JEE Main 26 February 2021, Shift 2, Maths Q81

Question 81 of 90 in this shift, Maths question 21 of 30, Section B.

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}

\alpha \in \mathbf{R}

, then

\alpha

equals __________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 2× in all

5 Apr 2024, Shift 2 · Q11Let $\beta(m, n) = \int_0^1 x^{m-1}(1-x)^{n-1}\,dx$ , $m, n > 0$ . If $\int_0^1 (1-x^{10})^{20}\,dx = a \times \beta(b, c)$ , then…MediumSingle 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.