Find the total number of rectangles on the normal chessboard.

The number of rectangles that a chessboard has

The number of rectangles in the following figure is

Find the total number of proper factors of the number 35700. Also find (1)sum of all these factors (2)sum of the odd proper divisors (3)the number of proper divisors divisible by 10 and the sum of these divisors.

The half-life of a radioisotope is 10 h . Find the total number of disintergrations in the tenth hour measured from a time when the activity was 1 Ci.

Find the number of ways in which two small squares can be selected on the normal chessboard if they are not in same row or same column.

Find the total number of positive integral solutions for (x ,y ,z) such that x y z=24. Also find out the total number of integral solutions.