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JEE Advanced Binomial Theorem questions with solutions

Binomial expansion, general term and coefficient problems. 10 questions from our 2017–2025 JEE Advanced pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Binomial Theorem for JEE Main · Binomial Theorem for NDA

JEE Advanced 2025

Let n=10 and let Ck=binom10k.JEE Advanced 2025 Paper 1 · medium
The coefficient of x^6 in the expansion of (1+x)^5(1+x+x^2^4 is ______.JEE Advanced 2025 Paper 2 · medium

JEE Advanced 2023

Let N be the number of integers k with 0≤ k≤100 for which binom100k is odd and also divisible by 3. Find N.JEE Advanced 2023 Paper 1 · hard
The value of S=Σk=0^8((-1)^kbinom8k)/(k+3) isJEE Advanced 2023 Paper 2 · medium

JEE Advanced 2022

For the binomial coefficients with n=10, identify all the correct evaluations among the following.JEE Advanced 2022 Paper 1 · medium

JEE Advanced 2021

Let an=(3+√5)^n+(3-√5)^n. The remainder when lfloor(3+√5)^21rfloor is divided by 8 is ____.JEE Advanced 2021 Paper 1 · hard
Let N=Σk=1^2021kbinom2021k2^k-1. The remainder when N is divided by 7 isJEE Advanced 2021 Paper 2 · hard

JEE Advanced 2019

Which of the following statements is (are) correct?JEE Advanced 2019 Paper 1 · hard
Consider the sums U=Σk=0^10(binom10k)/(k+1), V=Σk=0^10((-1)^kbinom10k)/(k+1), W=Σk=0^10kbinom10k and Z=Σk=0^10binom10k^2.JEE Advanced 2019 Paper 2 · medium

JEE Advanced 2017

Consider the following sums built from binomial coefficients binom10k of the tenth row of Pascal's triangle. Which of them is/are evaluated correctly?JEE Advanced 2017 Paper 2 · hard

Other Mathematics topics

Area Under Curves 13 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9