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Saturday, 31 October

JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2026, Shift 1, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

Let ee be the base of natural logarithm and let f:{1,2,3,4}→{1,e,e2,e3}f:\{1,2,3,4\}\to\{1,e,e^2,e^3\} and g:{1,e,e2,e3}→{1,12,13,14}g:\{1,e,e^2,e^3\}\to\left\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4}\right\} be two bijective functions such that ff is strictly decreasing and gg is strictly increasing. If ϕ(x)=[f−1{g−1(12)}]x\phi(x)=\left[f^{-1}\left\{g^{-1}\left(\frac{1}{2}\right)\right\}\right]^{x}, then the area of the region R={(x,y):x2≤y≤ϕ(x), 0≤x≤1}\mathrm{R}=\{(x,y): x^2\le y\le\phi(x),\ 0\le x\le 1\} is:
  1. (1)3−log⁡e(2)3log⁡e(2)\frac{3-\log_e(2)}{3\log_e(2)}Official answer
  2. (2)13log⁡e(2)\frac{1}{3\log_e(2)}
  3. (3)3+log⁡e(2)3+\log_e(2)
  4. (4)3+log⁡e(2)2+log⁡e(3)\frac{3+\log_e(2)}{2+\log_e(3)}

Official answer

Option 1

NTA final key.

Chapter
Application of Integrals
Topic
Area Under Curves
Idea tested
Area Between Curves

Same idea in other shifts

Asked 22× in all
  1. 2 Apr 2026, Shift 2 · Q24If the area of the region bounded by 16x2−9y2=14416x^2 - 9y^2 = 144 and 8x−3y=248x - 3y = 24 is AA, then 3(A+6log⁡e(3))3(A + 6\log_e(3)) is equal toHardNumerical value
  2. 5 Apr 2026, Shift 2 · Q24Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a function such that f(x)+3f(π2−x)=sin⁡xf(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x, x∈Rx \in \mathbf{R}. Let the maximum…HardNumerical value
  3. 6 Apr 2026, Shift 2 · Q19The area of the region {(x,y):x2−8x≤y≤−x}\{(x,y): x^2-8x\le y\le -x\} is :EasySingle correct
  4. 8 Apr 2026, Shift 2 · Q18Let f:(1,∞)→Rf : (1, \infty) \to \mathbf{R} be a function defined as f(x)=x−1x+1f(x) = \frac{x-1}{x+1}. Let fi+1(x)=f(fi(x))f^{i+1}(x) = f\left(f^{i}(x)\right),…HardSingle correct
  5. 7 Apr 2025, Shift 1 · Q19If the area of the region bounded by the curves y=4−x24y = 4 - \frac{x^2}{4} and y=x−42y = \frac{x-4}{2} is equal to α\alpha, then 6α6\alpha equalsEasySingle correct
  6. 4 Apr 2024, Shift 1 · Q13One of the points of intersection of the curves y=1+3x−2x2y=1+3x-2x^2 and y=1xy=\frac{1}{x} is (12,2)\left(\frac{1}{2}, 2\right). Let the area of the…HardSingle correct
  7. 6 Apr 2024, Shift 1 · Q12Let the area of the region enclosed by the curves y=3xy=3x, 2y=27−3x2y=27-3x and y=3x−xxy=3x-x\sqrt{x} be AA. Then 10A10A is equal toMediumSingle correct
  8. 8 Apr 2024, Shift 2 · Q12The area of the region in the first quadrant inside the circle x2+y2=8x^2 + y^2 = 8 and outside the parabola y2=2xy^2 = 2x is equal to :MediumSingle 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.