If $X$ and $Y$ are two sets such that $X$ has $40$ elements,$X \cup Y$ has $60$ elements and $X \cap Y$ has $10$ elements,how many elements does $Y$ have?

In a school,$20$ teachers teach either Mathematics or Physics. If $12$ teachers teach Mathematics and $4$ teachers teach both subjects,then the number of teachers teaching only Physics is:

Let $A = \{1, 6, 11, 16, \dots\}$ and $B = \{9, 16, 23, 30, \dots\}$ be the sets consisting of the first $2025$ terms of two arithmetic progressions. Then $n(A \cup B)$ is

In a battle,$70\%$ of the soldiers lost one eye,$80\%$ lost one ear,$75\%$ lost one arm,and $85\%$ lost one leg. If $x\%$ of the soldiers lost all four,what is the minimum value of $x$?

$A$ 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:

If $S$ and $T$ are two sets such that $S$ has $21$ elements,$T$ has $32$ elements,and $S \cap T$ has $11$ elements,how many elements does $S \cup T$ have?