If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$ where $p \ne q$,then the equation whose roots are $3p - 2q$ and $3q - 2p$ is

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}+5x+6=0$
$II.$ $y^{2}+7y+12=0$

If $a < 0$,then the inequality $ax^2 - 2x + 4 > 0$ has the solution represented by:

If $10$ men and $15$ women complete a piece of work in $8$ days,while $12$ men and $8$ women can complete the same piece of work in $10$ days. $A$ boy,who is $50 \%$ less efficient than a man,can do the same work in $50$ days.
$Quantity \, I$: Time taken by $2$ men,$4$ women,and $18$ boys to complete the work.
$Quantity \, II$: Time taken by $9$ men,$3$ women,and $6$ boys to complete the same work.

Solve the given two equations and select the correct option.
$I.$ $x^{2} + 42 = 13x$
$II.$ $y = \sqrt[4]{1296}$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + qx - r = 0$,then find the equation whose roots are $\left( \beta \gamma + \frac{1}{\alpha} \right), \left( \gamma \alpha + \frac{1}{\beta} \right), \left( \alpha \beta + \frac{1}{\gamma} \right)$.