JEE MAIN - Mathematics (2024 - 8th April Morning Shift - No. 17)
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
20
120
25
24
Explanation
$$\begin{aligned} & A=\{2,3,5,7,11\} \\ & f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right] \\ & \text { Ranges } f(x)=\{2,3,5,6,8\} \end{aligned}$$
$$\text { Number of one-one } A \rightarrow R_f$$
_8th_April_Morning_Shift_en_17_1.png)
$$5 \times 4 \times 3 \times 2 \times 1=120$$
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