If $a=b=c,$ then find the value of $\frac{(a+b+c)^{2}}{a^{2}+b^{2}+c^{2}}.$

The roots of $4x^2 + 6px + 1 = 0$ are equal,then the value of $p$ is

Solve the given two equations and select the correct answer from the given options.
$I.$ $x = \sqrt{625}$
$II.$ $y = \sqrt{676}$

The value of $a (a \ge 3)$ for which the sum of the cubes of the roots of $x^2 - (a - 2)x + (a - 3) = 0$ assumes the least value is

If the roots of the equation $12x^2 - mx + 5 = 0$ are in the ratio $2 : 3$,then $m =$

The set of all real values of $\lambda$ for which the quadratic equation $(\lambda^{2}+1) x^{2}-4 \lambda x+2=0$ has exactly one root in the interval $(0,1)$ is