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Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 16 of 101 pages
Question 151.  if a = (1, 2, 3, 4). let ~= {(1, 2), (1, 3), (4, 2)}. then ~ is
  1.    reflexive
  2.    transitive
  3.    symmetric
  4.    not anti-symmetric
 Discuss Question
Answer: Option B. -> transitive
Explanation :
Question 152.  some group (g, 0) is known to be abelian. then which one of the following is true for g ?
  1.    G is of finite order
  2.    g = g² for every g ∈ G
  3.    g = g-1 for every g ∈ G
  4.    (g o h)² = g²o h² for every g,h ∈ G
 Discuss Question
Answer: Option D. -> (g o h)² = g²o h² for every g,h ∈ G
Explanation :
Question 153.  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 154.  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 155.  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 156.  some group (g, 0) is known to be abelian. then which one of the following is true for g ?
  1.    G is of finite order
  2.    g = g² for every g ∈ G
  3.    g = g-1 for every g ∈ G
  4.    (g o h)² = g²o h² for every g,h ∈ G
 Discuss Question
Answer: Option D. -> (g o h)² = g²o h² for every g,h ∈ G
Explanation :
Question 157.  if a = (1, 2, 3, 4). let ~= {(1, 2), (1, 3), (4, 2)}. then ~ is
  1.    reflexive
  2.    transitive
  3.    symmetric
  4.    not anti-symmetric
 Discuss Question
Answer: Option B. -> transitive
Explanation :
Question 158.  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 159.  the set of all nth roots of unity under multiplication of complex numbers form a/an
  1.    group
  2.    abelian group
  3.    semi group with identity
  4.    commutative semigroups with identity
 Discuss Question
Answer: Option B. -> abelian group
Explanation :
Question 160.  if a, b are positive integers, define a * b = a where ab = a (modulo 7), with this * operation, then inverse of 3 in group g (1, 2, 3, 4, 5, 6) is
  1.    1
  2.    3
  3.    5
  4.    7
 Discuss Question
Answer: Option C. -> 5
Explanation :

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