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

What would be the smallest natural number which when divided either by $$20$$ or by $$42$$ or by $$76$$ leaves a remainder of $$7$$ in each case?

What would be the smallest natural number which when divided either by $$20$$ or by $$42$$ or by $$76$$ leaves a remainder of $$7$$ in each case?

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