JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A =\{1,2,3,4, \ldots .10\}\) and \(B =\{0,1,2,3,4\}\) The number of elements in the relation \(R =\{( a , b )\) \(\left.\in A \times A : 2( a - b )^2+3( a - b ) \in B \right\}\) is \(.........\).
- A \(12\)
- B \(14\)
- C \(16\)
- D \(18\)
Answer & Solution
Correct Answer
(D) \(18\)
Step-by-step Solution
Detailed explanation
\(A=\{1,2,3, \ldots \ldots 10\}\) \(B=\{0,1,2,3,4\}\) \(R=\left\{(a, b) \in A \times A: 2(a-b)^2+3(a-b) \in B\right\}\) \(\text { Now } 2(a-b)^2+3(a-b)=(a-b)(2(a-b)+3)\) \(\Rightarrow a=b \text { or } a-b=-2\) Now \(2(a-b)^2+3(a-b)=(a-b)(2(a-b)+3)\)…
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