🛠️ JEE➗ Maths

Let \( A=\{1,2,3 \ldots ., 10\} \) and \( f: A \rightarrow A \) be defined as \( f(k)=\left\{\begin{array}{ll}k+1 & …

Q1

Let \( A=\{1,2,3 \ldots ., 10\} \) and \( f: A \rightarrow A \) be defined as \( f(k)=\left\{\begin{array}{ll}k+1 & \text { if } k \text { is odd } \\ k, & \text { if } k \text { is even }\end{array}\right. \). Then the number of possible functions \( g: A \rightarrow A \) such that \( g o f=f \) is

[JEE Main 2021, 26 Feb (Shift 2)]

a

\( 10^{5} \)

b

\( { }^{10} \mathrm{C}_{5} \)

c

\( 5^{5} \)

d

5 !

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