Solve the given two equations and select the correct answer from the given options.
$I.$ $81x^2 - 9x - 2 = 0$
$II.$ $56y^2 - 13y - 3 = 0$

If $\frac{m-a^{2}}{b^{2}+c^{2}}+\frac{m-b^{2}}{c^{2}+a^{2}}+\frac{m-c^{2}}{a^{2}+b^{2}}=3,$ then the value of $m$ is

Let one root of $ax^2 + bx + c = 0$,where $a, b, c$ are integers,be $3 + \sqrt{5}$. Then the other root is:

The value of $2 + \frac{1}{2 + \frac{1}{2 + \dots \infty}}$ 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 $2$: $21 \pi \,cm/s$.

The sum of all the real values of $x$ satisfying the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$ is