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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

_ r=0 ²⁴ 100 4 r 100 4 t+2 _ r=1 ²⁵ 200 8 r-6 is equal to

Correct answer

1

Step-by-step solution

aligned & S = ¹⁰⁰ C ₀ ¹⁰⁰ C ₂+ ¹⁰⁰ C ₄ ¹⁰⁰ C ₆+ + ¹⁰⁰ C ₉₆ ¹⁰⁰ C ₉₈ & = Coefficient of x ^0 in (1+ x )¹⁰⁰ (1+ x )¹⁰⁰ x ^2 + (1+ x )¹⁰⁰ x ^4 (1+ x )¹⁰⁰ x ^6 + + (1+ x )¹⁰⁰ x ⁹⁰ (1+ x )¹⁰⁰ x ⁹⁸ & = Coefficient of x ^0 in (1+ x )²⁰⁰ (1- x ²⁰⁰ ) x ¹⁹⁴ (1- x ^8 ) & = Coefficient of x ¹⁹⁴ in (1+ x )²⁰⁰ (1- x ^8 )⁻¹= ²⁰⁰ C ₂+ ²⁰⁰ C ₁₀+ + ²⁰⁰ C ₁₉₄ . aligned

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