The number of ordered pairs of positive integers `(m,n)` satisfying `m le 2n le 60`, `n le 2m le 60` is

Options

A. `240`
B. `480`
C. `960`
D. none of these

Answer

B

Explanation

`(b)` Given `m le 30`, `n le 30`
`implies`Total cases `=30xx30=900`
[Required condition : `2n ge m`, `2m ge n`
Let us food ordered pairs `(m,n)` such that `2n lt m`, `2m lt n`. By symmetry we will get same answer for both conditions. Hence, let us evaluate only one `2m lt n`
`{:("Value of"n,,"No. of points"(m,n)),("1,2",,0),("3,4",,1),("5,6",,2),("...",,),("29,30",,14):}`
`:. ` Required number `=900-2xxsum_(r=0)^(14)r=480`