JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 January 2024, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

(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

I_2=\int_a^b \sin(4x-x^2)\,dx

, then

36\dfrac{I_1}{I_2}

is equal to :

(1) $72$ Official answer
(2) $80$
(3) $88$
(4) $66$

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

3 Apr 2025, Shift 2 · Q18The integral $\int_0^{\pi} \frac{8x\,dx}{4\cos^2 x + \sin^2 x}$ is equal toMediumSingle correct
8 Apr 2025, Shift 2 · Q18Let $f(x)$ be a positive function and $I_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx$ and…HardSingle correct
4 Apr 2024, Shift 1 · Q25If $\int_0^{\pi/4}\frac{\sin^2x}{1+\sin x\cos x}dx=\frac{1}{a}\log_e\left(\frac{a}{3}\right)+\frac{\pi}{b\sqrt{3}}$ , where…HardNumerical value
5 Apr 2024, Shift 1 · Q10The value of $\int_{-\pi}^{\pi}\frac{2y(1+\sin y)}{1+\cos^2 y}\,dy$ is :MediumSingle correct
5 Apr 2024, Shift 2 · Q25If $f(t) = \int_0^{\pi} \frac{2x\,dx}{1-\cos^2 t \sin^2 x}$ , $0 < t < \pi$ , then the value of…HardNumerical value
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
31 Jan 2024, Shift 1 · Q26Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by $f(x)=\frac{4^x}{4^x+2}$ and…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.