JEE Main 2022 — Functions Question with Solution

A = \left\{ {\matrix{ {x \in N,} & {{x^2} - 10x + 9 \le 0} \cr } } \right\}

$$=\{1,2,3,....,9\}$$

$$B=\{1,4,9,16,.....\}$$

$$f(x)\le (x-3{)}^2+1$$

$$f(1)\le 5,f(2)\le 2,..........f(9)\le 37$$

$$x=1$$ has 2 choices

$$x=2$$ has 1 choice

$$x=3$$ has 1 choice

$$x=4$$ has 1 choice

$$x=5$$ has 2 choices

$$x=6$$ has 3 choices

$$x=7$$ has 4 choices

$$x=8$$ has 5 choices

$$x=9$$ has 6 choices

$$\therefore$$ Total functions = $$2\times 1\times 1\times 1\times 2\times 3\times 4\times 5\times 6=1440$$