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JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2026, Shift 2, Maths Q8

Question 8 of 75 in this shift, Maths question 8 of 25, Section A.

If

26\left(\frac{2^3}{3}\,({}^{12}\mathrm{C}_2) + \frac{2^5}{5}\,({}^{12}\mathrm{C}_4) + \frac{2^7}{7}\,({}^{12}\mathrm{C}_6) + \ldots + \frac{2^{13}}{13}\,({}^{12}\mathrm{C}_{12})\right) = 3^{13} - \alpha

, then

\alpha

is equal to :

(1)45
(2)48
(3)51Official answer
(4)54

Official answer

Option 3

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Integration Method for Sums

Same idea in other shifts

Asked 2× in all

29 Jan 2024, Shift 1 · Q23If $\frac{{}^{11}C_1}{2}+\frac{{}^{11}C_2}{3}+\ldots+\frac{{}^{11}C_9}{10}=\frac{n}{m}$ with $\gcd(n,m)=1$ , then $n+m$ is equal to ______.MediumNumerical value

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 42 of the 174 JEE Main shifts held from 2017 to 2026.