JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 June 2022, Shift 2, Maths Q11

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

m

is the slope of a common tangent to the curves

\frac{x^2}{16} + \frac{y^2}{9} = 1

and

x^2 + y^2 = 12

, then

12\, m^2

is equal to :

(1) $6$
(2) $9$ Official answer
(3) $10$
(4) $12$

Official answer

Option 2

NTA final key.

Chapter: Conic Sections
Topic: Tangents and Normals
Idea tested: Common Tangents to Two Curves

Same idea in other shifts

Asked 4× in all

26 Jul 2022, Shift 2 · Q12The equation of a common tangent to the parabolas $y=x^2$ and $y=-(x-2)^2$ isMediumSingle correct
27 Jul 2022, Shift 2 · Q29A common tangent T to the curves $C_1 : \frac{x^2}{4} + \frac{y^2}{9} = 1$ and $C_2 : \frac{x^2}{42} - \frac{y^2}{143} = 1$ does not pass…HardNumerical value
29 Jul 2022, Shift 2 · Q27If the tangent to the curve $y=x^3-x^2+x$ at the point $(a, b)$ is also tangent to the curve $y=5x^2+2x-25$ at the point $(2,-1)$ , 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.