CAT Quantitative Ability Questions | CAT Permutation, Combination and Probability questions
CAT/2002
Question . 35
10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. Thetotal number of regions (including finite and infinite regions) into which the plane would be divided by the lines is
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Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question
(a) For 2 such lines, no. of regions formed are 4
For 3 lines no. of regions formed are 7 (= 4 + 3)
For 4 lines, no. of regions formed are 11 (= 7 + 4)
For 5 lines no. of regions formed are 16 (= 11 + 5)
Similarly for 6, 7, 8, 9 and 10 lines, no. of regions are
16 + 6 = 22
22 + 7 = 29
29 + 8 = 37
37 + 9 = 46
46 + 10 = 56
∴ for 10 lines no. of regions = 10C2 10 + 1 = 45 + 11 = 56