The number of values of 'r' satisfying the equation
`""^(39)C_(3r-1)- ""^(39)C_(r^(2) )= ""^(39)C_(r^(2)-1) - ""^(39)C_(3r)` is

Options

A. 1
B. 2
C. 3
D. 4

Answer

b

Explanation

We have , `""^(39)C_(3r-1) + ""^(39)C_(3r) = ""^(39)C_(r^(2)) + ""^(39)C_(r^(2) - 1)`
` rArr ""^(40)C_(3r) + ""^(40)C_(r^(2))`
`rArr 3r = r^(2) or 40 - 3r = r^(2)`
` rArr r= 0,3 or r^(2) + 3r - 40 = 0 `
`rArr (r + 8)(r-5) = 0 rArr r= 0 , 3,5-8`
But r = 0 , - 8 do not satisfy the given equation
` therefore r = 3,5 `