If f:left{ {1,2,3,4} right} to left{ {1,2,3,4} right} and y=f(x) be a function such that left|

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1.Relation and Function

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If $f:\left\{ {1,2,3,4} \right\} \to \left\{ {1,2,3,4} \right\}$ and $y=f(x)$ be a function such that $\left| {f\left( \alpha \right) - \alpha } \right| \leqslant 1$,for $\alpha \in \left\{ {1,2,3,4} \right\}$ then total number of such functions are

A

$81$

B

$36$

C

$54$

D

none of these

Solution

Total cases $= 2\times 3 \times 3 \times 2 = 36$

Standard 12

Mathematics

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(JEE MAIN-2020)