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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 February 2021, Shift 1, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

All possible values of θ∈[0,2π]\theta \in [0, 2\pi] for which sin⁡2θ+tan⁡2θ>0\sin 2\theta + \tan 2\theta > 0 lie in :
  1. (1)(0,π2)∪(π,3π2)\left(0, \frac{\pi}{2}\right) \cup \left(\pi, \frac{3\pi}{2}\right)
  2. (2)(0,π4)∪(π2,3π4)∪(3π2,11π6)\left(0, \frac{\pi}{4}\right) \cup \left(\frac{\pi}{2}, \frac{3\pi}{4}\right) \cup \left(\frac{3\pi}{2}, \frac{11\pi}{6}\right)
  3. (3)(0,π2)∪(π2,3π4)∪(π,7π6)\left(0, \frac{\pi}{2}\right) \cup \left(\frac{\pi}{2}, \frac{3\pi}{4}\right) \cup \left(\pi, \frac{7\pi}{6}\right)
  4. (4)(0,π4)∪(π2,3π4)∪(π,5π4)∪(3π2,7π4)\left(0, \frac{\pi}{4}\right) \cup \left(\frac{\pi}{2}, \frac{3\pi}{4}\right) \cup \left(\pi, \frac{5\pi}{4}\right) \cup \left(\frac{3\pi}{2}, \frac{7\pi}{4}\right)Official answer

Official answer

Option 4

NTA final key.

Chapter
Trigonometric Functions
Topic
General Solutions
Idea tested
Trigonometric Inequality Intervals

Same topic in other shifts

All General Solutions questions
  1. 2 Apr 2026, Shift 1 · Q12Let S={x∈[−π,π]:sin⁡x(sin⁡x+cos⁡x)=a,a∈Z}S=\{x \in [-\pi, \pi] : \sin x(\sin x+\cos x)=a, a \in \mathbb{Z}\}. Then n(S)n(S) is equal to :HardSingle correct
  2. 5 Apr 2026, Shift 2 · Q23If S={θ∈[−π,π]:cos⁡θcos⁡5θ2=cos⁡7θcos⁡7θ2}S=\left\{\theta \in [-\pi, \pi] : \cos\theta\cos\frac{5\theta}{2}=\cos 7\theta\cos\frac{7\theta}{2}\right\}, then n(S) is equal to…HardNumerical value
  3. 6 Apr 2026, Shift 1 · Q14Let S={θ∈(−2π,2π):cos⁡θ+1=3sin⁡θ}\mathrm{S}=\left\{\theta\in(-2\pi,2\pi):\cos\theta+1=\sqrt{3}\sin\theta\right\}. Then ∑θ∈Sθ\sum_{\theta\in \mathrm{S}}\theta is equal to:MediumSingle correct
  4. 2 Apr 2025, Shift 1 · Q3If θ∈[−2π,2π]\theta\in[-2\pi, 2\pi], then the number of solutions of 22cos⁡2θ+(2−6)cos⁡θ−3=02\sqrt{2}\cos^2\theta+(2-\sqrt{6})\cos\theta-\sqrt{3}=0, is equal to :MediumSingle correct
  5. 2 Apr 2025, Shift 2 · Q13If θ∈[−7π6,4π3]\theta \in \left[-\frac{7\pi}{6}, \frac{4\pi}{3}\right], then the number of solutions of…MediumSingle correct
  6. 3 Apr 2025, Shift 1 · Q10The number of solutions of the equation 2x+3tan⁡x=π2x + 3\tan x = \pi, x∈[−2π,2π]−{±π2,±3π2}x \in [-2\pi, 2\pi] - \left\{\pm\frac{\pi}{2}, \pm\frac{3\pi}{2}\right\} 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.