If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$, then

If $x$ be real, then the minimum value of ${x^2} - 8x + 17$ is

If $3$ distinct real number $a$,$b$,$c$ satisfy $a^2(a + p) = b^2 (b + p) = c^2 (c + p)$ where $p \in R$, then value of $bc + ca + ab$ is

What is the sum of all natural numbers $n$ such that the product of the digits of $n$ (in base $10$ ) is equal to $n^2-10 n-36 ?$

If $|{x^2} - x - 6| = x + 2$, then the values of $x$ are

If $S$ is a set of $P(x)$ is polynomial of degree $ \le 2$ such that $P(0) = 0,$$P(1) = 1$,$P'(x) > 0{\rm{ }}\forall x \in (0,\,1)$, then