Description for Correct answer:
Let \( \Large f \left(x\right)=\sqrt{3} \cos x + \sin x \)

=> \( \Large f \left(x\right)=2 \left(\frac{\sqrt{3}}{2}\cos x + \frac{1}{2} \sin x\right)=2 \sin \left(x+\frac{ \pi }{3}\right) \)

Since, \( \Large -1 \le \sin \left(x+\frac{ \pi }{3}\right) \le 1 \)

Hence, \( \Large f \left(x\right)\ is\ maximum\ if\ x+\frac{ \pi }{3}=\frac{ \pi }{2} \)

=> \( \Large x = \frac{ \pi }{6} = 30 ^{\circ} \)