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Friday, 9 October

JEE Main Maths · Integrals

King's Property

King's Property (Integrals) was asked 3 times in 3 JEE Main shifts, 2024–2025, out of the 42 shifts Lumi analysed. 1 of the 3 had a numerical answer.

Times asked
3
in 3 shifts
Years
2024–2025
Usual format
Single correct
Multi-step
Pattern
New since 2024
repeats across shifts

How it is asked

  • Definite integral using king's property
  • Ratio of integrals using substitution and symmetry

Difficulty

Easy 0Medium 1Hard 2

Where it sits

Chapter: Integrals. Topic: Definite Integral Properties, 30 questions over 12 ideas.

Other repeat ideas in this topic

Every time it came

All 3 questions

Newest first, each with its options and official answer.

  1. 3 Apr 2025, Shift 2 · Q18The integral ∫0π8x dx4cos⁡2x+sin⁡2x\int_0^{\pi} \frac{8x\,dx}{4\cos^2 x + \sin^2 x} is equal toMediumSingle correct
  2. 8 Apr 2025, Shift 2 · Q18Let f(x)f(x) be a positive function and I1=∫−1212x f(2x(1−2x)) dxI_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx and…HardSingle correct
  3. 31 Jan 2024, Shift 1 · Q26Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a function defined by f(x)=4x4x+2f(x)=\frac{4^x}{4^x+2} and…HardNumerical value