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Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 4 of 101 pages
Question 31.  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 32.  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 33.  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 34.  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 35.  in the group g = {2, 4, 6, 8) under multiplication modulo 10, the identity element is
  1.    2
  2.    4
  3.    6
  4.    8
 Discuss Question
Answer: Option D. -> 8
Explanation :
Question 36.  which of the following statements is false ?
  1.    The set of rational numbers form an abelian group under multiplication
  2.    The set of rational numbers is an abelian group under addition
  3.    The set of rational integers is an abelian group under addition
  4.    None of these
 Discuss Question
Answer: Option A. -> The set of rational numbers form an abelian group under multiplication
Explanation :
Question 37.  in the group g = {2, 4, 6, 8) under multiplication modulo 10, the identity element is
  1.    2
  2.    4
  3.    6
  4.    8
 Discuss Question
Answer: Option D. -> 8
Explanation :
Question 38.  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 :
Question 39.  which of the following statements is false ?
  1.    The set of rational numbers form an abelian group under multiplication
  2.    The set of rational numbers is an abelian group under addition
  3.    The set of rational integers is an abelian group under addition
  4.    None of these
 Discuss Question
Answer: Option A. -> The set of rational numbers form an abelian group under multiplication
Explanation :
Question 40.  hasse diagrams are drawn for
  1.    lattices
  2.    boolean Algebra
  3.    partially ordered sets
  4.    none of these
 Discuss Question
Answer: Option D. -> none of these
Explanation :

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