JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q24

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

If the sum of the co-efficients of all the positive even powers of

x

in the binomial expansion of

\left(2x^3 + \frac{3}{x}\right)^{10}

5^{10} - \beta \cdot 3^9

, then

\beta

is equal to ______________.

Official answer

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Sum of Even and Odd Coefficients

Same idea in other shifts

Asked 4× in all

3 Apr 2025, Shift 2 · Q21Let $(1 + x + x^2)^{10} = a_0 + a_1 x + a_2 x^2 + \ldots + a_{20} x^{20}$ . If $(a_1 + a_3 + a_5 + \ldots + a_{19}) - 11a_2 = 121k$ , then…HardNumerical value
4 Aug 2021, Shift 1 · Q65If $(1+x+x^2)^4=a_0+a_1x+a_2x^2+\ldots\ldots+a_8x^8$ , then the value of $a_0+4a_2+16a_4+\ldots.+2^8a_8$ is equal toMediumSingle correct
18 Mar 2021, Shift 1 · Q66Let $(1+x+2x^2)^{20} = a_0 + a_1x + a_2x^2 + \ldots + a_{40}x^{40}$ . Then, $a_1 + a_3 + a_5 + \ldots + a_{37}$ is equal to :HardSingle 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.