Let $A = \{x : |x^{2} - 10| \le 6\}$ and $B = \{x : |x - 2| > 1\}$. Then:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $A$ but not $C$.

In a group of $70$ people,$37$ like coffee,$52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

The probability of failing in Physics is $20\%$,and the probability of failing in Mathematics is $10\%$. What is the probability of failing in at least one subject (in $\%$)?

In a class of $55$ students,$23$ study Mathematics,$24$ study Physics,$19$ study Chemistry,$12$ study Mathematics and Physics,$9$ study Mathematics and Chemistry,$7$ study Physics and Chemistry,and $4$ study all three subjects. Find the number of students who study exactly one subject.

$A$ group of $40$ students appeared in an examination of $3$ subjects - Mathematics,Physics,and Chemistry. It was found that all students passed in at least one of the subjects. $20$ students passed in Mathematics,$25$ students passed in Physics,and $16$ students passed in Chemistry. At most $11$ students passed in both Mathematics and Physics,at most $15$ students passed in both Physics and Chemistry,and at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students who passed in all the three subjects is . . . . . . .