JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 24 February 2021, Shift 2, Maths Q84

Question 84 of 90 in this shift, Maths question 24 of 30, Section B.

Let

i=\sqrt{-1}

. If

\frac{(-1+i\sqrt{3})^{21}}{(1-i)^{24}}+\frac{(1+i\sqrt{3})^{21}}{(1+i)^{24}}=k

, and

\mathrm{n}=[|k|]

be the greatest integral part of

|k|

. Then

\sum_{j=0}^{n+5}(j+5)^2-\sum_{j=0}^{n+5}(j+5)

is equal to __________.

Official answer

310

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: De Moivre's Theorem for Integer Powers

Same idea in other shifts

Asked 4× in all

4 Aug 2021, Shift 2 · Q81If $z=\frac{\sqrt3-i}{2}$ and $(z^{95}+i^{95})^{94}=z^n$ , then the minimum positive integral value of ‘ $n$ ’ is ________ .MediumNumerical value
26 Aug 2021, Shift 2 · Q62If $(\sqrt{3}+i)^{100}=2^{99}(\mathrm{p}+i\mathrm{q})$ , then p and q are roots of the equation :MediumSingle correct
26 Aug 2021, Shift 2 · Q88The least positive integer n such that $\frac{(2i)^{\mathrm{n}}}{(1-i)^{\mathrm{n}-2}}$ , $i=\sqrt{-1}$ , is a positive integer, is…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 108 of the 174 JEE Main shifts held from 2017 to 2026.