# Algebra MCQ (Multiple Choice Questions) with answers

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.

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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