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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

If (x-2+ 1 x )³⁰=n₀ x³⁰+n₁ x²⁹+ +n₂₉ x+n₃₀+n₃₁ x⁻¹+ +n₆₀ x⁻³⁰ and C=n₀+n₁+n₂+ +n₆₀ . Find the value of (a+b) if C-n₃₀=- ( array l a b array ) . [Note: ( array l n r array ) denotes ^n C_r . ]

Correct answer

90

Step-by-step solution

aligned & (x-2+ 1 x )³⁰=n₀ x³⁰+n₁ x²⁹+ .+n₂₉ x+n₃₀+n₃₁ x⁻¹+ .+n₆₀ x⁻³⁰ & (x-1)⁶⁰=n₀ x⁶⁰+n₁ x⁵⁹+ .+n₂₉ x³¹+n₃₀ x³⁰+n₃₁ x²⁹+ .+n₆₀ & n₀= ⁶⁰ C₀, n₁=- ⁶⁰ C₁, n₂= ⁶⁰ C₂, . n₃₀= 60 30 . . n₆₀= 60 60 & C=n₀+n₁+n₂+ .+n₆₀=0 aligned Hence, C-n₃₀=- ( array l a b array ) array ll & 0-1 ( 60 30 ) & a=60, b=30 array Hence, a+b=90 .

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