Question : If [n] denotes the greatest integer < n and (n) denotes the smallest integer > n, where n is any real number, then the value of $(1\frac{1}{5})×[1\frac{1}{5}]-(1\frac{1}{5})+[\frac{1}{5}]+(1.5)$ is:
Option 1: 1.5
Option 2: 2
Option 3: 2.5
Option 4: 3.5
Correct Answer: 2
Solution : $(1\frac{1}{5}) × [1\frac{1}{5}] – (1\frac{1}{5}) + [\frac{1}{5}] + (1.5)$ = ($\frac{6}{5}) × [\frac{6}{5}] – (\frac{6}{5}) + [\frac{1}{5}] + (1.5)$ = (1.2) × [1.2] – (1.2) + [0.2] +(1.5) Applying floor and ceiling functions = 2 × 1 – 2 + 0 + 2 = 2 – 2 + 2 = 2 Hence, the correct answer is 2.
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