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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q11

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

∫0∞6e3x+6e2x+11ex+6 dx=\int_0^{\infty}\frac{6}{e^{3x}+6e^{2x}+11e^x+6}\,dx=
  1. (1)log⁡e(51281)\log_e\left(\frac{512}{81}\right)
  2. (2)log⁡e(6427)\log_e\left(\frac{64}{27}\right)
  3. (3)log⁡e(25681)\log_e\left(\frac{256}{81}\right)
  4. (4)log⁡e(3227)\log_e\left(\frac{32}{27}\right)Official answer

Official answer

Option 4

NTA final key.

Chapter
Integrals
Topic
Integration by Substitution
Idea tested
Algebraic Manipulation

Same idea in other shifts

Asked 2× in all
  1. 15 Apr 2023, Shift 1 · Q26Let f(x)=∫dx(3+4x2)4−3x2f(x)=\int\frac{dx}{\left(3+4x^2\right)\sqrt{4-3x^2}}, ∣x∣<23|x|<\frac{2}{\sqrt{3}}. If f(0)=0f(0)=0 and…HardNumerical 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.