Divide $16$ into $2$ parts such that twice the square of the larger part exceeds the square of the smaller part by $164$.

The two roots of the equation $x^3 - 9x^2 + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots are:

Solve the given two equations and select the correct option.
$I.$ $\frac{x}{x-11} + \frac{x-11}{x} = 7$
$II.$ $\frac{4y}{4y-13} + \frac{4y-13}{4y} = 9$

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

If $|x - 2| + |x - 3| = 7$,then $x =$

$Quantity \, 1:$ 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.