Q106 / 155 · WBJEE 2024 · Mathematics

Choose the correct statement :

  • A
    x + sin 2x is a periodic function
  • Correct answer
    B
    x + sin 2x is not a periodic function
  • C
    $\cos (\sqrt{x}+1)$ is a periodic function
  • Correct answer
    D
    $\cos (\sqrt{x}+1)$ is not a periodic function

Solution

Hint : $f(x)=x+\sin 2 x$ is not a periodic function of $x$ (since ' $x$ ' is increasing function) also $\mathrm{g}(\mathrm{x})=\cos (\sqrt{x}+1)$ is not a periodic function of $\mathrm{x}($ since $g(x+T)$ can never be equal to $g(x))$

Hence, the correct answer is options: 'B', 'D'.

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