JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q81

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

Let

I_n=\int_1^e x^{19}(\log|x|)^n dx

, where

n\in\mathbf{N}

. If

(20)I_{10}=\alpha I_9+\beta I_8

, for natural numbers

\alpha

and

\beta

, then

\alpha-\beta

equals to __________.

Official answer

NTA final key.

Chapter: Integrals
Topic: Integration by Parts
Idea tested: Algebraic Reduction Formulas

Same idea in other shifts

Asked 3× in all

11 Apr 2023, Shift 1 · Q26For $m, n > 0$ , let $\alpha(m, n) = \int_0^2 t^m(1+3t)^n\,dt$ . If $11\,\alpha(10, 6) + 18\,\alpha(11, 5) = p\,(14)^6$ , then $p$ is equal…HardNumerical value
28 Jul 2022, Shift 2 · Q69Let $I_n(x)=\int_0^x\frac{1}{(t^2+5)^n}dt,\ n=1,2,3,....$ Then :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.