The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is
$( - \infty ,\,\, - 2)\, \cup (2,\,\infty )$
$( - \infty ,\,\, - \sqrt 2 )\, \cup (\sqrt 2 ,\,\infty )$
$( - \infty ,\,\, - 1)\, \cup (1,\,\infty )$
$(\sqrt 2 ,\,\infty )$
If $x+\frac{1}{x}=a, x^2+\frac{1}{x^3}=b$, then $x^3+\frac{1}{x^2}$ is
Number of integral values of '$m$' for which $\{x\}^2 + 5m\{x\} - 3m + 1 < 0 $ $\forall x \in R$, is (where $\{.\}$ denotes fractional part function)
If $\alpha , \beta$ and $\gamma$ are the roots of ${x^3} + 8 = 0$, then the equation whose roots are ${\alpha ^2},{\beta ^2}$ and ${\gamma ^2}$ is
If $a+b+c=1, a b+b c+c a=2$ and $a b c=3$, then the value of $a^{4}+b^{4}+c^{4}$ is equal to $....$
The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is