JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 13 April 2023, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let

a_1, a_2, a_3, \ldots

be a G.P. of increasing positive numbers. Let the sum of its

6^{th}

and

8^{th}

terms be

2

and the product of its

3^{rd}

and

5^{th}

terms be

\frac{1}{9}

. Then

6(a_2+a_4)(a_4+a_6)

is equal to

(1) $2$
(2) $2\sqrt{2}$
(3) $3\sqrt{3}$
(4) $3$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: GP General Term

Same idea in other shifts

Asked 6× in all

3 Apr 2025, Shift 1 · Q6Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive numbers. If $a_3 a_5 = 729$ and $a_2 + a_4 = \frac{111}{4}$ , then…EasySingle correct
7 Apr 2025, Shift 2 · Q7If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is…MediumSingle correct
30 Jan 2024, Shift 2 · Q6Let $a$ and $b$ be be two distinct positive real numbers. Let $11^{\mathrm{th}}$ term of a GP, whose first term is $a$ and third term is…EasySingle correct
31 Jan 2024, Shift 2 · Q7Let $2^{nd}$ , $8^{th}$ and $44^{th}$ terms of a non-constant A. P. be respectively the $1^{st}$ , $2^{nd}$ and $3^{rd}$ terms of a G. P. If…MediumSingle correct
16 Mar 2021, Shift 2 · Q89Let $\frac{1}{16}$ , a and b be in G.P. and $\frac1a,\frac1b$ , 6 be in A.P., where $a,b>0$ . Then $72(a+b)$ is equal to ________.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 42 of the 174 JEE Main shifts held from 2017 to 2026.