JEE Main 2023 (Online) 11th April Evening ShiftQuestion 1
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 $\_\_\_\_\_\_$ .
Permutation and Combination
Answer$360$
Solution
Concept. Once $f(1),f(2)$ are chosen, $f(4)=f(1)+f(2)+1$ is fixed. It must be at most 6. Formulas used. (1) Multiplication principleStep 1 - Condition. $f(1)+f(2)+1\le6\Rightarrow f(1)+f(2)\le5$, with $f(1),f(2)\ge1$. Step 2 - Count pairs. Sum 2: 1 pair; 3: 2; 4: 3; 5: 4. Total $10$. Step 3 - Free values. $f(3),f(5)$: $6\cdot6=36$. Step 4 - Total. $10\cdot36=360$. Answer: 360