JEE Main 2024 Mathematics question
The coefficient of x⁷⁰ in x²(1 + x)⁹⁸ + x³(1 + x)⁹⁷ + x⁴(1 + x)⁹⁶ + .... + x⁵⁴(1 + x)⁴⁶ is ⁹⁹ − ⁴⁶. Then a possible value of p + q is
Answer: (D)
Solution
The coefficient of x⁷⁰ is ⁹⁸C₆₈ + ⁹⁷C₆₇ + ⁹⁶C₆₆ + … + ⁴⁶C₁₆ = ⁹⁸C₃₀ + ⁹⁷C₃₀ + … + ⁴⁶C₃₀ = ⁹⁹C₃₁ − ⁴⁶C₃₁ (by the hockey-stick identity). Since
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