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Saturday, 31 October

JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 January 2024, Shift 1, Maths Q30

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

Let the set of all a∈Ra\in\mathbf{R} such that the equation cos⁡2x+asin⁡x=2a−7\cos 2x+a\sin x=2a-7 has a solution be [p,q][p, q] and r=tan⁡9∘−tan⁡27∘−1cot⁡63∘+tan⁡81∘r=\tan 9^\circ-\tan 27^\circ-\dfrac{1}{\cot 63^\circ}+\tan 81^\circ, then pqrpqr is equal to ________.

Official answer

48

NTA final key.

Chapter
Trigonometric Functions
Topic
Trigonometric Identities
Idea tested
Values of Non-Standard Specific Angles

Same idea in other shifts

Asked 6× in all
  1. 8 Apr 2024, Shift 2 · Q20If the value of 3cos⁡36∘+5sin⁡18∘5cos⁡36∘−3sin⁡18∘\frac{3\cos 36^\circ + 5\sin 18^\circ}{5\cos 36^\circ - 3\sin 18^\circ} is a5−bc\frac{a\sqrt{5} - b}{c}, where a, b, c are…MediumSingle correct
  2. 25 Jun 2022, Shift 2 · Q15The value of 2sin⁡(12∘)−sin⁡(72∘)2\sin(12^\circ) - \sin(72^\circ) is :MediumSingle correct
  3. 27 Jun 2022, Shift 2 · Q19α=sin⁡36∘\alpha=\sin 36^\circ is a root of which of the following equation?HardSingle correct
  4. 31 Aug 2021, Shift 1 · Q77cosec18∘\mathrm{cosec}18^\circ is a root of the equation :MediumSingle correct
  5. 25 Jul 2021, Shift 2 · Q73The value of cot⁡π24\cot\frac{\pi}{24} is :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.