Online MCQ Assignment Test

In question 1 through 5, classify the sets as finite or infinite set.
1. Set of four seasons in year
2. Set of vowels in word “fitted”
3. Set of multiples of 8 more than 95 and less than 97
4. Set of months of the year
5. Set of vowels in word “command”
Answers:

1. Finite Set
2. Finite Set
3. Finite Set
4. Finite Set
5. Finite Set

In question 6 through 10, classify the sets as empty or singleton set.
6. Set of multiples of 2 more than 0 and less than 4
7. {0}
8. Set of vowels in word “call”
9. Set of vowels in word “fair”
10 {9}
Answers:

1. Empty Set (consist of no elements)
2. Singleton Set (consist of one elements)
3. Singleton Set (consist of one elements)
4. Singleton Set (consist of one elements)
5. Singleton Set (consist of one elements)

In question 11 through 17, classify the non – equivalent or equal sets.
11. A= Set of vowels in word “ bottom”, B= Set of vowels in “word bottom”
12. A= {a, b, c, d, e, f, g ,h, x} B== {1 ,2, 3, 4, 5, 6, 7, 8, 24}
13. A = Set of vowels in word “March”, B = Set of vowels in word “May”
14. A = Set of multiples of 12, B = {12, 24, 36……}
15. A = Set of letters in “finance”, B = Set of letters in “mathematics”
16. A = Set of multiples of 12, B = {12, 24, 36……}
17. A = Set of multiples of 7, B = {7, 14, 21……}
Answers:

1. Non – equivalent Set
2. Non – equivalent Set
3. Equal Set
4. Equal Set
5. Non – equivalent Set
6. Equal Set
7. Equal Set

In question 18 through 21, find the truth table.
18. For every integer n, (2n+1) is an even integer.
19. f(x) = Cos x implies f’(x) = -Sin x

1. 20. The sum of one even and one odd integer is even integer
2. 21. 5+6=11

Answers:

1. True (if n=1, then 2n+1=3, integer: if n=2, 2n+1=5, integer: so the statement if true)
2. False ( if x=0 then cos0=1, sin0=0: so the statement is false)
3. True (if even number is 2, & odd number is 1 than the sum will 3: which is integer. So the statement is true)
4. True
5. 22. Calculate the arithmetic mean of 5.7, 6.6, 7.2, 9.3, and 6.2.

Answers: 7 (5.7+6.6+7.2+9.3+6.2=35: 35/5=7)
In question 23 through 25, the marks obtained by 12 students in a class test are
14, 13, 09, 19, 05, 08, 16, 17, 11, 10, 12, 16.
Find
23. The mean of their marks.
24. The mean of their marks when the marks of each student are increased by 3.
25. The mean of their marks when the marks of each student are doubled.
Answers:

1. Mean=12.5(sum of marks=150, mean 150/12)
2. Mean=15.5( sum of marks=186, mean 186/12)
3. Mean=24.17( sum of marks=290, mean290/12)

26. The number of vertices of odd degree in a graph is
a) always even b) always odd
c) either even or odd d) always zero
Answer: a) always even
27. A vertex of degree one is called as
a) Pendant b) isolated vertex
c) null vertex d) colored vertex
Answer: a) pendant

1. 28. A circuit in a connected graph, which includes every vertex of the graph is known

a) Euler b) Universal
c) Hamilton d) None of these
Answer: b) Universal

1. 29. A given connected graphic is a Euler graph if and only if all vertices of G are of

a) same degree b) even degree
c) odd degree d) different degrees
Answer: b) even degree

1. 30. The length of Hamilton path (if exists) in a connected graph of n vertices is

a) n-1 b) n
c) n+1 d) n/2
Answer: a) n-1
31. A graph with n vertices and n+1 edges that is not a tree, is
a) connected b) disconnected
c) eculer d)a circuit
Answer: d) circuit

1. 32. A graph is a tree if and only if

a) is completely connected b) is minimum connected
c) contains a circuit d) is planer
Answer: c) contains a circuit

1. 33. The minimum number of spanning trees in a connected graph with n nodes is

a) 1 b) 2
c) n-1 d) n/2
Answers: b) 2

1. 34. The number of different rooted labeled trees with n vertices

a) 2^n-1 b) 2ⁿ
c) n^n-1 d) nⁿ
Answers: c) n^n-1

1. 35. The number of circuit in a tree with n nodes

a) zero b) 1
b) n-1 d) n/2
Answer: d) n/2
 
36. Which of the following is false?

• 1. a) The set of all objective functions on a finite set forms a group
  2. under function composition
  3. b) The set {1,2,…p-1} forms a group under function composition.
  4. c) The set of all strings over a finite alphabet forms a group under

concatenation.
d) A subset of G is a sub group of the group (G,*) if and only if for
any pair of elements a, b D, a*b^-1 S
Answer 36 d): A subset of G is a sub group of the group (G,*) if and only if for
any pair of elements a, b D, a*b^-1 S

1. 37. Let (Z, *) be an algebraic structure where Z is the set of integers and the operation *
2. is defined by n * m = maximum (n, m), which of the following statements is true for
3. (z,*).

a) (z,*) is a monoid b) (z,*) is an Abelian group
c) (z,*) is a group d) None of the above
 
Answer: a) (z,*) is a monoid
In question 38 through 40 determine whether the set together with binary operation is a group.
38. Z, where * is subtraction
Answer: False
39. R, where a * b = a + b + 2
Answer: False
40. The set of all matrices under the operation of matrix addition
Answer: True