JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 1, Maths Q12

Question 12 of 75 in this shift, Maths question 12 of 25, Section A.

Let

C_1

be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let

C_2

be the circle with centre

(1, 3)

that touches

C_1

externally at the point

(\alpha, \beta)

. If

(\beta - \alpha)^2 = \frac{m}{n}

\gcd(m, n) = 1

, then

m + n

is equal to

(1) $9$
(2) $13$
(3) $22$ Official answer
(4) $31$

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

8 Apr 2024, Shift 1 · Q15Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$ touch each other externally at…MediumSingle correct
9 Apr 2024, Shift 1 · Q29Let the centre of a circle, passing through the points $(0,0)$ , $(1,0)$ and touching the circle $x^2+y^2=9$ , be $(h,k)$ . 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.