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?
$\left(p_{1}+p_{2}+p_{3}+p_{4}+p_{5}\right)=26$
$\mathrm{p}_{5}=11$
$\mathrm{p}_{3}=\mathrm{p}_{5}-\mathrm{p}_{4}$
$\mathrm{p}_{5}=\mathrm{p}_{2} \cdot \mathrm{p}_{3}$
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)
The number of positive integers $x$ satisfying the equation $\frac{1}{x}+\frac{1}{x+1}+\frac{1}{x+2}=\frac{13}{2}$ is.
Let $y = \sqrt {\frac{{(x + 1)(x - 3)}}{{(x - 2)}}} $, then all real values of $x$ for which $y$ takes real values, are
If $x$ is real, then the maximum and minimum values of the expression $\frac{{{x^2} - 3x + 4}}{{{x^2} + 3x + 4}}$ will be
The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are