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JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 8 April 2023, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

S_K=\frac{1+2+\ldots+K}{K}

and

\sum_{j=1}^{n}S_j^2=\frac{n}{A}(Bn^2+Cn+D)

, where

A,B,C,D\in\mathbb{N}

and

A

has least value. Then

(1) $A+B+C+D$ is divisible by $5$
(2) $A+B$ is divisible by $D$ Official answer
(3) $A+B=5(D-C)$
(4) $A+C+D$ is not divisible by $B$

Official answer

Option 2

NTA final key.

Chapter: Sequences and Series
Topic: No close match in our taxonomy
Idea tested: No close match in our taxonomy

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.