Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

If ^n C₁+3^ 2 n C₃+5^ 2 n C₅+ n(n+1) =2^ n- n 3, n N then is equal to

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aligned & n(x-1)^ n-1 +n(n-1) x(x-1)^ n-2 =n^n C_n x^ n-1 -(n-1)^ 2 n C_ n-1 x^ n-2 + +(-1)^ n-1 ^n C₁...(1) & also n(x+1)^ n-1 +n(n-1) x(x+1)^ n-2 = ^n C₁+2^ 2 n C₂ x+ +n^2 C₁₁ x^ n-1 ....(2) & Puting x=1 and adding (1) and (2) we get 1^ 2 n C₁+3^ 2 n C₃+5^2 ^n C₅+ =n(n+1) 2^ n-3 & Hence =3 . aligned

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