JEE Main 2022 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 26 June 2022, Shift 2, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

\left({}^{40}C_0\right) + \left({}^{41}C_1\right) + \left({}^{42}C_2\right) + \ldots + \left({}^{60}C_{20}\right) = \frac{m}{n}\,{}^{60}C_{20}

m

and

n

are coprime, then

m + n

is equal to ______.

Official answer

102

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Hockey Stick Identity

Same idea in other shifts

Asked 4× in all

4 Apr 2026, Shift 1 · Q9Let the smallest value of $k\in\mathbb{N}$ , for which the coefficient of $x^3$ in…MediumSingle correct
24 Feb 2021, Shift 2 · Q71If $n\geq2$ is a positive integer, then the sum of the series ${}^{n+1}C_2+2\left({}^{2}C_2+{}^{3}C_2+{}^{4}C_2+\ldots.+{}^{n}C_2\right)$ …MediumSingle correct
4 Sep 2020, Shift 1 · Q55The value of $\sum_{r=0}^{20} {}^{50-r}C_6$ is equal to :MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.