A) 1
B) 2
C) infinitely many
D) 0
Correct Answer: D
Solution :
\[\cos \,\frac{\pi x}{3\sqrt{3}}={{x}^{2}}-2\sqrt{3}\,x+3+1\] \[\cos \,\frac{\pi x}{3\sqrt{3}}={{(x-\sqrt{3})}^{2}}+1\] \[\because \] \[{{(x-\sqrt{3})}^{2}}+1\ge 1\] and \[\cos \,\frac{\pi x}{3\sqrt{3}}\le 1\] For \[x=\sqrt{3},\,\,\cos \,\,\frac{\pi x}{3\sqrt{3}}\,=\cos \,\frac{\pi }{3}\,=\frac{1}{2}\] and \[{{(x-\sqrt{3})}^{2}}+1=1\]
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