The value of discriminant $D$ of the quadratic equation $25x^{2} - 10x + 1 = 0$ is ..... .

If the value of the discriminant of the quadratic equation $2x^{2} + 5x - k = 0$ is $81$,then $k = \dots$

$A$ train,travelling at a uniform speed for $360\, km$,would have taken $48\, min$ less to travel the same distance,if its speed were $5\, km/h$ more. Find the original speed of the train (in $km/h$).

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $2x^{2} - 2\sqrt{6}x + 3 = 0$

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\frac{1}{x} - \frac{1}{x-2} = 3, x \neq 0, 2$.

$x=2$ is a solution of the equation $\ldots \ldots \ldots \ldots.$