Q42 / 160 · TS EAMCET 2004 · Mathematics

If $f: N \rightarrow Z$ is defined by $$ f(n)=\left\{\begin{array}{l} 2 \text { if } n=3 k, k \in Z \\ 10 \text { if } n=3 k+1, k \in Z \\ 0 \text { if } n=3 k+2, k \in Z \end{array}\right. $$ Then , $\{n \in N: f(n)>2\}$ is equal to

  • A
    $\{3,6,4\}$
  • Correct answer
    B
    $\{1,4,7\}$
  • C
    $\{4,7\}$
  • D
    $\{7\}$

Solution

We have, $$ f(n)= \begin{cases}2 & \text { if } n=3 k, k \in Z \\ 10 & \text { if } n=3 k+1, k \in Z \\ 0 & \text { if } n=3 k+2, k \in Z\end{cases} $$ For $f(n)>2$, we take $n=3 k+1, k \in Z$ $$ \begin{aligned} & \Rightarrow \quad n=1,4,7 \\ & \therefore \text { Required set }\{n \in Z ; f(n)>2\} \\ & =\{1,4,7\} \\ & \end{aligned} $$

Hence, the correct answer is option: 'B'.

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