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

Let $A = \{(x, y) \in \mathbb{R} \times \mathbb{R} : |x + y| \geq 3\}$ and $B = \{(x, y) \in \mathbb{R} \times \mathbb{R} : |x| + |y| \leq 3\}$. If $C = \{(x, y) \in A \cap B : x = 0 \text{ or } y = 0\}$,then $\sum_{(x, y) \in C} |x + y|$ is :

$A$ two-digit number $\overline{ab}$ is called almost prime if one obtains a two-digit prime number by changing at most one of its digits $a$ or $b$. (For example,$18$ is an almost prime number because $13$ is a prime number). The number of almost prime two-digit numbers is:

Let $A$ denote the set of all real numbers $x$ such that $x^3-[x]^3=(x-[x])^3$,where $[x]$ is the greatest integer less than or equal to $x$. Then,

If $A=\{x \in R: \sqrt{x^2-8x+15} \in R\}$ and $B=\{x \in R: \frac{x-3}{2x-5} < \frac{x-6}{2x-11}\}$, then $A \cap B=$

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