Find the sum of all integral values of $a$ such that the equation $||x - 2| - |3 - x|| = 2 - a$ has a solution.

The cost and revenue functions of a product are given by $C(x) = 20x + 4000$ and $R(x) = 60x + 2000$ respectively,where $x$ is the number of items produced and sold. The value of $x$ to earn profit is

The solution set of the inequation $\sqrt{x^2+x-2} > (1-x)$ is

To receive grade $A$ in a course,one must obtain an average of $90$ marks or more in five examinations (each of $100$ marks). If Sunita's marks in the first four examinations are $87, 92, 94,$ and $95,$ find the minimum marks that Sunita must obtain in the fifth examination to get grade $A$ in the course.

$A$ solution of $8 \%$ boric acid is to be diluted by adding a $2 \%$ boric acid solution to it. The resulting mixture is to be more than $4 \%$ but less than $6 \%$ boric acid. If we have $640$ litres of the $8 \%$ solution,how many litres of the $2 \%$ solution will have to be added?

$\left\{x \in R : \frac{\sqrt{6+x-x^2}}{2x+5} \geq \frac{\sqrt{6+x-x^2}}{x+4}\right\}=$