JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 August 2021, Shift 2, Maths Q79

Question 79 of 90 in this shift, Maths question 19 of 30, Section A.

The maximum value of

(\cos\theta_1)\cdot(\cos\theta_2)\cdot(\cos\theta_3)\cdot\ldots\cdot(\cos\theta_{10})

under the restrictions

0 < \theta_1, \theta_2, \ldots, \theta_{10} < \frac{\pi}{2}

and

(\cot\theta_1)\cdot(\cot\theta_2)\cdot\ldots\cdot(\cot\theta_{10}) = 1

(1) $1$
(2) $\frac{1}{512}$
(3) $\frac{1}{1024}$
(4) $\frac{1}{32}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Trigonometric Functions
Topic: Trigonometric Identities
Idea tested: Trigonometric Bounds and Inequalities

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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.