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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q19

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

Let S={θ∈(0,π2):∑m=19sec⁡(θ+(m−1)π6)sec⁡(θ+mπ6)=−83}S = \left\{\theta \in \left(0, \frac{\pi}{2}\right) : \sum_{m=1}^{9} \sec\left(\theta + (m-1)\frac{\pi}{6}\right)\sec\left(\theta + \frac{m\pi}{6}\right) = -\frac{8}{\sqrt{3}}\right\}. Then
  1. (1)S={π12}S = \left\{\frac{\pi}{12}\right\}
  2. (2)S={2π3}S = \left\{\frac{2\pi}{3}\right\}
  3. (3)∑θ∈Sθ=π2\sum_{\theta \in S} \theta = \frac{\pi}{2}Official answer
  4. (4)∑θ∈Sθ=3π4\sum_{\theta \in S} \theta = \frac{3\pi}{4}

Official answer

Option 3

NTA final key.

Chapter
Trigonometric Functions
Topic
Trigonometric Identities
Idea tested
Telescopic Trigonometric Series

Same topic in other shifts

All Trigonometric Identities questions
  1. 2 Apr 2026, Shift 1 · Q11If sin⁡(π18)sin⁡(5π18)sin⁡(7π18)=K\sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=K, then the value of…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q13Let P={θ∈[0,4π]:tan⁡2θ≠1}P = \{\theta \in [0, 4\pi]: \tan^2\theta \ne 1\} and…MediumSingle correct
  3. 4 Apr 2026, Shift 1 · Q23If A=sin⁡3∘cos⁡9∘+sin⁡9∘cos⁡27∘+sin⁡27∘cos⁡81∘A=\frac{\sin 3^\circ}{\cos 9^\circ}+\frac{\sin 9^\circ}{\cos 27^\circ}+\frac{\sin 27^\circ}{\cos 81^\circ} and…MediumNumerical value
  4. 5 Apr 2026, Shift 1 · Q6Let tan⁡A\tan A, tan⁡B\tan B, where A,B∈(−π2,π2)A, B \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right), be the roots of the quadratic equation…MediumSingle correct
  5. 8 Apr 2026, Shift 2 · Q22If…HardNumerical value
  6. 4 Apr 2025, Shift 2 · Q3Let the product of ω1=(8+i)sin⁡θ+(7+4i)cos⁡θ\omega_1=(8+i)\sin\theta+(7+4i)\cos\theta and ω2=(1+8i)sin⁡θ+(4+7i)cos⁡θ\omega_2=(1+8i)\sin\theta+(4+7i)\cos\theta be α+iβ\alpha+i\beta,…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 108 of the 174 JEE Main shifts held from 2017 to 2026.