Solve the given two equations and select the correct answer from the given options.
$I.$ $821 x^{2} - 757 x^{2} = 256$
$II.$ $\sqrt{196} y^{3} - 12 y^{3} = 16$

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

Roots of $2 k x^{2}+5 k x+2=0$ are equal if $k$ is equal to

Solve the given two equations and select the correct option.

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$ ($a \ne 0$; $a, b, c$ being distinct),then $(1 + \alpha + \alpha^2)(1 + \beta + \beta^2) = $

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.