JEE Main 2026 (Online) 5th April Morning ShiftQuestion 1
Let $A=\{1,2,3,4,5,6\}$. The number of one-one functions $f:A\to A$ such that $f(1)\ge3$, $f(3)\le4$ and $f(2)+f(3)=5$, is ________.
Permutation and Combination
Answer$72$
Solution
$f(3)\le4$ and $f(2)+f(3)=5$ give $(f(2),f(3))\in\{(4,1),(3,2),(2,3),(1,4)\}$; in each case $f(1)\ge3$ has $3$ choices and the rest $3!$, so $4\cdot3\cdot6=72$.