JEE Advanced 2025 · Paper 1 · Mathematics Q8

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MathematicsNumerical+4Question 8 of 48

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 $\mathcal{S}$ .

Then the number of elements in $\mathcal{S}$ is _____.

Your answer

Answer and worked solution

Official answer: 105

Reflexive. All 6 pairs $(x,x)$ must be in $R$ .

Symmetric. The other $10-6=4$ elements come in symmetric pairs $\{(x,y),(y,x)\}$ , so exactly 2 such pairs are chosen.

There are ${}^6C_2=15$ unordered pairs $\{x,y\}$ , so
$n(\mathcal S)={}^{15}C_2=105.$

Topics:Relations Combinations

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JEE Advanced 2025 · Paper 1, Mathematics question 8