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

By Renuka Miglani|Updated : May 19th, 2022

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

  1. The set of zeros of byjusexamprepin byjusexamprepforms a group under multiplication.
  2. byjusexamprep
  3. The splitting field of byjusexamprephas degree 3 over byjusexamprep
  4. The splitting field of byjusexamprephas degree 4 over byjusexamprep

2. Which of the following cannot be order of byjusexamprep

  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 byjusexamprep is irreducible in byjusexamprep
  3. Units of the ring byjusexamprep are units of byjusexamprep
  4. The element byjusexamprep is prime element in byjusexamprep

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 byjusexamprep

  1. 1
  2. 15
  3. 8
  4. 2
6. G is a finite group of order byjusexamprep where p & q are distinct primes such that byjusexamprep and byjusexamprep then which of the following is/are correct.
  1. G is an abelian group.
    byjusexamprepthe group G which is non-abelian.
  3. byjusexamprepp & 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 byjusexamprep. Consider the groups and byjusexamprep 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 byjusexamprep,where e is the identity element in the group G>

  1. š = φ
  2. byjusexamprep
  3. byjusexamprep
  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 NumberAnswer Key
10A,B,& D

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