If the roots of the equation $8{x^3} - 14{x^2} + 7x - 1 = 0$ are in $G.P.$, then the roots are
$1,\frac{1}{2},\frac{1}{4}$
$2, 4, 8$
$3, 6, 12$
None of these
The number of solutions, of the equation $\mathrm{e}^{\sin x}-2 e^{-\sin x}=2$ is
The value of $x$ in the given equation ${4^x} - {3^{x\,\; - \;\frac{1}{2}}} = {3^{x + \frac{1}{2}}} - {2^{2x - 1}}$is
If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$, then
Let $r_1, r_2, r_3$ be roots of equation $x^3 -2x^2 + 4x + 5074 = 0$, then the value of $(r_1 + 2)(r_2 + 2)(r_3 + 2)$ is
Let $\alpha$ and $\beta$ be the roots of the equation $\mathrm{x}^{2}-\mathrm{x}-1=0 .$ If $\mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geq 1,$ then which one of the following statements is not true?