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

Examine whether the following equation is quadratic or not: $x^{2} + 5\sqrt{x} - 7 = 0$.

The value of the discriminant of a quadratic equation $kx^{2} - 4x - 4 = 0$ is $64$,then $k = \dots$

Examine whether the following equation is quadratic or not: $(x-2)^{2}+1=2x-3$.

Solve the following equation using the method of factorization and write its solution set: $\frac{x}{1-x} + \frac{1-x}{x} = \frac{13}{6}$

We get $2 \ kg$ of pure butter less in Rs. $960$ if the price of pure butter increases by Rs. $40$ per $kg$. Find the original price of pure butter per kilogram.