In a class of $60$ students,$25$ students play cricket and $20$ students play tennis,and $10$ students play both the games. The number of students who play neither is:

Each set $X_r$ contains $5$ elements and each set $Y_r$ contains $4$ elements. If $\bigcup_{r=1}^{24} X_r = S = \bigcup_{r=1}^{n} Y_r$,and each element of set $S$ belongs to exactly $10$ of the $X_r$'s and to exactly $6$ of the $Y_r$'s,then find the value of $n$.

$A$ college awarded $38$ medals in football,$15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports,how many received medals in exactly two of the three sports?

If $A = \{1, 2, 3, 4, 5, 6\}$,then the number of subsets of $A$ which contain at least two elements is

The sum of all integers from $1$ to $100$ that are divisible by $2$ or $5$ is...........

In a class of $30$ pupils,$12$ take needle work,$16$ take physics,and $18$ take history. If all the $30$ students take at least one subject and no one takes all three,then the number of pupils taking exactly $2$ subjects is: