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Binary Operations Maths - Binary Operations

Uttarakhand Board (UBSE) - STD 12 Science - Maths (Uttarakhand - English Medium). 134 questions in this chapter.

Question types

Binary Operations question types

134 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

134
Questions
4
Question groups
5
Question types
Sample Questions

Binary Operations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
On the power set P of a non-empty set A, we define an operation $\triangle \text{ by }\text{X}\triangle\text{Y}=(\text{X}\cap\text{Y})∪(\text{X}∩\text{Y})\text{X}\triangle\text{Y}=\text{X}∩\text{Y}∪\text{X}∩\text{Y}$
Then which are of the following statements is true about $\triangle$
  • A
    Commutative and associative without an identity.
  • B
    Commutative but not associative with an identity.
  • C
    Associative but not commutative without an identity.
  • ✓
    Associative and commutative with an identity.

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark
Let $*$ be a binary operation defined on $Q^+$ by the rule $\text{a}^*\text{b}=\frac{\text{ab}}3\forall\text{ a, b}\in \text{Q}^+.$ The inverse of $4 ^* 6$ is:
  • ✓
    $\frac{9}{8}$
  • B
    $\frac{2}3$
  • C
    $\frac{3}2$
  • D
    None of these.

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
Let * be a binary operation defined on set Q − {1} by the rule a * b = a + b − ab. Then, the identify element for * is:
  • A
    $1$
  • B
    $\frac{\text{a}-1}{\text{a}}$
  • C
    $\frac{\text{a}}{\text{a}-1}$
  • ✓
    $0$

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark
On the set $Q^+$ of all positive rational numbers a binary operation $*$ is defined by $\text{a}^*\text{b}=\frac{\text{ab}}2\forall\text{ a, b}\in \text{Q}^+$. The inverse of $8$ is:
  • A
    $\frac{1}{8}$
  • ✓
    $\frac{1}2$
  • C
    $2$
  • D
    $4$

Answer: B.

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Q 143 Marks Question3 Marks
The binary operation * is defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{7}$ on the set Q of all rational numbers. Show that * is associative.
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Q 165 Marks Questions5 Marks
Let S be the set of all real numbers except -1 and let '*' be an operation defined by a * b = a + b + ab for all a, b ∈ S. Determine whether '*' is a binary operation on S. If yes, check its commutativity and associativity. Also, solve the equation (2 * x) * 3 = 7.
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Q 175 Marks Questions5 Marks
Let S be the set of all rational numbers except 1 and * be defined on S by a * b = a + b - ab, for all a, b ∈ S.
Prove that:
  1. * is a binary operation on S.
  2. * is commutative as well as associative.
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Q 185 Marks Questions5 Marks
On R − {1}, a binary operation * is defined by a * b = a + b − ab. Prove that * is commutative and associative. Find the identity element for * on R − {1}. Also, prove that every element of R − {1} is invertible.
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Q 195 Marks Questions5 Marks
Let A =R×R and * be a binary operation on A defined by,
(a, b) * (c, d) = (a + c, b + d).
Show that * is commutative and associative. Find the binary element for * on A, if any.
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Q 205 Marks Questions5 Marks
Define a binary operation * on the set ${0, 1, 2, 3, 4, 5}$ as:
$\text{a}\times\text{b}=\begin{cases}\text{a + b},&\text{if }\text{a + b}<6\\\text{a + b}-6,&\text{if }\text{a + b}\geq6\end{cases}$
Show that 0 is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a.
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