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ALGEBRA MCQs

Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 8 of 101 pages
Question 71.  if (g, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ g, then g is a/an
  1.    commutative semi group
  2.    non-abelian group
  3.    abelian group
  4.    None of these
 Discuss Question
Answer: Option C. -> abelian group
Explanation :
Question 72.  the inverse of - i in the multiplicative group, {1, - 1, i , - i} is
  1.    -1
  2.    1
  3.    -i
  4.    i
 Discuss Question
Answer: Option D. -> i
Explanation :
Question 73.  if (g, .) is a group such that a2 = e, ∀a ∈ g, then g is
  1.    abelian group
  2.    non-abelian group
  3.    semi group
  4.    none of these
 Discuss Question
Answer: Option A. -> abelian group
Explanation :
Question 74.  if (g, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ g, then g is a/an
  1.    commutative semi group
  2.    non-abelian group
  3.    abelian group
  4.    None of these
 Discuss Question
Answer: Option C. -> abelian group
Explanation :
Question 75.  the inverse of - i in the multiplicative group, {1, - 1, i , - i} is
  1.    -1
  2.    1
  3.    -i
  4.    i
 Discuss Question
Answer: Option D. -> i
Explanation :
Question 76.  if (g, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ g, then g is a/an
  1.    commutative semi group
  2.    non-abelian group
  3.    abelian group
  4.    None of these
 Discuss Question
Answer: Option C. -> abelian group
Explanation :
Question 77.  the set of integers z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ z, is a group. the identity element of this group is
  1.    -1
  2.    0
  3.    1
  4.    2
 Discuss Question
Answer: Option A. -> -1
Explanation :
Question 78.  the inverse of - i in the multiplicative group, {1, - 1, i , - i} is
  1.    -1
  2.    1
  3.    -i
  4.    i
 Discuss Question
Answer: Option D. -> i
Explanation :
Question 79.  the set of all real numbers under the usual multiplication operation is not a group since
  1.    zero has no inverse
  2.    identity element does not exist
  3.    multiplication is not associative
  4.    multiplication is not a binary operation
 Discuss Question
Answer: Option A. -> zero has no inverse
Explanation :
Question 80.  if (g, .) is a group such that a2 = e, ∀a ∈ g, then g is
  1.    abelian group
  2.    non-abelian group
  3.    semi group
  4.    none of these
 Discuss Question
Answer: Option A. -> abelian group
Explanation :

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