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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Functions

NDA 2022 · Mathematics · Functions

Let z=[y] and y=[x]-x , where [.] is the greatest integer function....

Let z=[y]z=[y] and y=[x]−xy=[x]-x, where [.] is the greatest integer function. If xx is not an integer but positive, then what is the value of zz ?

Options

  1. A−1-1
  2. B00
  3. C11
  4. D22

Correct answer

A. −1-1

Step-by-step solution

We have x=[x]+{x}∴y=[x]−x=−{x}x=[x]+\{x\}\therefore y=[x]-x=-\{x\} Now, z=[y]=[−{x}][∵0<{x}<1]=−1z=[y]=[-\{x\}][\because 0 < \{x\} < 1]=-1
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