8
- 13
- 40

Answer: 4 | Chapter No. 29 |

*Question*

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.

- 9
- 24
- 288
- 14

Answer: 2 | Chapter No. 29 |

*Question*

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

- 4
- 15
- 25
- 100

Answer: 3 | Chapter No. 29 |

*Question*

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-Selection
- K-Sample
- K-combination
- K-Permuatation

Answer: 2 | Chapter No. 30 |

*Question*

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

- 30
- 10
- 1440
- 240

Answer: 1 | Chapter No. 30 |

*Question*

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

- 5/3
- 5!/3
- 5!/3!
- 5/3!

Answer: 3 | Chapter No. 30 |

*Question*

In how many ways can 6 people be seated on 6 available seats?

- 120
- 6
- 12
- 720

Answer: 4 | Chapter No. 30 |

*Question*

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

- 4
- 8
- 16
- 32

Answer: 3 | Chapter No. 30 |

*Question*

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

- 8
- 15
- 125
- 243

Answer: 3 | Chapter No. 30 |

*Question*

P(0, 0)=______?

- 0
- 1
- 2
- undefined

Answer: 2 | Chapter No. 30 |

*Question*

(-2)! = _________ ?

- -2
- 0
- 2
- Undefined

Answer: 4 | Chapter No. 30 |

*Question*

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

- {1, 2}, {1, 3} and {2, 3}
- {1, 2}, {2, 1}, {1, 3}, {3, 1}, {2, 3}, and {3, 2}
- {1, 2}, {2, 1}, {1, 3} and {2, 3}
- {1, 2}, {2, 1},{1, 3} and {3, 1}

Answer: 1 | Chapter No. 31 |

*Question*

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

- 216
- 316
- 126
- None of the given

Answer: 3 | Chapter No. 31 |

*Question*

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

- 120
- 110
- 220
- None of the given

Answer: 1 | Chapter No. 32 |

*Question*

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

- 120
- 220
- 320
- 420

Answer: 4 | Chapter No. 32 |

*Question*

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

- 9p9
- 9C9
- 9! / (2!2!2!)
- None of the given

Answer: 3 | Chapter No. 32 |

*Question*

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

- 6
- 16
- 24
- 46

Answer: 2 | Chapter No. 33 |

*Question*

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

Answer: 1 | Chapter No. 33 |

*Question*

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

- n(A) − n(B)
- n(A) + n(B) − n(A ∩ B)
- n(A) + n(B)
- n(A) + n(B) + n(A ∩ B)

Answer: 3 | Chapter No. 33 |

*Question*

A tree is normally constructed from ________.

- right
- center
- left to right
- right to left

Answer: 3 | Chapter No. 33 |

*Question*

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)=______ .

- 27
- 29
- 20
- 35

Answer: 2 | Chapter No. 33 |

*Question*

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

- 11
- 12
- 13
- 14

Answer: 3 | Chapter No. 34 |

*Question*

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) = ________ .

- 2/3
- 5/12
- 1/24
- 1/2

Answer: 2 | Chapter No. 36 |

*Question*

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)
- (a + b)[Var(X) + Var(Y)]
- Var(aX) + Var(bY)
- a^2 Var(X) + b^2 Var(Y)

Answer: 1 | Chapter No. 38 |

*Question*

A Random variable is also called a _________.

- Chance Variable
- Constant

Answer: 1 | Chapter No. 38 |

*Question*

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

- E(XY)
- XE(Y)
- YE(X)
- E(x)E(y)

Answer: 4 | Chapter No. 38 |

*Question*

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

- E(aX)
- aE(X)
- aX
- None of the given

Answer: 2 | Chapter No. 38 |