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NDA Binomial Theorem questions with solutions

Expansion and coefficients of binomial powers. 16 questions from our 2016–2025 NDA 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 JEE Advanced

NDA 2025

The number of terms in the expansion of (a+b)^10+(a-b)^10 after simplification isNDA 2025 Maths · hard
The number of terms in the expansion of (x+y)^10+(x-y)^10 after simplification isNDA 2025 Maths · easy
In the expansion of (1+2x)^7, the ratio of the coefficient of x^3 to the coefficient of x^2 isNDA 2025 Maths · medium

NDA 2024

What is the sum of the coefficients of the even powers of x in the expansion of (1+x)^10?NDA 2024 Maths · hard

NDA 2023

The sum of the coefficients in the expansion of (2x-3)^5 isNDA 2023 Maths · easy
In the expansion of (1+x)^n, the coefficients of x^3 and x^4 are in the ratio 1:2. The value of n isNDA 2023 Maths · hard
The value of dbinom121+dbinom123+dbinom125+…+dbinom1211 isNDA 2023 Maths · medium
If binom n0+binom n2+binom n4+…=128, then n equalsNDA 2023 Maths · medium

NDA 2020

The term independent of x in the expansion of (2x-(1)/(x^2)^9 isNDA 2020 Maths · hard
The expansion of (x+a)^10 has two middle terms. 2. The expansion of (x+a)^11 has two middle terms.NDA 2020 Maths · easy
Binomn0+binomn1+…+binomnn=2^n. 2. binomn0+binomn2+binomn4+…=2^n-1 for every positive integer n.NDA 2020 Maths · medium

NDA 2019

The coefficient of x^3 in the expansion of (3-2x)^5 isNDA 2019 Maths · medium
If the coefficients of the 5th, 6th and 7th terms in the expansion of (1+x)^n are in AP, the sum of all possible values of n isNDA 2019 Maths · hard
All the binomial coefficients in the expansion of (1+x)^8 are even. 2. The expansion of (a+b)^9 has a single middle term.NDA 2019 Maths · medium

NDA 2017

In the expansion of (1+x)^10, consider the statements. 1. The greatest binomial coefficient is 252. 2. The number of terms is 10.NDA 2017 Maths · easy

NDA 2016

The greatest binomial coefficient in the expansion of (1+x)^9 isNDA 2016 Maths · easy