UPSC NDA I 2025 Mathematics Paper

Concept:A linear function $f(x)=px+q$ with $p\neq0$ is always one-one (injective). For onto, the range must equal the entire codomain.Explanation:Given $f$ is linear, different $x$ give different $f(x)$, so statement I is correct.The actual outputs are $\{1,4,7,10\}$, which is a finite set.The codomain is the set of natural numbers $\mathbb{N}$, which is infinite.Since $\{1,4,7,10\}\neq\mathbb{N}$, $f$ is not onto. Thus statement II is incorrect.Answer:Only statement I is correct. Hence the correct option is A (I only).