JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 24 February 2021, Shift 2, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

The sum of first four terms of a geometric progression (G.P.) is

\frac{65}{12}

and the sum of their respective reciprocals is

\frac{65}{18}

. If the product of first three terms of the G.P. is 1, and the third term is

\alpha

, then

2\alpha

is __________.

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: GP Reciprocal Transformation

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 108 of the 174 JEE Main shifts held from 2017 to 2026.