JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 February 2021, Shift 1, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

The value of

-{}^{15}C_1 + 2 \cdot {}^{15}C_2 - 3 \cdot {}^{15}C_3 + \dots - 15 \cdot {}^{15}C_{15} + {}^{14}C_1 + {}^{14}C_3 + {}^{14}C_5 + \dots + {}^{14}C_{11}

is :

(1) $2^{16} - 1$
(2) $2^{13} - 14$ Official answer
(3) $2^{13} - 13$
(4) $2^{14}$

Official answer

Option 2

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Zero Alternating Moments

Same topic in other shifts

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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.