Q.On the set of real numbers, which of the following binary operations is commutative?

Showing the 12 most recent of 28 on this concept.

1. CBSE 2026Set A1 markMCQ
   Q.If the operation $*$ is defined as $a * b = a + 2b$, then $(2 * 3) * 4$ is

   (a) $30$

   (b) $20$

   (c) $16$

   (d) $15$

   ›Reveal solutionSolution

   Apply the binary operation twice: $2*3=8$, then $8*4=16$.

   Given $a*b=a+2b$. Compute the inner operation first:

   …

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2. CBSE 2026Set A1 markMCQ
   Q.If operation $*$ is defined as $a * b = a^3 + b^3$, then $4 * (1 * 2) =$

   (a) $729$

   (b) $793$

   (c) $783$

   (d) $792$

   ›Reveal solutionSolution

   Evaluate the inner operation first (BODMAS with the defined $*$).

   Given $a * b = a^3 + b^3$:

   • Inner: $1 * 2 = 1^3 + 2^3 = 1 + 8 = 9$. …

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3. CBSE 2025Set E1 markMCQ
   Q.If operation '$o$' is defined as $(a \circ b) = a^3 + b^3$, then $4 \circ (1 \circ 2) =$

   (a) $729$

   (b) $793$

   (c) $783$

   (d) $792$

   ›Reveal solutionSolution

   Evaluate the inner bracket first: $1\circ2 = 9$, then $4\circ9 = 793$.

   The operation is $a\circ b = a^3 + b^3$. Compute the inner one first:

   $1\circ2 = 1^3 + 2^3 = 1 + 8 = 9.$

   Then …

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4. CBSE 2025Set E1 markMCQ
   Q.If operation '$o$' is defined as $(a \circ b) = a^2 + b^2 - ab$, then $(1 \circ 2) \circ 3 =$

   (a) $18$

   (b) $27$

   (c) $9$

   (d) $12$

   ›Reveal solutionSolution

   Inner bracket $1\circ2 = 3$, then $3\circ3 = 9$.

   The operation is $a\circ b = a^2 + b^2 - ab$. Compute the inner bracket first:

   $1\circ2 = 1^2 + 2^2 - (1)(2) = 1 + 4 - 2 = 3.$

   Then …

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5. CBSE 2025Set ANNUAL1 markMCQ
   Q.If ab = a²+b² ∀a,b∈IN, then (45)*3 is equal to

   (a) 50

   (b) 60

   (c) 1230

   (d) 1690

   ›Reveal solutionSolution

   Apply the binary operation $a*b=a^2+b^2$ twice, from the inside out.

   The symbol $*$ is a binary operation on $\mathbb{N}$ defined by $a*b=a^2+b^2$. To evaluate $(4*5)*3$ we must first evaluate the inner operation, then use that result as the left operand of the outer operation.

   …

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6. CBSE 2025Set ANNUAL1 markMCQ
   Q.Subtraction is not a binary operation in :

   (a) $N$

   (b) $R$

   (c) $Q$

   (d) $Z$

   ›Reveal solutionSolution

   A binary operation on a set must be closed on that set; subtraction fails closure only on $N$ among the four choices, since a smaller natural number minus a larger one is negative.

   1. A binary operation $*$ on a set $S$ requires $a*b\in S$ for every $a,b\in S$ (closure).
   2. Test subtraction on $N=\{1,2,3,\ldots\}$: take $a=2,b=5$. Then $a-b=2-5=-3$, which is not a natural number, so $-3\notin N$.
   3. Hence subtraction is NOT closed on $N$, so it is not a binary operation on $N$. …

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7. CBSE 2024Set D1 markMCQ
   Q.If the operation $*$ is defined as $a * b = 2a + b$, then $(2 * 3) * 4$ is

   (a) $30$

   (b) $20$

   (c) $18$

   (d) $15$

   ›Reveal solutionSolution

   $(2 * 3) * 4 = 18$.

   The binary operation is defined by $a * b = 2a + b$. Work from the innermost bracket first.

   Step 1: $2 * 3 = 2(2) + 3 = 4 + 3 = 7.$

   …

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8. CBSE 2023Set M1 mark
   Q.Let $*$ be the binary operation on $N$ of natural numbers given by $a * b = \text{LCM of } a \text{ and } b$. Find $5 * 7$.

   ›Reveal solutionSolution

   Tests a binary operation defined as LCM; $5*7=35$.

   By definition $a*b = \operatorname{LCM}(a,b)$. Since $5$ and $7$ are both prime (hence coprime), their LCM is their prod …

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9. CBSE 2023Set E1 markMCQ
   Q.If the operation 'o' is defined as $a\,o\,b=3a+b$ then $(2\,o\,3)\,o\,5 =$

   (a) $28$

   (b) $32$

   (c) $36$

   (d) $22$

   ›Reveal solutionSolution

   $(2\,o\,3)\,o\,5=32$.

   Using $a\,o\,b=3a+b$:

   …

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10. CBSE 2023Set ANNUAL1 markMCQ
    Q.For any operation $*$, defined on $0$ as $a * b = \dfrac{a+b}{3}$, then $1 * 2 =$

    (a) 3

    (b) 1

    (c) 0

    (d) none of these

    ›Reveal solutionSolution

    Substitute directly into the given binary operation formula.

    …

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11. CBSE 2023Set ANNUAL1 markMCQ
    Q.The operation $*$ defined by $a*b=\dfrac{ab}{7}$ is not a binary operation on :

    (a) $\mathbb{R}$

    (b) $\mathbb{Q}^+$

    (c) $\mathbb{C}$

    (d) $\mathbb{Z}$

    ›Reveal solutionSolution

    A binary operation must map back into the same set; testing $a*b=ab/7$ on each option finds it fails closure only on the integers.

    1. For $*$ to be a binary operation on a set $S$, we need $a*b=\dfrac{ab}{7}\in S$ for every $a,b\in S$ (closure).
    2. On $\mathbb R$: $a,b$ real $\Rightarrow ab/7$ real. Closed.
    3. On $\mathbb Q^+$: $a,b$ positive rationals $\Rightarrow ab/7$ is a positive rational. Closed. …

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12. CBSE 2023Set ANNUAL1 markMCQ
    Q.Let * be a binary operation on the set of all non-zero real numbers, defined by a * b = ab/5. The value of x given that 2 * (x * 5) = 10 is –

    (a) 25

    (b) 30

    (c) 40

    (d) 50

    ›Reveal solutionSolution

    Using $a*b=ab/5$ repeatedly: first find $x*5$, then apply the operation with $2$ to solve for $x$.

    Given $a*b = \dfrac{ab}{5}$ and $2*(x*5) = 10$.

    First compute the inner operation:

    $x*5 = \frac{x\cdot 5}{5} = x.$

    So the equation becomes …

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