isi-entrance 2024 Q18

isi-entrance · India · UGA Composite & Inverse Functions Counting Functions with Composition or Mapping Constraints

Let $A = \{1, \ldots, 5\}$ and $B = \{1, \ldots, 10\}$. Then the number of ordered pairs $(f, g)$ of functions $f : A \rightarrow B$ and $g : B \rightarrow A$ satisfying $(g \circ f)(a) = a$ for all $a \in A$ is
(A) $\frac{10!}{5!} \times 5^5$
(B) $5^{10} \times 5!$
(C) $10! \times 5!$
(D) $\binom{10}{5} \times 10^5$

Let $A = \{1, \ldots, 5\}$ and $B = \{1, \ldots, 10\}$. Then the number of ordered pairs $(f, g)$ of functions $f : A \rightarrow B$ and $g : B \rightarrow A$ satisfying $(g \circ f)(a) = a$ for all $a \in A$ is\\
(A) $\frac{10!}{5!} \times 5^5$\\
(B) $5^{10} \times 5!$\\
(C) $10! \times 5!$\\
(D) $\binom{10}{5} \times 10^5$

Paper Questions

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