Discrete Mathematics (3140708) MCQs

MCQs of Algebraic Structures

Showing 31 to 40 out of 65 Questions
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31.
Let S3={I, (1  2), (1  3), (2  3), (1  2  3), (1  3  2)} be a group with respect to composition of function. The inverse of (1 2 3) is _____.
(a) (1 2)
(b) (2 3)
(c) (1 3 2)
(d) (1 2 3)
Answer:

Option (c)

32.
If δ=1234512354∈S5 then δ-1 is _____.
(a) (1 3)(4 5)
(b) (1 3 4 5)
(c) (1 2 3 4 5)
(d) (2 3 4 5)
Answer:

Option (a)

33.
Let σ=(1  3  5  6  2)∈S6 then σ-1 is _____..
(a) (1 2 6 3 5)
(b) (1 2 6 5 3)
(c) (2 6 5 1 3)
(d) (1 2 6 3 4 5)
Answer:

Option (b)

34.
Let f=(1  2  3)(1  4  5)∈S5 then find f99.
(a) (1 3 2 5 4)
(b) (1 4 5)(1 2 3)
(c) (1 2 3 4 5)
(d) (1 2 3)(4 5)
Answer:

Option (a)

35.
How many generators of the cyclic group ℤ?
(a) 0
(b) 1
(c) 2
(d) 3
Answer:

Option (c)

36.
Every cyclic group is _____.
(a) a group with finite order
(b) a group with prime order
(c) a non Abelian group
(d) an Abelian group
Answer:

Option (d)

37.
Which of the following is not subgroup of (ℝ, +)?
(a) (ℤ, +)
(b) (ℚ, +)
(c) (ℝ, +)
(d) (ℂ, +)
Answer:

Option (d)

38.
For any group G, how many improper/trivial subgroups of G?
(a) 2
(b) 3
(c) 4
(d) o(G)
Answer:

Option (a)

39.
If H1 and H2 are subgroups of the group G, Then which one of the following is also a subgroup of G?
(a) H1∪H2
(b) H1∩H2
(c) H1∆H2
(d) none of these
Answer:

Option (b)

40.
For G=(ℤ5, +5), how many generators of the cyclic group G?
(a) 2
(b) 3
(c) 4
(d) 5
Answer:

Option (c)

Showing 31 to 40 out of 65 Questions
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