JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 February 2021, Shift 1, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

Let the lines

(2-i)z = (2+i)\bar{z}

and

(2+i)z + (i-2)\bar{z} - 4i = 0

, (here

i^2 = -1

) be normal to a circle C. If the line

iz + \bar{z} + 1 + i = 0

is tangent to this circle C, then its radius is :

(1) $3\sqrt{2}$
(2) $\frac{1}{2\sqrt{2}}$
(3) $\frac{3}{2\sqrt{2}}$ Official answer
(4) $\frac{3}{\sqrt{2}}$

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Circle Tangents
Idea tested: Normal Passes Through Center

Same idea in other shifts

Asked 4× in all

13 Apr 2023, Shift 2 · Q13Let the centre of a circle C be $(\alpha,\beta)$ and its radius $r<8$ . Let $3x+4y=24$ and $3x-4y=32$ be two tangents and $4x+3y=1$ be a…MediumSingle correct
28 Jun 2022, Shift 1 · Q30Let the lines $y+2x=\sqrt{11}+7\sqrt{7}$ and $2y+x=2\sqrt{11}+6\sqrt{7}$ be normal to a circle $C:(x-h)^2+(y-k)^2=r^2$ . If the line…HardNumerical value
17 Mar 2021, Shift 1 · Q74The line $2x-y+1=0$ is a tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x-2y=4$ . Then, the radius of…MediumSingle correct

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.