If $\alpha, \beta$ are the roots of $x^2-a(x-1)+b=0$, then the value of $\frac{1}{\alpha^2-a \alpha}+\frac{1}{\beta^2-a \beta}+\frac{2}{a+b}$ is:

The set of all real values of the expression $\frac{x^2-x+2}{x^2+x-2}$ for all $x \in R-\{-2, 1\}$ is

Let $\alpha_\theta$ and $\beta_\theta$ be the distinct roots of $2x^2 + (\cos \theta)x - 1 = 0$,where $\theta \in (0, 2\pi)$. If $m$ and $M$ are the minimum and the maximum values of $\alpha_\theta^4 + \beta_\theta^4$,then $16(M + m)$ equals:

If $ax + by = 1$,where $a, b, x$ and $y$ are integers,then which one of the following is not true?

If $x, y, z$ are real and distinct,then $u = x^2 + 4y^2 + 9z^2 - 6yz - 3zx - 2xy$ is always

If $p$ and $q$ are positive real numbers such that $p^{2} + q^{2} = 1$,then the maximum value of $(p+q)$ is: