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NDA 2 2024 Maths, question 83

Topic: Differential calculus

Passage · Q83 to Q84

Let f(x)=[x]2−[x2]f(x)=[x]^{2}-[x^{2}].

Q83

What is f(0.999)+f(1.001)f(0.999)+f(1.001) equal to?

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

Solution.

Answer: (b) 00

  1. At x=0.999, ⌊x⌋=0 and ⌊x²⌋=0, so f=0.
  2. At x=1.001, ⌊x⌋=1 and ⌊x²⌋=1, so f=1−1=0.
  3. Their sum is zero.