Sets, Relations & Functions
Counting Functions Satisfying Linear Condition
nta_pyq_2023_apr
Grade 11
Question:
Let $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of functions $f:A\to B$ satisfying $f(1)+f(2)=f(4)-1$ is equal to........
Step-by-Step Solution
Key Concept: $f(4)=f(1)+f(2)+1\leq 6\Rightarrow f(1)+f(2)\leq5$. Count pairs $(f(1),f(2))$ with sum $1$ to $5$: $1+2+3+4=10$ pairs. $f(3),f(5)$ each have 6 choices.
$10\times 6\times 6=360$.
Correct Answer: 360