Mathematics · Sets and Relations

JEE Main 2024 — 30 January, Shift 1 — Question 21

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is.

Answer: 10

Numerical answer — enter this value.

Step-by-step solution

$11-\mathrm{x} \geq 0$ (Maths and Physics) $\mathrm{x} \leq 11$

$\mathrm{x}=11$ does not satisfy the data. $11+\mathrm{z} \leq 15 \Rightarrow \mathrm{z} \leq 4$

$11+\mathrm{y} \leq 15 \Rightarrow \mathrm{y} \leq 4$

Now $9-z+0+14-y+z+11+y+5-y-z=40$

$\Rightarrow \mathrm{y}+\mathrm{z}=-1$

Not possible $\Rightarrow \mathrm{x} \leq 10$

For $\mathrm{x}=10$

Hence maximum number of students passed in all the three subjects is 10 .

Answer key and solution verified before publishing.

Practise Sets and Relations

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 30 January, Shift 1
Subject: Mathematics
Chapter: Sets and Relations
Topic: Sets