UPSC CDS 2 2019 Math Paper

Concept:The question tests the correctness of basic number properties.Explanation:Statement A: $1$ is neither prime nor composite – this is correct.Statement B: $0$ is neither positive nor negative – this is correct.Statement C: If $p \times q$ is even, then $p$ and $q$ are always even – this is false because an even number multiplied by any odd number gives an even product. For example, $2 \times 3 = 6$ where $p=2$ (even) and $q=3$ (odd). So $p$ and $q$ need not both be even.Statement D: $\sqrt{2}$ is an irrational number – this is correct.Thus, the incorrect statement is option C.Answer:Option C (or option 3) is not correct.