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

Solve the given two equations and choose the correct option.
$I.$ $99 x^{2} + 149 x + 56 = 0$
$II.$ $156 y^{2} + 287 y + 132 = 0$

If $\left(\frac{p^{-1} q^{2}}{p^{3} q^{-2}}\right)^{\frac{1}{3}}+\left(\frac{p^{5} q^{-3}}{p^{-2} q^{3}}\right)^{\frac{1}{3}}=p^{a} q^{b},$ then the value of $a+b,$ where $p$ and $q$ are different positive positive primes,is

If $3$ distinct real numbers $a, b, c$ satisfy $a^2(a + p) = b^2(b + p) = c^2(c + p)$ where $p \in R$,then the value of $bc + ca + ab$ is

Wheels of diameters $7 \,cm$ and $14 \,cm$ start rolling simultaneously from $X$ and $Y$,which are $1990.50 \,cm$ apart,towards each other in opposite directions. Both of them make the same number of revolutions per second. Both of them meet after $10 \,s$.
Quantity $1$: Speed of the smaller wheel.
Quantity $2$: $21 \pi \,cm/s$.

$I. \quad p^{2}-18 p+77=0$
$II. \quad 3 q^{2}-25 q+28=0$
$Quantity \, 1$: Value of $p$
$Quantity \, 2$: Value of $q$