If `(n-1)C_r=(k^2-3)nC_(r+1)`,then k belong to

Options

A. `(-oo,-2]`
B. `(2,oo]`
C. `[-sqrt(3),sqrt(3)]`
D. `(sqrt(3),2]`

Explanation

We have,
`""^(n-1)C_(r)=(k^(2)-3)""^(n)C_(r+1)`
`implies((n-1)!)/((n-1-r)!r)=(k^(2)-3)(n!)/((n-r-1)!(r+1)!)`
`implies1=((k^(2)-3)n)/((r+1)`
`implies(r+1)/(n)=k^(2)-3" "[:'0lerlen-1impliesr+1len]`
`impliesk^(2)-3le1impliesk^(2)-4le0implies-2lekle2" "....(i)`
Again, `""^(n-1)C_(r)=(k^(2)-3)""^(n)C_(r+1)`
`impliesk^(2)-3=(""^(n-1)C_(r))/(""^(n)C_(r+1))gt0`
`impliesk^(2)-3gt0impliesklt-sqrt3orkgtsqrt3" "....(ii)`
From (i) and (ii), we have `kin(sqrt3,2]`.