The values of $\frac{x^2-2x+1}{x^2+x-1}$ do not lie in the interval

If both roots of the quadratic equation $x^2 + (\sin \theta + \cos \theta)x + \frac{3}{8} = 0$ are positive and distinct,then the complete set of values of $\theta$ in $[0, 2\pi]$ is:

For $x \in R$, the least value of $\frac{x^2-6x+5}{x^2+2x+1}$ is

If $\frac{x^2+ax+3}{x^2+x+1}$ takes all real values for all real values of $x$,then $a$ lies in the interval

The population of cattle in a farm increases such that the difference between the population in year $n+2$ and that in year $n$ is proportional to the population in year $n+1$. If the populations in years $2010, 2011$ and $2013$ were $39, 60$ and $123$ respectively,then the population in $2012$ was:

If $\alpha$ and $\beta$ are the distinct roots of the equation $x^{2}+(3)^{1/4}x+3^{1/2}=0$,then the value of $\alpha^{96}(\alpha^{12}-1) + \beta^{96}(\beta^{12}-1)$ is equal to: