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ALGEBRA MCQs

Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 3 of 101 pages
Question 21.  if (g, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ g, then g is a/an
  1.    abelian group
  2.    non-abelian group
  3.    commutative semi group
  4.    none of these
 Discuss Question
Answer: Option A. -> abelian group
Explanation :
Question 22.  if (g, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ g, then g is a/an
  1.    abelian group
  2.    non-abelian group
  3.    commutative semi group
  4.    none of these
 Discuss Question
Answer: Option A. -> abelian group
Explanation :
Question 23.  which of the following statements is false ?
  1.    If R is relexive, then R ∩ R-1 ≠ φ
  2.    R ∩ R-1 ≠ φ   =>R  is anti-symmetric.
  3.    If R, R' are relexive relations in A, then R - R' is reflexive
  4.    If R, R' are equivalence relations in a set A, then  R ∩ R'  is also an equivalence relation in A
 Discuss Question
Answer: Option C. -> If R, R' are relexive relations in A, then R - R' is reflexive
Explanation :
Question 24.  if r = {(1, 2),(2, 3),(3, 3)} be a relation defined on a= {1, 2, 3} then r . r (= r2) is
  1.    {(1, 2),(1, 3),(3, 3)}
  2.    {(1, 3),(2, 3),(3, 3)}
  3.    {(2, 1),(1, 3),(2, 3)}
  4.    R itself
 Discuss Question
Answer: Option B. -> {(1, 3),(2, 3),(3, 3)}
Explanation :
Question 25.  if r = {(1, 2),(2, 3),(3, 3)} be a relation defined on a= {1, 2, 3} then r . r (= r2) is
  1.    {(1, 2),(1, 3),(3, 3)}
  2.    {(1, 3),(2, 3),(3, 3)}
  3.    {(2, 1),(1, 3),(2, 3)}
  4.    R itself
 Discuss Question
Answer: Option B. -> {(1, 3),(2, 3),(3, 3)}
Explanation :
Question 26.  which of the following statements is false ?
  1.    If R is relexive, then R ∩ R-1 ≠ φ
  2.    R ∩ R-1 ≠ φ   =>R  is anti-symmetric.
  3.    If R, R' are relexive relations in A, then R - R' is reflexive
  4.    If R, R' are equivalence relations in a set A, then  R ∩ R'  is also an equivalence relation in A
 Discuss Question
Answer: Option C. -> If R, R' are relexive relations in A, then R - R' is reflexive
Explanation :
Question 27.  let a be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. then
  1.    < A, * > is a monoid but not a group
  2.    < A, * > is a group but not an abelian group
  3.    < A, * > is a semi group but not a monoid
  4.    A is closed under * but < A, * > is not a semi group
 Discuss Question
Answer: Option B. -> < A, * > is a group but not an abelian group
Explanation :
Question 28.  let (z, *) be an algebraic structure, where z is the set of integers and the operation * is defined by n * m = maximum (n, m). which of the following statements is true for (z, *) ?
  1.    (Z, *) is a group
  2.    (Z, *) is a monoid
  3.    (Z, *) is an abelian group
  4.    None of these
 Discuss Question
Answer: Option D. -> None of these
Explanation :
Question 29.  if the binary operation * is deined on a set of ordered pairs of real numbers as (a,b)*(c,d)=(ad+bc,bd) and is associative, then (1, 2)*(3, 5)*(3, 4) equals
  1.    (7,11)
  2.    (23,11)
  3.    (32,40)
  4.    (74,40)
 Discuss Question
Answer: Option D. -> (74,40)
Explanation :
Question 30.  let a be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. then
  1.    < A, * > is a monoid but not a group
  2.    < A, * > is a group but not an abelian group
  3.    < A, * > is a semi group but not a monoid
  4.    A is closed under * but < A, * > is not a semi group
 Discuss Question
Answer: Option B. -> < A, * > is a group but not an abelian group
Explanation :

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