If$\frac{{2x}}{{2{x^2} + 5x + 2}} > \frac{1}{{x + 1}}$, then
$ - 2 > x > - 1$
$ - 2 \ge x \ge - 1$
$ - 2 < x < - 1$
$ - 2 < x \le - 1$
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
If the inequality $kx^2 -2x + k \geq 0$ holds good for atleast one real $'x'$ , then the complete set of values of $'k'$ is
If $a, b, c$ are real numbers such that $a+b+c=0$ and $a^2+b^2+c^2=1$, then $(3 a+5 b-8 c)^2+(-8 a+3 b+5 c)^2$ $+(5 a-8 b+3 c)^2$ is equal to
The equation $\sqrt {3 {x^2} + x + 5} = x - 3$ , where $x$ is real, has
Let $\alpha$ and $\beta$ be the roots of $x^2-6 x-2=0$, with $\alpha>\beta$. If $a_n=\alpha^n-\beta^n$ for $n \geq 1$, then the value of $\frac{a_{10}-2 a_8}{2 a_9}$ is