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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

_ r=0 ^9 ²⁰ c_ 2 r ²⁰ c_ 2 r+2 = a a+1 ( ³⁹ c₂₁- ¹⁹ c₁₀ ) and x y=4 a then total number of ordered pair solution (x, y) where x, y I⁺ is

Correct answer

8

Step-by-step solution

aligned & (1+x)²⁰+(1-x)²⁰ 2 = ²⁰ c₀+ ²⁰ c₂ x^2+ ²⁰ c₄ x^4+---- ²⁰ c₂₀ x²⁰ & = ²⁰ c₀ x²⁰+ ²⁰ c₂ x¹⁸+ ²⁰ c₄ x¹⁶+----- ²⁰ c₂₀ & So, _ r=0 ^9 ²⁰ c_ 2 r ²⁰ c_ 2 r+2 = coeff of x²² in [(1+x)^ 2 n +(1-x)^ 2 n ] 4 & a=10 x y=40 has total order pair (x, y) solution =4 2=8 aligned

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