Solve the given two equations and select the correct option.
$I. 13x - 8y + 81 = 0$
$II. 15x - 5y + 65 = 0$

The values of $a$ for which $(a^2 - 1)x^2 + 2(a - 1)x + 2$ is positive for any $x$ are

If $\lambda$ is the ratio of the roots of the quadratic equation in $x$,$3m^2x^2 + m(m - 4)x + 2 = 0$,then the least value of $m$ for which $\lambda + \frac{1}{\lambda} = 1$ is:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 2x + 2 = 0$,then the least value of $n$ for $(\frac{\alpha}{\beta})^n = 1$ is

If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$,then the equation whose roots are $2 + \alpha$ and $2 + \beta$ is:

Let $\alpha$ and $\beta$ be the roots of the equation $px^2 + qx + r = 0$ (where $p \neq 0$). If $p, q, r$ are in $A.P.$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is