JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

Let 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 the equation of the circle described on PQ as diameter is

2(x^2+y^2)-11x-14y-22=0

, then

2r+s-2q+p

is equal to __________.

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
27 Aug 2021, Shift 1 · Q86Let 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…HardNumerical 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.