Solve the given two equations and select the correct option.
$I.$ $\sqrt{500} x + \sqrt{402} = 0$
$II.$ $\sqrt{360} y + \sqrt{200} = 0$

If $\alpha$ and $\beta$ are the roots of the equation $4x^2 + 3x + 7 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} =$

If one root of the quadratic equation $ix^2 - 2(i + 1)x + (2 - i) = 0$ is $2 - i$,then the other root is

Solve the given two equations and select the correct answer from the given options.
$I.$ $2x^2 + 3x - 20 = 0$
$II.$ $2y^2 + 19y + 44 = 0$

$Quantity \, 1:$ Original duration of flight. In a flight of $3000 \, km$,an aircraft was slowed down by bad weather. Its average speed for the trip was reduced by $100 \, km/hr$ and the time increased by $1 \, hour$.
$Quantity \, 2:$ Usual time of a man who,when walking at $\frac{3}{4}$ of his usual pace,reaches his office $20 \, minutes$ late.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2} = 14641$
$II.$ $y = \sqrt{14641}$