List of top Mathematics Questions on Properties of Determinants asked in AMUEEE

If $f(x)$ = $ \begin{vmatrix}x+1&x&1\\ x\left(x+1\right)&x\left(x-1\right)&2x\\ x\left(x+1\right)\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&3x\left(x-1\right)\end{vmatrix} $ , then $ f(1000) $ is equal to
If $ \begin{vmatrix}\left(x+a\right)&b&c\\ a&\left(x+b\right)&c\\ a&b&\left(x+c\right)\end{vmatrix} $ = 0 , then $ x $ =