JEE Advanced · Mathematics · 11. Sets & Relations
Let the set of all relations \(R\) on the set \(\{a, b, c, d, e, f\}\), such that \(R\) is reflexive and symmetric, and \(R\) contains exactly 10 elements, be denoted by \(S\). Then the number of elements in \(S\) is ______
- A 100
- B 105
- C 110
- D 115
Answer & Solution
Correct Answer
(B) 105
Step-by-step Solution
Detailed explanation
For relation to be reflexive all the diagonal elements must be taken and out of remaining 30 elements there are 15 pairs and we need 2 pairs such that R contains exactly 10 elements and is both reflexive and symmetric.
\(\therefore\) number of ways \(={ }^{15} \mathrm{C}_2=105\)
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