NDA 2017 Maths · Mathematics · Application of Derivatives · medium

The minimum value of 5cos x+12sin x+20 is

Single correct option

The minimum value of

5\cos x+12\sin x+20

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Answer: (A) $7$

5\cos x+12\sin x

ranges over

[-13,13]

because

\sqrt{25+144}=13

. The minimum of the expression is

20-13=7

. The value

33

would be the maximum;

13

and

20

take only part of the expression into account.

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake