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Let $\mathbb{N}$ be the set of all natural numbers and $f: \mathbb{N} \rightarrow \mathbb{N}$ be such that $1990 < \mathrm{f}(1990) < 2100$ and satisfies the equation $x-f(x)=19\left[\frac{x}{19}\right]-90\left[\frac{f(x)}{90}\right] \text {, }$ where $[y]$ denotes the greatest integer less than or equal to $y$. Then the number of possible values of $f(1990)$ is
MathematicsFunctionsAP EAMCETAP EAMCET 2017 (25 Apr Shift 1)
Options:
  • A 1
  • B 2
  • C 3
  • D 4
Solution:
2171 Upvotes Verified Answer
The correct answer is: 2
No solution. Refer to answer key.

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