The product of two consecutive odd numbers is $4623$. Which is the greater of the two numbers?

What will come in place of both the question marks (?) in the following equation?

$\frac{{\left(?\right)}^2}{108}=\frac{16}{\left(?\right)}$

In a college the students in Arts and Commerce faculties were in the ratio of $4:5$ respectively. When $65$ more students joined Commerce faculty the ratio became $8:11$ respectively. How many students are there in Arts faculty?

The sum of the square of the first number and the cube of the second number is $568$ together. Also square of the second number is $15$ less than the square of $8$. What is the value of three-fifth of the first number? (assuming both the numbers are positive)