Learn

Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let the circles C1:(x−α)2+(y−β)2=r12C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2 and C2:(x−8)2+(y−152)2=r22C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2 touch each other externally at the point (6,6)(6,6). If the point (6,6)(6,6) divides the line segment joining the centres of the circles C1C_1 and C2C_2 internally in the ratio 2:12:1, then (α+β)+4(r12+r22)(\alpha+\beta)+4\left(r_1^2+r_2^2\right) equals
  1. (1)110110
  2. (2)125125
  3. (3)130130Official answer
  4. (4)145145

Official answer

Option 3

NTA final key.

Chapter
Conic Sections
Topic
Circle Tangents
Idea tested
Common Tangent of Touching Circles

Same idea in other shifts

Asked 3× in all
  1. 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
  2. 9 Apr 2024, Shift 1 · Q29Let the centre of a circle, passing through the points (0,0)(0,0), (1,0)(1,0) and touching the circle x2+y2=9x^2+y^2=9, be (h,k)(h,k). Then for all…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 42 of the 174 JEE Main shifts held from 2017 to 2026.