## Objective Questions

*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 |

*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*

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

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

Answer: 2 | Chapter No. 36 |

*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*

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*

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 U 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*

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*

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*

A tree is normally constructed from ______.

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

Answer: 3 | Chapter No. 33 |

*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*

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*

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*

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*

(-2)! = _________ ?

- -2
- 0
- 2
- Undefined

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*

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

- 120
- 6
- 12
- 720

Answer: 4 | Chapter No. 30 |

*Question*

P(0, 0)=______?

- 0
- 1
- 2
- undefined

Answer: 2 | Chapter No. 30 |

*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 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*

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*

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*

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*

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 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*

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*

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*

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

- sentence
- statement
- algorithm
- iteration

Answer: 2 | Chapter No. 27 |

*Question*

The set of prime numbers is _________.

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

Answer: 2 | Chapter No. 26 |

*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*

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*

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*

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*

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*

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 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*

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 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*

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*

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*

If A And B are any two sets, then A-B= B-A

- True
- False

Answer: 2 | Chapter No. 8 |

*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*

The switches in parallel act just like ________.

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

Answer: 3 | Chapter No. 5 |

*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*

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 AND ~ q
- p OR ~q
- ~p AND q
- ~p OR q

Answer: 1 | Chapter No. 3 |

*Question*

The conjunction p and 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 |