Find the roots of the equation $\sqrt{3y+1} = \sqrt{y-1}$.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 2x - 5 = 0$ and the equation $x^3 + bx^2 + cx + d = 0$ has roots $2\alpha + 1, 2\beta + 1, 2\gamma + 1$,then the value of $|b + c + d|$ is (where $b, c, d$ are constants):

If the equation $x^2 + \lambda x + \mu = 0$ has equal roots and one root of the equation $x^2 + \lambda x - 12 = 0$ is $2$,then $(\lambda, \mu) = $

If $\sin A, \sin B, \cos A$ are in $G.P.$,then the roots of ${x^2} + 2x \cot B + 1 = 0$ are always

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-7 \sqrt{3} x+35 \sqrt{15}=5 \sqrt{5} x$
$II.$ $y^{2}-5 \sqrt{5} y+30=0$

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 - x - 1 = 0$,then the equation whose roots are $\frac{1}{\beta + \gamma}, \frac{1}{\gamma + \alpha}, \frac{1}{\alpha + \beta}$ is: