Mathematics
Statement I: The terms circle and circular region have the same meaning.
Statement II: The interior of a circle together with its boundary is called the circular region.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Answer
Statement I is false but Statement II is true.
Explanation
A circle is just the simple closed curve — i.e. the collection of all points in a plane which are at a fixed distance (the radius) from a fixed point (the centre). It does not include the interior.
The circular region, on the other hand, is the collection of all points of the plane which either lie on the circle or are inside it, i.e. the interior of the circle together with its boundary.
So, "circle" and "circular region" do not have the same meaning — Statement I is false, while Statement II correctly describes the circular region and is true.
Hence, option 2 is the correct option.
Related Questions
Statement I: The diagonal of a polygon is the line segment joining two non-adjacent vertices.
Statement II: The polygon with the minimum number of sides is a triangle.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Statement I: If r is the radius of a circle and l is the length of any chord then 0 ≤ l ≤ 2r.
Statement II: A chord is formed by joining any two points on a circle.
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Statement II: A chord which passes through the centre of a circle is its diameter.
Statement I is true but statement II is false.
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