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

In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student has opted for neither $NCC$ nor $NSS$.

In a study about a pandemic,data of $900$ persons was collected. It was found that:
$190$ persons had symptom of fever,
$220$ persons had symptom of cough,
$220$ persons had symptom of breathing problem,
$330$ persons had symptom of fever or cough or both,
$350$ persons had symptom of cough or breathing problem or both,
$340$ persons had symptom of fever or breathing problem or both,
$30$ persons had all three symptoms (fever,cough and breathing problem).
If a person is chosen randomly from these $900$ persons,then the probability that the person has at most one symptom is . . . . .

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?

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?

There is a group of $265$ persons who like either singing, dancing, or painting. In this group, $200$ like singing, $110$ like dancing, and $55$ like painting. If $60$ persons like both singing and dancing, $30$ like both singing and painting, and $10$ like all three activities, then the number of persons who like only dancing and painting is: