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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

is

(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

Same idea in other shifts

Asked 2× in all

25 Feb 2021, Shift 2 · Q77If $0 < x, y < \pi$ and $\cos x + \cos y - \cos(x+y) = \frac{3}{2}$ , then $\sin x + \cos y$ 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.