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

- A
$35$

- B
$48$

- C
$60$

- D
$22$

In a class of $35$ students, $24$ like to play cricket and $16$ like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?

In a Mathematics test, the average marks of boys is $x \%$ and the average marks of girls is $y \%$ with $x \neq y$. If the average marks of all students is $z \%$, the ratio of the number of girls to the total number of students is

- [KVPY 2017]

$20$ teachers of a school either teach mathematics or physics. $12$ of them teach mathematics while $4$ teach both the subjects. Then the number of teachers teaching physics is

In a group of students, $100$ students know Hindi, $50$ know English and $25$ know both. Each of the students knows either Hindi or English. How many students are there in the group?

In a certain school, $74 \%$ students like cricket, $76 \%$ students like football and $82 \%$ like tennis. Then, all the three sports are liked by at least $......\%$

- [KVPY 2009]