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The area (in sq. units) enclosed by the solution set of is equal to (where denotes greatest integer function)

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Important Questions on Functions
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Let be the set of real numbers and be defined by where is the greatest integer less than or equal to and Which of the following statement are true?
I. The range of is closed interval
II. is continuous on
III. is one-one on

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Where denotes the largest integer not exceeding . The positive integer for which is


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