JEE Advanced Binomial Theorem — previous year questions
8 questions from 2025, 2023, 2019, 2018, 2016, 2014, 2013, 2010.
- Let a₀, a₁, …, a₂₃ be real numbers such that (1 + 2/5x)²³ = ∑ᵢ₌₀²³ aᵢ xⁱ for every real number x. Let aᵣ be…
- Let a and b be two non-zero real numbers. If the coefficient of x^5 in the expansion of (ax^2 + 70/(27bx))^4…
- Suppose det ∑ₖ₌₀ⁿ k ∑ₖ₌₀ⁿ ⁿCₖk² ∑ₖ₌₀ⁿ ⁿCₖk ∑ₖ₌₀ⁿ ⁿCₖ3ᵏ = 0 holds for some positive integer n. The ∑ₖ₌₀ⁿ…
- Let X = (10C_1)^2 + 2(10C_2)^2 + 3(10C_3)^2 + ... + 10(10C_10)^2, where 10C_r, r in {1,2,...,10} denote…
- Let m be the smallest positive integer such that the coefficient of x² in the expansion of (1 + x)² + (1 +…
- Coefficient of x¹¹ in the expansion of (1+x²)⁴(1+x³)⁷(1+x⁴)¹² is
- The coefficients of three consecutive terms of (1 + x)^(n+5) are in the ratio 5 : 10 : 14. Then n =
- For r = 0, 1, …, 10, let Aᵣ, Bᵣ and Cᵣ denote, respectively, the coefficient of xʳ in the expansions of…