UPSC NDA I 2019 Mathematics Solved Paper

Concept:The signs of trigonometric functions in each quadrant determine the quadrant of an angle.Explanation:Given $\sin \theta = -\frac{1}{2}$ (negative) and $\tan \theta = \frac{1}{\sqrt{3}}$ (positive).$\sin \theta$ is negative in the third and fourth quadrants.$\tan \theta$ is positive in the first and third quadrants.The common quadrant where both conditions hold is the third quadrant.Thus, $\theta$ lies in the third quadrant.Answer:Third quadrant (Option C).