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Friday, 9 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

The curve y(x)=ax3+bx2+cx+5y(x)=ax^3+bx^2+cx+5 touches the xx-axis at the point P(−2,0)\mathrm{P}(-2,0) and cuts the yy-axis at the point Q\mathrm{Q}, where y′y' is equal to 33. Then the local maximum value of y(x)y(x) is :
  1. (1)274\frac{27}{4}Official answer
  2. (2)294\frac{29}{4}
  3. (3)374\frac{37}{4}
  4. (4)92\frac{9}{2}

Official answer

Option 1

NTA final key (2022 Session 2).

Chapter
Application of Derivatives
Topic
Maxima and Minima
Idea tested
First Derivative Test

Same idea in other shifts

Asked 3× in all
  1. 9 Apr 2024, Shift 1 · Q27Let the set of all positive values of λ\lambda, for which the point of local minimum of the function (1+x(λ2−x2))(1+x(\lambda^2-x^2)) satisfies…MediumNumerical value
  2. 6 Sep 2020, Shift 2 · Q60The set of all real values of λ\lambda for which the function f(x)=(1−cos⁡2x)⋅(λ+sin⁡x)f(x)=(1-\cos^2 x)\cdot(\lambda+\sin x),…HardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.