In a class of $100$ students, $55$ students have passed in Mathematics and $67$ students have passed in Physics. Then the number of students who have passed in Physics only is

  • A

    $22$

  • B

    $33$

  • C

    $10$

  • D

    $45$

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A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone

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 .............................

  • [JEE MAIN 2024]

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In a group of $400$ people, $250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?