Number of rational roots of equation $x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0,$ is equal to

Let $p(x)=x^2-5 x+a$ and $q(x)=x^2-3 x+b$, where $a$ and $b$ are positive integers. Suppose HCF $(p(x), q(x))=x-1$ and $k(x)=1 cm (p(x), q(x))$ If the coefficient of the highest degree term of $k(x)$ is 1 , then sum of the roots of $(x-1)+k(x)$ is

If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to

The number of non-negative integer solutions of the equations $6 x+4 y+z=200$ and $x+y+z=100$ is

One root of the following given equation $2{x^5} - 14{x^4} + 31{x^3} - 64{x^2} + 19x + 130 = 0$ is

The sum of all the real values of $x$ satisfying the equation ${2^{\left( {x - 1} \right)\left( {{x^2} + 5x - 50} \right)}} = 1$  is