Solve the following mathematical problems:

A maximum sized rectangular playground is made within a circular space of radius$2\sqrt{41}$ meter. Calculate the area of the playground if its length and width are distributed in the proportion of 4: 5.

Solving the following mathematical problems:

70 students are studying physics, mathematics and chemistry. 40 students study mathematics, 35 study physics and 30 study chemistry, 15 students are studying all the subjects. How many students are studying exactly two of the subjects?

Solving the following mathematical problems:

A committee of 5 is to be formed from 6 male students and 5 female students. In how many ways can this be done so that the committee contains at least one male and one female student?

Solving the following mathematical problems:

The profit of a company in Taka is given by P-3x² - 35x + 50, where x is the amount in Taka in lac spent on advertising. For what values of x does the company make a profit?

Solving the following mathematical problems:

A man's salary in 2014 was 20 thousand Taka per month and it is increased by 10% each year. Find how much he earned in the years 2015 to 2017 inclusive.

Solving the following mathematical problems:

Find the three-digit prime number whose sum of the digits is 11 and each digit representing a prime number. Justify your answer.