JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 September 2020, Shift 2, Maths Q58

Question 58 of 75 in this shift, Maths question 8 of 25.

Let S be the sum of the first 9 terms of the series :

\{x+ka\}+\{x^2+(k+2)a\}+\{x^3+(k+4)a\}+\{x^4+(k+6)a\}+\ldots

where

a \neq 0

and

x \neq 1

. If

S=\frac{x^{10}-x+45a(x-1)}{x-1}

, then k is equal to :

(1) $-3$ Official answer
(2) $-5$
(3) $1$
(4) $3$

Official answer

Option 1

NTA final key (Sep 2020).

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: AP Sum of n terms

Same idea in other shifts

Asked 31× in all

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2 Apr 2025, Shift 1 · Q19Let $a_1, a_2, a_3,\ldots$ be in an A.P. such that $\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1$ , $a_1\neq0$ . If $\sum_{k=1}^{n}a_k=0$ , then…MediumSingle correct
7 Apr 2025, Shift 2 · Q6Let $a_n$ be the $n^{\mathrm{th}}$ term of an A.P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700$ , $a_6=7$ and $S_7=7$ , then $a_n$ is equal to :MediumSingle correct
5 Apr 2024, Shift 1 · Q25Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms. Let…HardNumerical value
6 Apr 2024, Shift 2 · Q7A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start…MediumSingle 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.