The value of `|1 1 1\ ^n C_1\ ^(n+2)C_1\ ^(n+4)C_1\ ^n C_2\ ^(n+2)C_2\ ^(n+4)C_2|` is (a) 2 (b) 4 (c) 8 (d) `n^2`

Explanation

Given, `[[1, 1, 1],[ ^n C_1, ^(n+2)C_1, ^(n+4)C_1],[^n C_2, ^(n+2)C_2, ^(n+4)C_2]]`


We know that
`.^(n+2)C_1=(n+2)` and `.^(n+4)C_1=(n+4)`

Also,`.^n C_2=(n(n-1))/2`,`.^(n+2)C_2=((n+2)(n+1))/2`,`.^(n+4)C_2=((n+4)(n+3))/2`

Thus,`/_\=|[1,1,1],[n,n+2,n+4],[(n(n-1))/2,((n+2)(n+1))/2,((n+4)(n+3))/2]|`

Solving we get

`∆ = 1/2 [8n + 20 - 8n - 4] `

`∆ = 8`