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JEE Main 201323 AprilOnline
Exam
JEE Main
Year
2013
Date
23 April
Mode
Online
Subject
Mathematics
Chapter
Properties of Triangles

JEE Main 2013 · 23 April · Online · Mathematics · Properties of Triangles

On the sides AB, BC, CA of a ABC, 3,4,5 distinct points (excluding...

On the sides AB,BC,CA\mathrm{AB}, \mathrm{BC}, \mathrm{CA} of a △ABC,3,4,5\triangle \mathrm{ABC}, 3,4,5 distinct points (excluding vertices A,B,C\mathrm{A}, \mathrm{B}, \mathrm{C} ) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are :

Options

  1. A210
  2. B205
  3. C215
  4. D220

Correct answer

B. 205

Step-by-step solution

Required number of triangles ={ }^{12} \mathrm{C}}_{3}-\left({ }^3 \mathrm{C}}_{3}+{ }^4 \mathrm{C}}_{3}+{ }^5 \mathrm{C}}_{3}\right)=205
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