An equation equivalent to the quadratic equation $x^{2}-6x+5=0$ is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}+20=9x$
$II.$ $y^{2}+42=13y$

Solve the given two equations and select the correct answer from the given options.
$I. \quad 3x + 4y = (1681)^{1/2}$
$II. \quad 3x + 2y = (961)^{1/2}$

The value of $m$ for which the equation $\frac{a}{x + a + m} + \frac{b}{x + b + m} = 1$ has roots equal in magnitude but opposite in sign is

The number of integral values of $m$ for which the equation $(1 + m^2) x^2 - 2(1 + 3m) x + (1 + 8m) = 0$ has no real root is

If $\left\{\frac{1}{2}(a-b)\right\}^{2}+a b=p(a+b)^{2},$ then the value of $p$ is (assume that $a \neq-b).$