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 $NSS$.

The number of integers from $1$ to $1000$ which are divisible by $2$ or $3$ is

Let $A = \{n \in N \mid n^{2} \leq n + 10,000\}$,$B = \{3k + 1 \mid k \in N\}$,and $C = \{2k \mid k \in N\}$. Then the sum of all the elements of the set $A \cap (B - C)$ is equal to $.....$

Consider the set $A$ of natural numbers $n$ whose units digit is non-zero,such that if this units digit is erased,then the resulting number divides $n$. If $K$ is the number of elements in the set $A$,then

In a class of $55$ students,the number of students studying different subjects are $23$ in Mathematics,$24$ in Physics,$19$ in Chemistry,$12$ in Mathematics and Physics,$9$ in Mathematics and Chemistry,$7$ in Physics and Chemistry,and $4$ in all the three subjects. The total number of students who have taken exactly one subject is

If $A$ and $B$ are subsets of universal set $X$ such that $n(X)=200, n(A)=90, n(B)=80$ and $n(A' \cap B')=40$,then $n(A \cap B')=$