The number of non-negative integer solutions of the equations $6 x+4 y+z=200$ and $x+y+z=100$ is
$3$
$5$
$7$
Infinite
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
If the sum of the two roots of the equation $4{x^3} + 16{x^2} - 9x - 36 = 0$ is zero, then the roots are
If $x$ be real, the least value of ${x^2} - 6x + 10$ is
The solution of the equation $2{x^2} + 3x - 9 \le 0$ is given by
If for a posiive integer $n$ , the quadratic equation, $x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right) + .\;.\;.\; + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right) = 10n$ has two consecutive integral solutions, then $n$ is equal to: