UPSC NDA I 2017 Mathematics Solved Paper

Concept:An empty set has no elements. Real numbers are those that can be plotted on the number line; imaginary numbers are not real.Explanation:The set $S$ is defined by $x^2 + 1 = 0$ with the condition that $x$ is real.Solving $x^2 + 1 = 0$ gives $x^2 = -1$.The square root of $-1$ is $\sqrt{-1} = i$, where $i$ is the imaginary unit.Thus $x = \pm i$, which are not real numbers.Since no real value of $x$ satisfies the equation, the set $S$ contains no elements.Therefore, $S$ is an empty set.Answer:$S$ is an empty set (Option D).