Question 13 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by

The maximum value of sin x . cos x is

(A) 1/4                     (B) 1/2

(C) √2                      (D) 2 √2

 

This question is similar to Ex 6.5, 9 - Chapter 6 Class 12 - Application of Derivatives

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Transcript

Question 13 The maximum value of sin x . cos x is (A) 1/4 (B) 1/2 (C) √2 (D) 2 √2 Let f(𝒙)=sin⁑π‘₯βˆ™cos⁑π‘₯ =(2 sin⁑π‘₯ cos⁑π‘₯)/2 =(π’”π’Šπ’ πŸπ’™)/𝟐 Since, βˆ’πŸβ‰€π’”π’Šπ’ πœ½β‰€πŸ Putting πœƒ=2π‘₯ βˆ’1≀sin⁑2π‘₯≀1 Dividing by 2 βˆ’1/2≀(𝑠𝑖𝑛 2π‘₯)/2≀1/2 βˆ’πŸ/πŸβ‰€π’‡(𝒙)β‰€πŸ/𝟐 ∴ Maximum value of 𝑓(π‘₯) is 𝟏/𝟐. So, the correct answer is (B).

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