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NDA 2 2025 Maths, question 35

Topic: Algebra

Passage · Q35 to Q36

There are 88 points on a plane out of which 44 points are collinear.

Q35

How many triangles can be formed by joining these points?

  1. (a) 5656
  2. (b) 5454
  3. (c) 5353
  4. (d) 5252Correct answer

Solution.

Answer: (d) 5252

  1. Any 3 of the 8 points: (83)=56\binom{8}{3} = 56.
  2. The 4 collinear points give (43)=4\binom{4}{3} = 4 sets that form no triangle.
  3. 56−4=5256 - 4 = 52.

Trap: This assumes no other three points are collinear, which is the standard reading.