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Number of values of r satisfying the equ...

Number of values of r satisfying the equation
` ""^(69)C_(3r-1)- ""^(69)C_(r^(2)) = ""^(69)C_(r^(2)-1) - ""^(69)C_(3r) ` is

A

1

B

2

C

3

D

7

Text Solution

Verified by Experts

The correct Answer is:
c,d
`""^(69)C_(3r) + ""^(69)C_(3r) = ""^(69)C_(r^(2)-1) + ""^(69)C_(r^(2))`
` rArr ""^(70)C_(3r) = ""^(70)C_(r^(2))`
` rArr r^(2) = 3r or 70 - 3r = r^(3)`
`rArr r = 0 , 3 or r^(3( + 3r - 70 = 0 `
` rArr r = 0 , 3 or (r + 10 ) (r - 7) = 0 `
` rArr r = 0, 3, 7, - 10 `
But r = 0 , - 10 do not satisfiles the given equation .
Hence , two values of r satisfies ,
i.e. r = 3,7
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