ISRO EC 2025 Q.92: solution and answer

Official answer: DSource: ISRO's final answer key of 15 May 2026

1. Read the regions from the diagram: Football and Cricket only $=14$, Football and Basketball only $=7$, all three $=5$, Cricket and Basketball only $=9$.

2. Football total: $50=F_{\text{only}}+14+7+5$, so $F_{\text{only}}=24$.

3. Cricket total: $40=C_{\text{only}}+14+5+9$, so $C_{\text{only}}=12$.

4. Players who play Football or Cricket but not Basketball are those in the Football-only, Cricket-only and Football-and-Cricket-only regions, so the count is $F_{\text{only}}+C_{\text{only}}+14$.

5. $24+12+14=50$.

6. The regions with $7$, $5$ and $9$ lie inside the Basketball circle, so they are excluded. The answer is option (d), $50$.