JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2025, Shift 2, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

Let

f(x)

be a positive function and

I_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx

and

I_2 = \int_{-1}^{2} f\big(x(1-x)\big)\,dx

. Then the value of

\frac{I_2}{I_1}

is equal to __________

(1)12
(2)9
(3)6
(4)4Official answer

Official answer

Option 4

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
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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
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
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.