CSIR-NET Mathematical Science - ALGEBRA MCQ - Attempt Here!

ALGEBRA MCQ 

1. Consider the polynomial in the ring of polynomial in the variable x with the coefficient in the field of rational numbers. Then

1. The set of zeros of in forms a group under multiplication.
2. 
3. The splitting field of has degree 3 over 
4. The splitting field of has degree 4 over 

2. Which of the following cannot be order of 

1. 15
2. 33
3. 10
4. 19

3. Pick out the correct statement from the following:

1. A homomorphism image of UFD is again UFD
2. The element  is irreducible in 
3. Units of the ring  are units of 
4. The element  is prime element in 

4. If the sum of positive integer relatively prime to n and less than n is 6n then which of the following is not possible.

1. n=12
    
2. n=28
    
3. n=13
    
4. n=21

5. If F is a field of order 16, then how many numbers of elements are there such that 

1. 1
    
2. 15
    
3. 8
    
4. 2

6. G is a finite group of order  where p & q are distinct primes such that  and  then which of the following is/are correct.

1. G is an abelian group.
2.  
   the group G which is non-abelian.
    
3. p & q for which the number of non-isomorphic groups is 2
    
4. The number of non-isomorphic groups is 2 for all p & q.

7. Let . Consider the groups and  under matrix multiplication. Then the number of cosets of H in G is:

1. 1010
2. 2019
3. 2020
4. Infinite

8. The number of elements of order 3 in a non-cyclic group of order 57

1. 38
    
2. 57
    
3. 19
    
4. 34

9. Let G be a finite group. Let S be the set of elements g such that ,where e is the identity element in the group G>

1. š = φ
2. 
3. 
4. None of these

10. Which among the following is/are not the class equation of a group?

1. 9=3+3+3
2. 21=1+1+3+3+3+3+7
3. 10=1+2+2+5
4. 18=1+3+6+8

Answer Keys for ALGEBRA MCQs
Question Number	Answer Key
1	B
2	A,B,D
3	B,C
4	A
5	C
6	A,C,D
7	C
8	A
9	B
10	A,B,& D

 

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