JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 August 2021, Shift 1, Maths Q86

Question 86 of 90 in this shift, Maths question 26 of 30, Section B.

Let the equation

x^2+y^2+px+(1-p)y+5=0

represent circles of varying radius

r \in (0, 5]

. Then the number of elements in the set

S=\{q : q=p^2 \text{ and } q \text{ is an integer}\}

is __________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Condition for a Circle

Same idea in other shifts

Asked 5× in all

8 Apr 2023, Shift 1 · Q27Consider a circle $C_1:x^2+y^2-4x-2y=\alpha-5$ . Let its mirror image in the line $y=2x+1$ be another circle…MediumNumerical value
26 Jul 2022, Shift 1 · Q12A point P moves so that the sum of squares of its distances from the points $(1,\ 2)$ and $(-2,\ 1)$ is 14. Let $f\,(x,\ y) = 0$ be the…MediumSingle correct
25 Jun 2022, Shift 1 · Q24Let the abscissae of the two points P and Q be the roots of $2x^2-rx+p=0$ and the ordinates of P and Q be the roots of $x^2-sx-q=0$ . If…MediumNumerical value
24 Feb 2021, Shift 1 · Q88If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord of another circle 'C', whose center is at $(2, 1)$ , then…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.