Question : What is the value of $5 \sqrt{3} \cos 60^{\circ} \tan 30^{\circ}-3 \cos 0^{\circ}+3 \cos ^2 45^{\circ}+2 \sin ^2 60^{\circ}$?
Option 1: $2\sqrt{3}$
Option 2: $2.5$
Option 3: $3.5$
Option 4: $3\sqrt{2}$
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Correct Answer: $2.5$
Solution :
$5 \sqrt{3} \cos 60^{\circ} \tan 30^{\circ}-3 \cos 0^{\circ}+3 \cos ^2 45^{\circ}+2 \sin ^2 60^{\circ}$
$= 5 \sqrt{3} \times \frac{1}{2} \times\frac{1}{\sqrt3}-3 \times1+3 \times \frac{1}{(\sqrt2)^2}+2(\frac{\sqrt3}{2})^2$
$= \frac{5}{2} -3+\frac{3}{2} + \frac{3}{2}$
$= \frac{5-6+3+3}{2}$
$= \frac{5}{2}$
$= 2.5$
Hence, the correct answer is $2.5$.
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