JEE Main 2021 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 17 March 2021, Shift 1, Maths Q75

Question 75 of 90 in this shift, Maths question 15 of 30, Section A.

Choose the incorrect statement about the two circles whose equations are given below :

x^{2}+y^{2}-10x-10y+41=0

and

x^{2}+y^{2}-16x-10y+80=0

(1)Circles have two intersection points.
(2)Both circles pass through the centre of each other.
(3)Both circles’ centres lie inside region of one another.Official answer
(4)Distance between two centres is the average of radii of both the circles.

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Number of Common Tangents

Same idea in other shifts

Asked 6× in all

1 Feb 2024, Shift 1 · Q15Let $C: x^2+y^2=4$ and $C': x^2+y^2-4\lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles C and C'…MediumSingle correct
15 Apr 2023, Shift 1 · Q13The number of common tangents, to the circles $x^2+y^2-18x-15y+131=0$ and $x^2+y^2-6x-6y-7=0$ , isEasySingle correct
17 Mar 2021, Shift 1 · Q86The minimum distance between any two points $P_1$ and $P_2$ while considering point $P_1$ on one circle and point $P_2$ on the other…EasyNumerical value
18 Mar 2021, Shift 1 · Q75Choose the correct statement about two circles whose equations are given below : $x^2+y^2-10x-10y+41=0$ $x^2+y^2-22x-10y+137=0$ EasySingle correct
9 Jan 2020, Shift 2 · Q73If the curves, $x^2-6x+y^2+8=0$ and $x^2-8y+y^2+16-k=0$ , $(k>0)$ touch each other at a point, then the largest value of $k$ is ______.MediumNumerical 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.