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JEE Main 20248 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2024 · 8 April · Morning Shift · Mathematics · Functions

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

Let [t][t] be the greatest integer less than or equal to tt. Let AA be the set of all prime factors of 2310 and f:A→Zf: A \rightarrow \mathbb{Z} be the function f(x)=[log⁡2(x2+[x35])]f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]. The number of one-to-one functions from AA to the range of ff is

Options

  1. A25
  2. B24
  3. C20
  4. D120

Correct answer

D. 120

Step-by-step solution

\mathrm{N}=2310=231 \times 10 =3 \times 11 \times 7 \times 2 \times 5 A=\{2,3,5,7,11\} f(x)=[log⁡2(x2+[x35])]f(2)=[log⁡2(5)]=2f(3)=[log⁡2(14)]=3f(5)=[log⁡2(25+25)]=5f(7)=[log⁡2(117)]=6f(11)=[log⁡2387]=8\begin{aligned} & f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right] \\ & f(2)=\left[\log _2(5)\right]=2 \\ & f(3)=\left[\log _2(14)\right]=3 \\ & f(5)=\left[\log _2(25+25)\right]=5 \\ & f(7)=\left[\log _2(117)\right]=6 \\ & f(11)=\left[\log _2 387\right]=8\end{aligned}RangeofRange off: B=\{2,3,5,6,8\}No.ofone−onefunctionsNo. of one-one functions=5 !=120
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