Solve the following mathematical problems:

A committee of 5 persons is to be formed form 6 male and 5 female members. In how many this committee can be formed so that there is at least 1 male and 1 female member in the committee?

Solve the following mathematical problems:

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

Solve the following mathematical problems:

A two digit number is four times the sum of the two digits. If the digits are reversed, the number so obtained is 18 more than the original number. What is the original number?

Solve the following mathematical problems:

Solve:$x^2-xy=7, y^2+xy=30$

Solve the following mathematical problems:

Someone plans to invest x taka in the bond of 'M' company, which pays 10% interest and y taka in 'N' company bonds, which pay 9% interest. He will invest 9,000 taka require that he receives 850 taka as interest. How much should be invest in each company?

Solve the following mathematical problems:

A circle is inscribed inside a right angled triangle with equal sides. What is the area of the circle if the length of one side of the right angled triangle is 4cm?