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Friday, 9 October

JEE Main 2023 · MathsMultiple choiceSingle correctHardConceptual

JEE Main 8 April 2023, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

The integral ∫((x2)x+(2x)x)log⁡2x dx\int \left(\left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x\right)\log_2 x \, dx is equal to
  1. (1)(x2)x+(2x)x+C\left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x + C
  2. (2)(x2)x−(2x)x+C\left(\frac{x}{2}\right)^x - \left(\frac{2}{x}\right)^x + C
  3. (3)(x2)xlog⁡2(x2)+C\left(\frac{x}{2}\right)^x \log_2\left(\frac{x}{2}\right) + C
  4. (4)(x2)xlog⁡2(2x)+C\left(\frac{x}{2}\right)^x \log_2\left(\frac{2}{x}\right) + C

Official answer

Dropped by NTA (marks given to all)

NTA final key.

Chapter
Integrals
Topic
No close match in our taxonomy
Idea tested
No close match in our taxonomy

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.