JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

Let the circle

\mathrm{S}:36x^2+36y^2-108x+120y+\mathrm{C}=0

be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines,

x-2y=4

and

2x-y=5

lies inside the circle

\mathrm{S}

, then :

(1) $100<\mathrm{C}<156$ Official answer
(2) $81<\mathrm{C}<156$
(3) $\frac{25}{9}<\mathrm{C}<\frac{13}{3}$
(4) $100<\mathrm{C}<165$

Official answer

Option 1

NTA final key.

Chapter: Conic Sections
Topic: Power of a Point
Idea tested: Point position relative to circle

Same topic in other shifts

All Power of a Point questions

5 Apr 2026, Shift 2 · Q11Let the point P be the vertex of the parabola $y=x^2-6x+12$ . If a line passing through the point P intersects the circle…HardSingle correct
5 Apr 2024, Shift 2 · Q15Let the circle $C_1 : x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1, 0)$ and radius 2. If the line of the common chord…EasySingle correct
30 Jan 2024, Shift 2 · Q28Consider two circles $C_1: x^2 + y^2 = 25$ and $C_2: (x - \alpha)^2 + y^2 = 16$ , where $\alpha \in (5, 9)$ . Let the angle between the two…HardNumerical value
13 Apr 2023, Shift 1 · Q21Let $w=z\bar{z}+k_1z+k_2iz+\lambda(1+i)$ , $k_1,k_2\in\mathbb{R}$ . Let $\mathrm{Re}(w)=0$ be the circle C of radius 1 in the first quadrant…HardNumerical value
28 Jun 2022, Shift 2 · Q23If one of the diameters of the circle $x^2+y^2-2\sqrt{2}x-6\sqrt{2}y+14=0$ is a chord of the circle…MediumNumerical value
24 Feb 2021, Shift 2 · Q82Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point ( $-$ 5, 0). If the locus of the…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.