If the discriminant of $x^{2}-10x+(2k-1)=0$ is $40$,then $k=$...............

Examine whether the following equation is quadratic or not: $x+\frac{1}{x}=x^{2} (x \neq 0)$

When there is a decrease of $5\, km/hr$ in the usual uniform speed of a train,it takes $4$ hours more than the usual time for covering the distance of $400\, km$. Find the usual speed of the train.

If the roots of the following quadratic equation exist,find them by the method of completing the square: $x + \frac{2}{x} - 8 = 0$.

The standard form of a quadratic equation in one variable is $\ldots \ldots \ldots \ldots . .$

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $6x^{2}-x-2=0, x=3$.