CUET · MATHS · PYQ PAPER 2023
Consider a binary operation \(*\) on \(N\) defined as \(a * b=a^3+b^3\), choose the correct answer :
- A * is both associative and commutative
- B * is associative but not commutative
- C * is commutative but not associative
- D * is neither commutative nor associative
Answer & Solution
Correct Answer
(C) * is commutative but not associative
Step-by-step Solution
Detailed explanation
\(a * b = a^3 + b^3 = b^3 + a^3 = b * a \implies\) commutative. Let \(a=1, b=2, c=3\). \((a * b) * c = (1^3 + 2^3) * 3 = 9 * 3 = 9^3 + 3^3 = 729 + 27 = 756\). \(a * (b * c) = 1 * (2^3 + 3^3) = 1 * 35 = 1^3 + 35^3 = 1 + 42875 = 42876\). Since \(756 \neq 42876\), not associative.
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