One root of the equation $3x^2 - 10x + 3 = 0$ is $\frac{1}{3}$. Find the other root.

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 2(m^2 + 1)x + m^4 + m^2 + 1 = 0$,then $\alpha^2 + \beta^2$ equals:

If the quadratic equation $x^2 + (2 - \tan \theta)x - (1 + \tan \theta) = 0$ has $2$ integral roots,then the sum of all possible values of $\theta$ in the interval $(0, 2\pi)$ is $k\pi$. Then $k$ equals:

If both the roots of the quadratic equation ${x^2} - 2kx + {k^2} + k - 5 = 0$ are less than $5$,then $k$ lies in the interval

Consider the equation $x^2+x-n = 0$,where $n \in N$ and $n \in [5, 100]$. The total number of different values of $n$ such that the given equation has integral roots is:

Solve the given two equations and select the correct answer from the given options.
$I. \quad 4x + 7y = 209$
$II. \quad 12x - 14y = -38$