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Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 13 of 101 pages
Question 121.  simplify (x - 9)(x + 10) ⁄ (x² - 81)
  1.    (x + 10) ⁄ (x - 9)
  2.    (x + 10) ⁄ (x + 9)
  3.    (x² + x - 90) ⁄ (x² - 81)
  4.    None of above
 Discuss Question
Answer: Option B. -> (x + 10) ⁄ (x + 9)
Explanation :
Question 122.  expand and simplify (x + y)³
  1.    x³ - y³
  2.    x³ + y³
  3.    x³ + 3xy(x - y) + y³
  4.    x³ + 3xy(x + y) + y³
 Discuss Question
Answer: Option D. -> x³ + 3xy(x + y) + y³
Explanation :
Question 123.  (a - b)² =
  1.    a² + b²
  2.    a² - b²
  3.    a² + 2ab + b²
  4.    a² - 2ab + b²
 Discuss Question
Answer: Option D. -> a² - 2ab + b²
Explanation :
Question 124.  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 125.  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 126.  let g denoted the set of all n x n non-singular matrices with rational numbers as entries. then under multiplication g is a/an
  1.    subgroup
  2.    ininite, abelian
  3.    finite abelian group
  4.    infinite, non abelian group
 Discuss Question
Answer: Option D. -> infinite, non abelian group
Explanation :
Question 127.  let g denoted the set of all n x n non-singular matrices with rational numbers as entries. then under multiplication g is a/an
  1.    subgroup
  2.    ininite, abelian
  3.    finite abelian group
  4.    infinite, non abelian group
 Discuss Question
Answer: Option D. -> infinite, non abelian group
Explanation :
Question 128.  (z,*) is a group with a*b = a+b+1 ∀ a, b ∈z. the inverse of a is
  1.    0
  2.    -2
  3.    a-2
  4.    -a-2
 Discuss Question
Answer: Option D. -> -a-2
Explanation :
Question 129.  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 130.  (z,*) is a group with a*b = a+b+1 ∀ a, b ∈z. the inverse of a is
  1.    0
  2.    -2
  3.    a-2
  4.    -a-2
 Discuss Question
Answer: Option D. -> -a-2
Explanation :

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