Comparing the quadratic equation $x(2x - 1) - 5 = 0$ with the standard form $ax^2 + bx + c = 0$,we get $a = \ldots \ldots \ldots \ldots$.

In a rectangle $ABCD$,if $AB + BC = 47$ and the diagonal $AC = 37$,find the lengths of $AB$ and $BC$,given that $AB > BC$.

At present,Asha's age (in $years$) is $2$ more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age,Asha's age would be one year less than $10$ times the present age of Nisha. Find the present ages of both Asha and Nisha (in $years$).

Which of the following equations has $2$ as a root?

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $6x^{2}-5x-1=0$.

Examine whether the following equation is quadratic or not: $9x = 3x^3$.