The area of a square is $$𝑑.$$ What is the area of the circle which has the diagonal of the square as its diameter?

A cube is built using $$64$$ cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is __________ .

In a quadratic function, the value of the product of the roots $$\left( {\alpha ,\beta } \right)$$ is $$4.$$ Find the value of $$${{{\alpha ^n} + {\beta ^n}} \over {{\alpha ^{ - n}} + {\beta ^{ - n}}}}$$$

Among $$150$$ faculty members in an institute, $$55$$ are connected with each other through Facebook^® and $$85$$ are connected through WhatsApp^®. $$30$$ faculty members do not have Facebook^® or whatsApp^® accounts. The number of faculty members connected only through Facebook^® accounts is ______________.