99 Percentile Qs Bank for JEE MainMathematicsFunctions

Let f x = sin ⁡ x 3 + cos ⁡ 3 x 10 for all real x . The least natural number n such that f 10 n π + x = f x for all real values of x is

Correct answer

Step-by-step solution

f x = sin ⁡ x 3 + cos ⁡ 3 x 10 Period of sin ⁡ x 3 = 6 π Period of cos ⁡ 3 x 10 = 20 π 3 ∵ sin ⁡ a θ , cos ⁡ a θ a r e p e r i o d i c w i t h p e r i o d 2 π a LCM of 6 π , 20 π 3 = 60 π Therefore, the period of f x = 60 π Hence, n = 6 .

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