If $U$ is the universal set and $A \cup B \cup C = U$,then ${(A - B) \cup (B - C) \cup (C - A)}'$ is equal to:

Let $S = \{(m, n): m, n \in \{1, 2, 3, \ldots, 50\}\}$. If the number of elements $(m, n)$ in $S$ such that $6^{m} + 9^{n}$ is a multiple of $5$ is $p$ and the number of elements $(m, n)$ in $S$ such that $m + n$ is a square of a prime number is $q$, then $p + q$ is equal to :

In a regular graph of $15$ vertices,the sum of the degrees of the vertices is $60$. Then,the degree of each vertex is:

For a real number $x$,$[x]$ denotes the greatest integer less than or equal to $x$. The value of $\left[ \frac{1}{2} \right] + \left[ \frac{1}{2} + \frac{1}{100} \right] + \left[ \frac{1}{2} + \frac{2}{100} \right] + \dots + \left[ \frac{1}{2} + \frac{99}{100} \right]$ is

The number of polynomials $p(x)$ with integer coefficients such that the curve $y=p(x)$ passes through $(2,2)$ and $(4,5)$ is

Let $A$ be the set of first $101$ terms of an $A$.$P$.,whose first term is $1$ and the common difference is $5$, and let $B$ be the set of first $71$ terms of an $A$.$P$.,whose first term is $9$ and the common difference is $7$. Then, the number of elements in $A \cap B$ which are divisible by $3$ is: