$\quad$ The maximum value of the function $y=e^{5+\sqrt{3} \sin x+\cos x}$ is

$\quad$ The maximum value of the function $y=e^{5+\sqrt{3} \sin x+\cos x}$ is
  1. $e^{7}$
  2. $e^{2}$
  3. $e^{5}$
  4. $e^{8}$

Solution

Maximum value of $\sqrt{3} \sin x+\cos x$ is $\sqrt{(\sqrt{3})^{2}+(1)^{2}}=2$ Hence maximum value of given function is $\mathrm{e}^{5+2}=\mathrm{e}^{7}$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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