If `3^n` is a factor of the determinant `|{:(1,1,1),(.^nC_1,.^(n+3)C_1,.^(n+6)C_1),(.^nC_2, .^(n+3)C_2, .^(n+6)C_2):}|` then the maximum value of n is ……..

Options

A. 7
B. 5
C. 3
D. 1

Answer

C

Explanation

We have,
`Delta = (1)/(2) |(1,1,1),(n,n +3,n +6),(n(n-1),(n+2) (n+3),(n+5) (n +6))|`
`rArr Delta = (1)/(2) |(1,0,0),(n,3,6),(n(n-1),6n + 6,12n + 30)|`
`rArr Delta = 9 |(1,0,0),(n,1,1),(n(n-1),2(n +1),2n +5)| = 27`
Clearly, `Delta = 27` is divisible by 3, `3^(2) and 3^(3)`. Hence, n = 3