JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 July 2022, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

If 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

|2a+9b|

is equal to ________

Official answer

195

NTA final key.

Chapter: Application of Derivatives
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
26 Jun 2022, Shift 2 · Q11If $m$ 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…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.