jee-main 2022 Q70

jee-main · India · session1_28jun_shift1 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

Let a function $f : \mathbb{N} \rightarrow \mathbb{N}$ be defined by $$f(n) = \begin{cases} 2n, & n = 2,4,6,8,\ldots \\ n-1, & n = 3,7,11,15,\ldots \\ \frac{n+1}{2}, & n = 1,5,9,13,\ldots \end{cases}$$ then, $f$ is
(1) One-one and onto
(2) One-one but not onto
(3) Onto but not one-one
(4) Neither one-one nor onto

Let a function $f : \mathbb{N} \rightarrow \mathbb{N}$ be defined by
$$f(n) = \begin{cases} 2n, & n = 2,4,6,8,\ldots \\ n-1, & n = 3,7,11,15,\ldots \\ \frac{n+1}{2}, & n = 1,5,9,13,\ldots \end{cases}$$
then, $f$ is\\
(1) One-one and onto\\
(2) One-one but not onto\\
(3) Onto but not one-one\\
(4) Neither one-one nor onto

Paper Questions

Q21 Q22 Q23 Q24 Q25 Q26 Q28 Q29 Q30 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71