The area of a rectangle is thrice that of square. Length of the rectangle is 40 cm and the breadth of the rectangle is ( 3 / 2 ) times that of the side of the square. The side of the square in cm is?

We have to arrange 6 books.

The number of permutations of n objects is n! = n. (n ? 1) . (n ? 2) ... 2.1

Here n = 6 and therefore, number of permutations is 6.5.4.3.2.1 = 720

The number of arrangements of 4 different digits taken 4 at a time is given by  4 P 4 = 4! = 24.All the four digits will occur equal number of times at each of the position,namely ones,tens,hundreds,thousands.

Thus,each digit will occur 24/4 = 6 times in each of the position.The sum of digits in one's position will be 6 x (1+3+5+7) = 96.Similar is the case in ten's,hundred's and thousand's places.

Therefore,the sum will be 96 + 96 x 10 + 96 x 100 + 96 x 100 = 106656

In a 3 digit number one?s place can be filled in 5 different ways with (0,2,4,6,8)

10?s place can be filled in 10 different ways

100?s place can be filled in 9 different ways

There fore total number of ways = 5X10X9 = 450