In a survey,it was found that $63\%$ of Americans like cheese and $76\%$ like apples. If $x\%$ of Americans like both cheese and apples,then:

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$, $B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then, the correct order of their probabilities is:

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

Sets $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A \cup B$?

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

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?