JEE Main 5 April 2024, Shift 2, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let

\beta(m, n) = \int_0^1 x^{m-1}(1-x)^{n-1}\,dx

m, n > 0

. If

\int_0^1 (1-x^{10})^{20}\,dx = a \times \beta(b, c)

, then

100(a+b+c)

equals ________.

(1)2120Official answer
(2)2012
(3)1021
(4)1120

Official answer

Option 1

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Beta Function Integrals

Same idea in other shifts

Asked 2× in all

26 Feb 2021, Shift 2 · Q81If $I_{m,n}=\int_0^1 x^{m-1}(1-x)^{n-1}\,dx$ , for $m, n \ge 1$ , and $\int_0^1 \frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}}dx=\alpha I_{m,n}$ ,…HardNumerical 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 108 of the 174 JEE Main shifts held from 2017 to 2026.