Number of one-one function f :{ a , b , c , d } → {0,1,2, ldots ., 10} such that 2 f(a)-f(b)+3 f(c

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1.Relation and Function

hard

The number of one-one function $f :\{ a , b , c , d \} \rightarrow$ $\{0,1,2, \ldots ., 10\}$ such that $2 f(a)-f(b)+3 f(c)+$ $f ( d )=0$ is

A

$32$

B

$31$

C

$22$

D

$89$

(JEE MAIN-2022)

Solution

$2 f(a)+3 f(c)=f(d)-f(b)$

Using fundamental principle of counting

Number of one-one function is $31$

Standard 12

Mathematics

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