JEE Main 2024 — 8 April, Shift 1 — Question 14

$\mathrm{N}=2310=231 \times 10$

$=3 \times 11 \times 7 \times 2 \times 5$

$A=\{2,3,5,7,11\}$

$f(x)=\left[\log _{2}\left(x^{2}+\left[\frac{x^{3}}{5}\right]\right)\right]$

$f(2)=\left[\log _{2}(5)\right]=2$

$\mathrm{f}(3)=\left[\log _{2}(14)\right]=3$

$\mathrm{f}(5)=\left[\log _{2}(25+25)\right]=5$

$\mathrm{f}(7)=\left[\log _{2}(117)\right]=6$

$\mathrm{f}(11)=\left[\log _{2} 387\right]=8$

Range of $\mathrm{f}: \mathrm{B}=\{2,3,5,6,8\}$

No. of one-one functions $=5!=120$