JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q24

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

Let

0 < z < y < x

be three real numbers such that

\frac{1}{x}, \frac{1}{y}, \frac{1}{z}

are in an arithmetic progression and

x, \sqrt{2}y, z

are in a geometric progression. If

xy + yz + zx = \frac{3}{\sqrt{2}}xyz

, then

3(x + y + z)^2

is equal to ________

Official answer

150

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Simultaneous AP, GP, HP Condition

Same topic in other shifts

All AP and GP questions

2 Apr 2026, Shift 1 · Q5Let $A$ be the set of first $101$ terms of an A.P., whose first term is $1$ and the common difference is $5$ and let $B$ be the set of…MediumSingle correct
2 Apr 2026, Shift 2 · Q4Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1, g_2, g_3, \ldots$ be an increasing G.P. If $a_1 = a_2 + g_2 = 1$ and $a_3 + g_3 = 4$ ,…MediumSingle correct
2 Apr 2026, Shift 2 · Q5The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots$ up to 8 terms, is:MediumSingle correct
4 Apr 2026, Shift 1 · Q7The first term of an A.P. of $30$ non-negative terms is $\frac{10}{3}$ . If the sum of this A.P. is the cube of its last term, then its…MediumSingle correct
4 Apr 2026, Shift 2 · Q7Let $\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty$ and $\beta=\frac13+\frac19+\frac1{27}+\ldots\infty$ . Then the value of…EasySingle correct
5 Apr 2026, Shift 1 · Q2Let the sum of the first $n$ terms of an A.P. be $3n^2 + 5n$ . Then the sum of squares of the first 10 terms of the A.P. is:EasySingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.