10 straight lines no two of which are parallel and no three of which pass through any common point a...........

Quantitative Aptitude ( CCS) Number System

10 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

255

1024

Not unique

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Explanation:

R = regions created on plane by these lines
D = difference in no. of regions created by n lines w.r.t (n-1) lines
One can derive the no of regions for by using the D and R columns :
No. of regions by n lines = no. of regions by (n-1) lines + n = 2+ [2+3+...+(n-1)] + n
= n*(n+1)/2 + 1
So, for n= 10, no. of regions = 10* 11/2 +1 = 56

Hence, option 1 is the correct answer.