Let [[t]] be the greatest integer less than or equal to t.

Question

Let $$[t]$$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of 2310 and $$f: A \rightarrow \mathbb{Z}$$ be the function $$f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]$$. The number of one-to-one functions from $A$ to the range of $f$ is

Accepted Answer

$$\begin{aligned}
& A=\{2,3,5,7,11\} \
& f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right] \
& \text { Ranges } f(x)=\{2,3,5,6,8\}
\end{aligned}$$

$$\text { Number of one-one } A \rightarrow R_f$$

$$5 \times 4 \times 3 \times 2 \times 1=120$$

Solutions · 1