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If $Δ (x) = |\begin{array}{ccc} 1 & x & x + 1 \\ 2 x & x (x - 1) & x (x + 1) \\ 3 x (x - 1) & x (x - 1) (x - 2) & x (x^{2} - 1) \end{array}|$ then $∆ (100)$ equals

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Correct option is A

Taking x common from C2, x + 1 from C3and x – 1 from R3, we getΔ(x)=x(x+1)(x−1)1112xx−1x3xx−2xApplying C1→C1−C3,C2→C2−C3 we get Δ(x)=x(x+1)(x−1)001x−1x2x2x=0 [ C1 and C2 are proportional]Thus , ∆ (100) =0

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If Δ(x)=1xx+12xx(x−1)x(x+1)3x(x−1)x(x−1)(x−2)xx2−1 then ∆(100) equals

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If $Δ (x) = |\begin{array}{ccc} 1 & x & x + 1 \\ 2 x & x (x - 1) & x (x + 1) \\ 3 x (x - 1) & x (x - 1) (x - 2) & x (x^{2} - 1) \end{array}|$ then $∆ (100)$ equals