If |{:(.^(9)C(4),.^(9)C(5),.^(10)C(r)),(...

If `|{:(.^(9)C_(4),.^(9)C_(5),.^(10)C_(r)),(.^(10)C_(6 ),.^(10)C_(7),.^(11)C_(r+2)),(.^(11)C_(8),.^(11)C_(9),.^(12)C_(r+4)):}|=0` , then the value of `r` is equal to

A

`3`

B

`4`

C

`5`

D

`6`

Text Solution

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The correct Answer is:

C

`(c )` Given `|{:(.^(9)C_(4),.^(9)C_(5),.^(10)C_(r)),(.^(10)C_(6 ),.^(10)C_(7),.^(11)C_(r+2)),(.^(11)C_(8),.^(11)C_(9),.^(12)C_(r+4)):}|=0`
Apply `C_(2)toC_(1)+C_(2)`
`|{:(.^(9)C_(4),.^(9)C_(5),.^(10)C_(r)),(.^(10)C_(6 ),.^(10)C_(7),.^(11)C_(r+2)),(.^(11)C_(8),.^(11)C_(9),.^(12)C_(r+4)):}|=0`
Value of the determinant `=0`
`implies` Column `2` is same as column `3`
`impliesr=5`

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