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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 June 2022, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let S be the set of all natural numbers, for which the line xa+yb=2\frac{x}{a} + \frac{y}{b} = 2 is a tangent to the curve (xa)n+(yb)n=2\left(\frac{x}{a}\right)^n + \left(\frac{y}{b}\right)^n = 2 at the point (a,b)(a, b), ab≠0ab \neq 0. Then :
  1. (1)S=ϕS = \phi
  2. (2)n(S)=1n(S) = 1
  3. (3)S={2k:k∈N}S = \{2k : k \in \mathbf{N}\}
  4. (4)S=NS = \mathbf{N}Official answer

Official answer

Option 4

NTA final key.

Chapter
Application of Derivatives
Topic
Tangents and Normals
Idea tested
Tangents to Implicit Curves

Same idea in other shifts

Asked 3× in all
  1. 8 Jan 2020, Shift 1 · Q74Let the normal at a point P on the curve y2−3x2+y+10=0y^2-3x^2+y+10=0 intersect the yy-axis at (0,32)\left(0,\frac{3}{2}\right). If m is the slope of…MediumNumerical value
  2. 2 Sep 2020, Shift 1 · Q60If the tangent to the curve y=x+sin⁡yy=x+\sin y at a point (a,b)(a, b) is parallel to the line joining (0,32)\left(0, \frac{3}{2}\right) and…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.