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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Sets and Relations

In a survey of 220 students of a higher secondary school, it was...

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 m\mathrm{m} and n\mathrm{n} respectively be the least and the most number of students who studied all the three subjects. Then m+n\mathrm{m}+\mathrm{n} is equal to ______In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students

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In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students
125≤m+90−x≤13085≤P+70−x≤9575≤C+80−x≤90 m+P+C+120−2x=210⇒15≤x≤4530−x≥0⇒15≤x≤3030+15=45\begin{aligned} & 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 \\ & \Rightarrow 15 \leq \mathrm{x} \leq 30 \\ & 30+15=45\end{aligned}
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