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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

A circle C1C_1 passes through the origin O and has diameter 4 on the positive xx-axis. The line y=2xy = 2x gives a chord OA of circle C1C_1. Let C2C_2 be the circle with OA as a diameter. If the tangent to C2C_2 at the point A meets the xx-axis at P and yy-axis at Q, then QA : AP is equal to :
  1. (1)1:41 : 4Official answer
  2. (2)1:51 : 5
  3. (3)2:52 : 5
  4. (4)1:31 : 3

Official answer

Option 1

NTA final key.

Chapter
Conic Sections
Topic
Circle Tangents
Idea tested
Tangent at a point (T=0)

Same topic in other shifts

All Circle Tangents questions
  1. 6 Apr 2026, Shift 2 · Q10Let C be a circle having centre in the first quadrant and touching the xx-axis at a distance of 3 units from the origin. If the circle C…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point (−9,4)(-9, 4) and touching the lines…HardNumerical value
  3. 7 Apr 2025, Shift 1 · Q12Let C1C_1 be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C2C_2 be the circle with centre (1,3)(1, 3)…MediumSingle correct
  4. 5 Apr 2024, Shift 1 · Q13Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3,2)(3, 2) and parallel to the…MediumSingle correct
  5. 5 Apr 2024, Shift 2 · Q14Let ABCDABCD and AEFGAEFG be squares of side 4 and 2 units, respectively. The point EE is on the line segment ABAB and the point FF is on…MediumSingle correct
  6. 5 Apr 2024, Shift 2 · Q24Let the maximum and minimum values of (8x−x2−12−4)2+(x−7)2\left(\sqrt{8x-x^2-12}-4\right)^2 + (x-7)^2, x∈Rx \in R be MM and mm, respectively. Then…HardNumerical value

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.