JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 August 2021, Shift 2, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

The value of the integral

\int_1^6\frac{\log_e x\,dx}{\log_e x^2+\log_e(x^2-14x+49)}

(1) $\frac{5}{4}$ Official answer
(2) $\frac{5}{8}$
(3) $\frac{7}{4}$
(4) $\frac{5}{2}$

Official answer

Option 1

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: King's Property

Same idea in other shifts

Asked 18× in all

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1 Feb 2024, Shift 1 · Q10The value of the intergral $\int_0^{\pi/4}\frac{x\,dx}{\sin^4(2x)+\cos^4(2x)}$ equals :HardSingle correct
1 Feb 2024, Shift 2 · Q11The value of $\int_{-0}^{1}(2x^3-3x^2-x+1)^{\frac{1}{3}}\,dx$ is equal to :MediumSingle correct
27 Jan 2024, Shift 1 · Q12If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1, 2)$ , $(2, 3)$ and $(3, 1)$ , and $I_1=\int_a^b x\sin(4x-x^2)\,dx$ ,…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.