Question:
Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane will be divided by the lines is:
Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane will be divided by the lines is:
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Use the formula for regions created by lines in geometry to simplify counting.
Updated On: Aug 4, 2025
- 56
- 255
- 1024
- Not unique
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The Correct Option is B
Solution and Explanation
The formula for the maximum number of regions \( R \) created by \( n \) lines, where no two lines are parallel and no three lines are concurrent, is:
\[
R = 1 + \binom{n}{1} + \binom{n}{2}
\]
For \( n = 10 \):
\[
R = 1 + 10 + \binom{10}{2} = 1 + 10 + 45 = 255
\]
Thus, the Correct Answer is 255.
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