Let $a$ and $b$ be two positive real numbers such that $a+2b \leq 1$. Let $A_1$ and $A_2$ be respectively the areas of circles with radii $ab^3$ and $b^2$. Then,the maximum possible value of $\frac{A_1}{A_2}$ is

$A$ 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?

The common region of the solution of the inequations $x+y \geq 5$,$y \leq 4$,$x \geq 2$,$x, y \geq 0$ is

The solution set of the inequation $\frac{x^{2}+6x-7}{|x+4|} < 0$ is

For a positive integer $n$,the inequality $10^{n - 2} > 81n$ holds true if:

$A$ solution is to be kept between $86^{\circ} F$ and $95^{\circ} F$. What is the range of temperature in degree Celsius if the Celsius $(C)$/Fahrenheit $(F)$ conversion formula is given by $F = \frac{9}{5} C + 32$?