If $x$ is real and satisfies $x + 2 > \sqrt {x + 4} ,$ then
$x < - 2$
$x > 0$
$ - 3 < x < 0$
$ - 3 < x < 4$
If $(x + 1)$ is a factor of ${x^4} - (p - 3){x^3} - (3p - 5){x^2}$ $ + (2p - 7)x + 6$, then $p = $
If $x, y$ are real numbers such that $3^{(x / y)+1}-3^{(x / y)-1}=24$ then the value of $(x+y) /(x-y)$ is
For a real number $x$, let $[x]$ denote the largest integer less than or equal to $x$, and let $\{x\}=x-[x]$. The number of solutions $x$ to the equation $[x]\{x\}=5$ with $0 \leq x \leq 2015$ 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 $, $\beta$, $\gamma$ are roots of ${x^3} - 2{x^2} + 3x - 2 = 0$ , then the value of$\left( {\frac{{\alpha \beta }}{{\alpha + \beta }} + \frac{{\alpha \gamma }}{{\alpha + \gamma }} + \frac{{\beta \gamma }}{{\beta + \gamma }}} \right)$ is