Get access to Free Algebra MCQ with answers. In this blog post, we have written Multiple Choice Questions on Algebra. These MCQs on Algebra are very important for various exams.
Algebra MCQ with answers
1. Let V denote the set of 3×3 real matrices. As a vector space over the field R, it has dimensions:
3
6
9
27
2. Let V denote the set of 3×3 real matrices of trace zero. As a vector space over the field R, it has dimensions:
8
9
3
0
if
x≡3mod4x≡0mod6,
Then what is the value of x mod 12?
2
1
3
No solution
3. The number of ways of seating 6 people around a circular table is
6
30
120
720
4. Let A and B be square matrices of size 3×3. Is the following assertion true or false? ABAB=0 implies BABA=0
True
False
5. What is the result of the composition 3124∘4231:
4123
2134
3421
3124
6. What is the inverse of the permutation 231?
312
123
132
7. Consider the set M of all n×n matrices with real entries. Matrix multiplication gives rise to a binary operation M×M→M.
Which of the group axioms fail for this operation?
Associativity
Identity
Inverse
None
8. infinite groups have only infinite subgroups.
True
False
9. Which of the following elements are conjugate to 21543?
12534
21453
54231
42513
10. How many distinguishable ways are there to paint the three edges of an equilateral triangle with two different colors assuming that same color may be used in different edges?
2
4
6
8
11. How many distinguishable ways are there to paint the three edges of an equilateral triangle with four different colors assuming that different colors are used for different edges?
2
4
6
8
12. Any action of a group G of order 35 on a set X of 16 elements must have a fixed point.
True
False
13. A simple group is a group in which there are no proper non-trivial subgroups. In a simple group of order 168 how many elements are there of order 7.
6
12
24
48
14. True or False: Every finite group of order 72 is not a simple group.
True
False
15. Consider the following statements: (A) There exists a simple group of order 24; (B) There exists a simple group of order 36. Which of the following are correct?
Both (A) and (B) are true
(A) is true and (B) is false
(A) is false and (B) is true
Both (A) and (B) are false
16. Consider the following statements: (A) There exists a group of order 375 with no subgroup of order 15; (B) A group of order 105 has a subgroup of order 35. Which of the following are correct?
Both (A) and (B) are true
(A) is true and (B) is false
(A) is false and (B) is true
Both (A) and (B) are false
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