JEE Mains · Maths · STD 11 - 1. set theory
In a survey of \(220\) students of a higher secondary school, it was found that at least \(125\) and at most \(130\) students studied Mathematics; at least \(85\) and at most \(95\) studied Physics; at least \(75\) and at most \(90\) studied Chemistry; \(30\) studied both Physics and Chemistry; \(50\) studied both Chemistry and Mathematics; \(40\) studied both Mathematics and Physics and \(10\) studied none of these subjects. Let \(\mathrm{m}\) and \(\mathrm{n}\) respectively be the least and the most number of students who studied all the three subjects. Then \(\mathrm{m}+\mathrm{n}\) is equal to ...........
- A \(50\)
- B \(45\)
- C \(78\)
- D \(49\)
Answer & Solution
Correct Answer
(B) \(45\)
Step-by-step Solution
Detailed explanation
\( 125 \leq \mathrm{m}+90-\mathrm{x} \leq 130 \) \( 85 \leq \mathrm{P}+70-\mathrm{x} \leq 95 \) \( 75 \leq \mathrm{C}+80-\mathrm{x} \leq 90 \) \( \mathrm{~m}+\mathrm{P}+\mathrm{C}+120-2 \mathrm{x}=210 \) \( \Rightarrow 15 \leq \mathrm{x} \leq 45 \& 30-\mathrm{x} \geq 0 \)…
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