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NDA 2 2024 Maths, question 71

Topic: Algebra

Q71

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

  1. (a) −1-1Correct answer
  2. (b) 00
  3. (c) 11
  4. (d) 22

Solution.

Answer: (a) −1-1

  1. For any noninteger x, its fractional part x−⌊x⌋ lies strictly between 0 and 1.
  2. Thus y=⌊x⌋−x lies in (−1,0), and z=⌊y⌋=−1.