Learn

Saturday, 31 October

JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 16 March 2021, Shift 2, Maths Q87

Question 87 of 90 in this shift, Maths question 27 of 30, Section B.

Let n be a positive integer. Let A=∑k=0n(−1)k nCk[(12)k+(34)k+(78)k+(1516)k+(3132)k]A=\sum_{k=0}^{n}(-1)^k\,{}^nC_k\left[\left(\frac12\right)^k+\left(\frac34\right)^k+\left(\frac78\right)^k+\left(\frac{15}{16}\right)^k+\left(\frac{31}{32}\right)^k\right] If 63A=1−123063A=1-\frac{1}{2^{30}}, then n is equal to ________.

Official answer

6

NTA final key.

Chapter
Binomial Theorem
Topic
Binomial Coefficients
Idea tested
Alternating Binomial Series

Same idea in other shifts

Asked 2× in all
  1. 12 Apr 2023, Shift 1 · Q5The sum, of the coefficients of the first 5050 terms in the binomial expansion of (1−x)100(1-x)^{100}, is equal toMediumSingle 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.