If the sides AB, BC and CA of a triangle ABC have 3,5 and 6 integer points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to:

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

364

333

240

360

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Number of points on AB = 3

Number of points on BC = 5

Number of points on CA = 6

Number of triangles formed with these points

$\begin{array}{rcl} = & ^{(3 + 5 + 6)} C_{3} - (^{3} C_{3} +^{5} C_{3} +^{6} C_{3}) \\ = & ^{14} C_{3} - (1 + 10 + 20) \\ = & 364 - 31 \\ = & 333 \end{array}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th