Suppose that $x$ and $y$ are positive number with $xy = \frac{1}{9};\,x\left( {y + 1} \right) = \frac{7}{9};\,y\left( {x + 1} \right) = \frac{5}{{18}}$ . The value of $(x + 1) (y + 1)$ equals
$\frac {8}{9}$
$\frac {16}{9}$
$\frac {10}{9}$
$\frac {35}{18}$
If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to
The condition that ${x^3} - 3px + 2q$ may be divisible by a factor of the form ${x^2} + 2ax + {a^2}$ is
If $\alpha ,\beta ,\gamma$ are the roots of $x^3 - x - 2 = 0$, then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-
If $x$ is real, then the value of $\frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}}$ does not lie between
The set of all $a \in R$ for which the equation $x | x -1|+| x +2|+a=0$ has exactly one real root is: