Let A={(x, y): 2 x+3 y=23, x, y ∈ N} and B={x:(x, y) ∈ A} . Then number of one-one functions fro

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Let $A=\{(x, y): 2 x+3 y=23, x, y \in N\}$ and $B=\{x:(x, y) \in A\}$. Then the number of one-one functions from $\mathrm{A}$ to $\mathrm{B}$ is equal to ................

A

$24$

B

$28$

C

$42$

D

$11$

(JEE MAIN-2024)

Solution

$2 x+3y=23 $

$x=1 $ $ y=7 $

$x=4 $ $ y=5 $

$x=7 $ $ y=3 $

$x=10 $ $ y=1 $

$A $ $ B $

$(1,7) $ $ 1 $

$(4,5) $ $ 4 $

$(7,3) $ $ 7 $

$(10,1) $ $ 10$

The number of one-one functions from $\mathrm{A}$ to $\mathrm{B}$ is equal to $4$ !

Standard 12

Mathematics

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