## Discrete Mathematics MCQ1) If x is a set and the set contains an integer which is neither positive nor negative then the set x is ____________. - Set is Empty
- Set is Non-empty
- Set is Finite.
- Set is both Non- empty and Finite.
2) If x ∈ N and x is prime, then x is ________ set. - Infinite set
- Finite set
- Empty set
- Not a set
3) If x is a set and the set contains the real number between 1 and 2, then the set is ________. - Empty set
- Finite set
- Infinite set
- None of the mentioned
4) Which of the following is a subset of set {1, 2, 3, 4}? - {1, 2}
- {1, 2, 3}
- {1}
- All of the mentioned
5) Convert the set x in roster form if set x contains the positive prime number, which divides 72. - {∅}
- {2, 3}
- {2, 3, 7}
- {3, 5, 7}
6) Power set of empty or Null set has exactly _________ subset. - One
- Two
- Zero
- Three
7) What is the Cartesian product of set A and set B, if the set A = {1, 2} and set B = {a, b}? - { (1, a), (1, b), (2, a), (b, b) }
- { (1, 1), (2, 2), (a, a), (b, b) }
- { (1, a), (2, a), (1, b), (2, b) }
- { (1, 1), (a, a), (2, a), (1, b) }
8) The members of the set S = {x | x is the square of an integer and x < 100} is ________________ - {0, 2, 4, 5, 9, 55, 46, 49, 99, 81}
- {1, 4, 9, 16}
- {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
- {0, 1, 4, 9, 25, 36, 49, 123}
9) The intersection of the sets {1, 2, 8, 9, 10, 5} and {1, 2, 6, 10, 12, 15} is the set _____________ - {1, 2, 10}
- {5, 6, 12, 15}
- {2, 5, 10, 9}
- sd) {1, 6, 12, 9, 8}
10) The difference of {1, 2, 3, 6, 8} and {1, 2, 5, 6} is the set ____________ - {1, 3}
- {5, 6, 8}
- {3, 8}
- {2, 6, 5}
11) If n(A) = 20 and n(B) = 30 and n(A U B) = 40 then n(A ∩ B) is? - 20
- 30
- 40
- 10
n(A U B) = n(A) + n(B) - n(A ∩ B). n(A ∩ B) = n(A) + n(B) - n(A U B) n(A ∩ B) = 20 + 30 - 40 So, n(A ∩ B) = 10 12) Let the players who play cricket be 12, the ones who play football 10, those who play only cricket are 6, then the number of players who play only football are ___________, assuming there is a total of 16 players. - 16
- 8
- 4
- 10
13) Which among the following can be taken as the discrete object? - People
- Rational numbers
- Integers
- All of the mentioned
14) Which option contains two equal sets? - X = {5, 6} and Y = {6}
- X = {5, 6, 8, 9} and Y = {6, 8, 5, 9}
- X = {5, 6, 9} and Y = {5, 6}
- X = {5, 6} and Y = {5, 6, 3}
15) The cardinality of the Power set of the set {1, 5, 6} is______________. - 5
- 6
- 8
- 10
16) The Cartesian product of the (Set Y) x (Set X) is equal to the Cartesian product of (Set X) x (Set Y) or Not? - Yes
- No
- None of the above
- I Don't know
Let's suppose X = {5, 6, 7} and Y = {a, b, c}. The Cartesian product of (set X) x (set Y) = {(5, a), (5, b), (5, c), (6, a), (6, b), (6, c), (7, a), (7, b), (7, c) } and the Cartesian product of (set Y) x (set X) = {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7), (c, 5), (c, 6), (c, 7)}. So, both the Cartesian product are not equal. 17) How many elements in the Power set of set A= {{Φ}, {Φ, {Φ}}}? - 4 elements
- 2 elements
- 6 elements
- 5 elements
18) Mathematics can be broadly categorized into how many types? - 3 types
- 2 types
- 5 types
- 4 types
19) Which of the following function is not a mathematics function? - many to one
- one-to-many
- one to one
- All of the mentioned
20) Which of the following function is also referred to as an injective function? - Many-to-one
- Onto
- One-to-One
- None of the mentioned
21) How many injections are defined from set A to set B if set A has 4 elements and set B has 5 elements? - 24
- 64
- 144
- 120
Number of injections from set A to Set B= 5p 5! / (5 - 4)! = 5 x 4 x 3 x 2 = 120 22) The function (gof) is _________ , if the function f and g are onto function? - Into function
- one to one function
- onto function
- one-to-many function
23) How many bytes are needed for encoding 2000 bits of data? - 5 Byte
- 2 bytes
- 4 bytes
- 8 bytes
24) The cardinality of the set of even positive integers less than 20 is__________? - 8
- 10
- 9
- 12
25) If X = {2, 8, 12, 15, 16} and Y= {8, 16, 15, 18, 9} then union of X and Y is___________. - {2, 8, 12, 15, 16}
- { 8, 16, 15}
- {8, 16, 15, 18, 9}
- {2, 8, 9, 12, 15, 16, 18}
26) What is Floor function? - It maps the real number to the greatest previous integer
- It maps the real number to the smallest previous integer
- It maps the real number to the smallest following integer
- None of the mentioned
27) What is Ceil function? - It maps the real number to the greatest previous integer
- It maps the real number to the smallest previous integer
- It maps the real number to the smallest following integer
- None of the mentioned
28) What is the value of Floor(8.4) + Ceil(9.9)? - 18
- 19
- 20
- 17
29) If a and b are two positive numbers that are less than one, then the maximum value of Floor(a+b) and Ceil(a+b) is? - Floor(a+b) is 0 and Ceil(a+b) is 1.
- Floor(a+b) is 1 and Ceil(a+b) is 0.
- Floor(a+b) is 1 and Ceil(a+b) is 2.
- Floor(a+b) is 2 and Ceil(a+b) is 1
30) How many relations exist from set X to set Y if the set X and set Y has 7 and 8 elements? - 2
^{56} - 2
^{72} - 3
^{56} - 56
31) The number of reflexive closure of the relation {(0,1), (1,1), (1,3), (2,1), (2,2), (3,0)} on the set {0, 1, 2, 3} is________. - 36
- 8
- 6
- 2
^{6}
32) The number of transitive closure exists in the relation R = {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} where {1, 2, 3, 4, 5} ∈ A is__________. - {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}
- {(0,0), (4,4), (5,5), (1,1), (2,2), (3,3)}
- {(0,1), (1,2), (2,2), (3,4)}
- {(0,1), (5,3), (5,4), (1,1), (2,2)}
33) Which statement is incorrect if X and Y are the two non-empty relations on the set S. - If X and Y are transitive, then the intersection of X and Y is also transitive.
- If X and Y are reflexive, then the intersection of X and Y is also reflexive.
- If X and Y are symmetric, then the union of X and Y is not symmetric.
- If X and Y are transitive, then the union of X and Y is not transitive.
34) Which option is the negation of the bits "1001011"? - 11011011
- 10110100
- 0110100
- 1100100
35) What is the output of X (Ex-or) Y, if the bits of X is 001101 and the bits of Y is 100110? - Output of X (Ex-or) Y is 101011
- Output of X (Ex-or) Y is 1101010
- Output of X (Ex-or) Y is 101000
- Output of X (Ex-or) Y is 0010101
36) Boolean algebra deals with how many values. - It deals with only four discrete values.
- It deals with only five discrete values.
- It deals with only three discrete values.
- It deals with only two discrete values.
37) Which of the following Law of Boolean proofs the X.X=X? - Identity Law
- Double Complement Law
- Complement Law
- Idempotent Law
38) According to the symmetric matrix, which of the following statement is correct? - A = A
^{T} - All the diagonal elements of a symmetric matrix are One.
- A = -A
^{T} - All the diagonal elements of a symmetric matrix are Zero.
39) Which of the following matrix having only one row and multiple columns? - Diagonal Matrix
- Row Matrix
- Column Matrix
- None of the mentioned
Following are the various examples of row matrix: 1. [ 6 5 4 ]: The order of this matrix 1 x 3, i.e., 1 row and three columns. 2. [ 0 ]: The order of this matrix is 1 x 1, i.e., 1 row and 1 column. 3. [ 1 2 0 6 8 9 ]: The order of this matrix is 1 x 6, i.e., 1 row and 6 column. 40) Which of the following matrix having only one column and multiple rows? - Diagonal Matrix
- Row Matrix
- Column Matrix
- None of the mentioned
41) Which of the following condition is correct if we want to add two matrices? - Both rows and columns of both the matrices which we want to add are the same
- Columns of both the matrices which we want to add are equal
- Rows of both the matrices which we want to add are the same
- a number of the first matrix's rows should be equal to the number of the second matrix's column, which we want to add.
42) A+B = B+A is a true or false statement if the order of A matrix and B matrix is the same. - False
- True
43) XY = YX is a true or false statement if the order of A matrix and B matrix is the same. - False
- True
44) Universal logic gate is__________. - OR
- NOT
- NAND
- AND
45) In which year Maurice Karnaughin introduced the Karnaugh map? - 1953
- 1956
- 1952
- 1950
46) Canonical forms for a boolean expression has _______ types. - Three types
- Four types
- Two types
- Five types
47) The use of Boolean algebra is ____________. - in building the algebraic functions.
- in building logic symbols.
- in circuit theory.
- in designing the digital computers.
48) Boolean algebra deals with how many values. - It deals with only four discrete values.
- It deals with only five discrete values.
- It deals with only three discrete values.
- It deals with only two discrete values.
49) Which search compares each element with the searching element till not found? - Merge search
- Sequential Search
- Binary search
- none of the mentioned
50) If a user wants to sort the unsorted list of n elements, then the insertion sort starts with which element of the list. - First element of the list
- the second element of the list
- the Third element of the list
- the Fourth element of the list
51) What is the complexity of the bubble sort algorithm? - O(n
^{2}) - O(n)
- O(log n)
- O(n log n)
52) What is the worst case of a linear search algorithm? - When the searching item is present in the middle of the list.
- When the searching item is the last element in the list.
- When the searching is not available in the list.
- When the searching item is the last element in the list or is not present in the list.
53) Which algorithm uses the previous outputs for finding the new outputs? - Dynamic Programming algorithms
- Divide and Conquer algorithm
- Brute Force algorithm
- None of them
54) Which option is correct for representing an algorithm? - Pseudo codes
- Flow charts
- Statements in the common language
- All of them
55) Which case does not exist in complexity theory? - Average case
- Null case
- Best case
- Worst Case
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