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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Let α=tan⁡(5π16sin⁡(2cos⁡−1(15)))\alpha = \tan\left(\frac{5\pi}{16}\sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right) and β=cos⁡(sin⁡−1(45)+sec⁡−1(53))\beta = \cos\left(\sin^{-1}\left(\frac{4}{5}\right) + \sec^{-1}\left(\frac{5}{3}\right)\right) where the inverse trigonometric functions take principal values. Then, the equation whose roots are α\alpha and β\beta is :
  1. (1)15x2−8x−7=015x^2 - 8x - 7 = 0
  2. (2)5x2−12x+7=05x^2 - 12x + 7 = 0
  3. (3)25x2−18x−7=025x^2 - 18x - 7 = 0Official answer
  4. (4)25x2−32x+7=025x^2 - 32x + 7 = 0

Official answer

Option 3

NTA final key.

Chapter
Inverse Trigonometric Functions
Topic
Inverse Trig Identities
Idea tested
Trig of Sum of Inverse Trig Functions

Same idea in other shifts

Asked 4× in all
  1. 2 Apr 2025, Shift 2 · Q23If y=cos⁡(π3+cos⁡−1x2)y = \cos\left(\frac{\pi}{3} + \cos^{-1}\frac{x}{2}\right), then (x−y)2+3y2(x-y)^2 + 3y^2 is equal to __________.MediumNumerical value
  2. 29 Jun 2022, Shift 1 · Q26…MediumNumerical value
  3. 25 Feb 2021, Shift 2 · Q79cosec[2cot⁡−1(5)+cos⁡−1(45)]\mathrm{cosec}\left[2\cot^{-1}(5) + \cos^{-1}\left(\frac{4}{5}\right)\right] is equal to :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.