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Saturday, 31 October

JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

For real numbers a,ba, b (a>b>0a > b > 0), let Area {(x,y):x2+y2≤a2 and x2a2+y2b2≥1}=30π\left\{(x, y) : x^2 + y^2 \leq a^2 \text{ and } \frac{x^2}{a^2} + \frac{y^2}{b^2} \geq 1\right\} = 30\pi and Area {(x,y):x2+y2≥b2 and x2a2+y2b2≤1}=18π\left\{(x, y) : x^2 + y^2 \geq b^2 \text{ and } \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1\right\} = 18\pi Then the value of (a−b)2(a - b)^2 is equal to ___.

Official answer

12

NTA final key.

Chapter
Application of Integrals
Topic
Area Under Curves
Idea tested
Area of Ellipse and Sectors

Same idea in other shifts

Asked 2× in all
  1. 2 Sep 2020, Shift 1 · Q62Area (in sq. units) of the region outside ∣x∣2+∣y∣3=1\frac{|x|}{2}+\frac{|y|}{3}=1 and inside the ellipse x24+y29=1\frac{x^{2}}{4}+\frac{y^{2}}{9}=1 is :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.