The marks scored by Mohan in two tests were $62$ and $48$. Find the minimum marks he should score in the third test to have an average of at least $60$ marks.

The longest side of a triangle is twice the shortest side and the third side is $2 \text{ cm}$ longer than the shortest side. If the perimeter of the triangle is more than $166 \text{ cm}$, then find the minimum length of the shortest side. (in $\text{ cm}$)

The feasible region represented by the inequations $2x + 3y \leq 18$,$x + y \geq 10$,$x \geq 0$,$y \geq 0$ is

In an experiment,a solution of hydrochloric acid is to be kept between $30^{\circ} \text{C}$ and $35^{\circ} \text{C}$. What is the range of temperature in degree Fahrenheit if the conversion formula is given by $C = \frac{5}{9}(F - 32)$,where $C$ and $F$ represent temperature in degree Celsius and degree Fahrenheit,respectively?

The region represented by the inequation $x-y \leq -1, x-y \geq 0, x \geq 0, y \geq 0$ is $.....$

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