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CAT-2002-Previous Years Paper

Question
26 out of 50
 

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 would be divided by the lines is



A 56
B 255

C 1024
D Not unique

Ans. A

Number of regions where n = Number of lines, i.e., for 0 line we have region = 1.

For 1 line we have region = 2.

If can be shown as:

Therefore, for n = 10, it is 2 + 1= 56

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