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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 July 2022, Shift 2, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let P and Q be any points on the curves (x−1)2+(y+1)2=1(x-1)^2+(y+1)^2=1 and y=x2y=x^2, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval
  1. (1)(0,14)\left(0,\frac{1}{4}\right)
  2. (2)(12,34)\left(\frac{1}{2},\frac{3}{4}\right)
  3. (3)(14,12)\left(\frac{1}{4},\frac{1}{2}\right)Official answer
  4. (4)(34,1)\left(\frac{3}{4},1\right)

Official answer

Option 3

NTA final key.

Chapter
Application of Derivatives
Topic
Maxima and Minima
Idea tested
Shortest Distance Between Curves

Same idea in other shifts

Asked 3× in all
  1. 3 Apr 2025, Shift 2 · Q17The shortest distance between the curves y2=8xy^2 = 8x and x2+y2+12y+35=0x^2 + y^2 + 12y + 35 = 0 is:MediumSingle correct
  2. 24 Feb 2021, Shift 2 · Q63If P is a point on the parabola y=x2+4y=x^2+4 which is closest to the straight line y=4x−1y=4x-1, then the co-ordinates of P are :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.