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There are ‘n’ points in a plane. No three of which are on same straight line. All the possible straight lines are made by joining these ‘n’ points. (i) What is the maximum number of point of intersection of these straight lines? (ii) Taking point of intersection of these straight lines as vertices of triangles then what is the maximum number of triangles that can be formed?

by | Jan 12, 2024 | Uncategorized

(Q). There are ‘n’ points in a plane. No three of which are on same straight line. All the possible straight lines are made by joining these ‘n’ points. (i) What is the maximum number of point of intersection of these straight lines? (ii)...

Let Tₙ be the number of all possible triangles formed by joining vertices of an n – sided regular polygon. If Tₙ₊₁ – Tₙ = 10, then what will be the value of n

by | Jan 8, 2024 | Uncategorized

(Q). Let Tₙ be the number of all possible triangles formed by joining vertices of an n – sided regular polygon. if Tₙ₊₁ – Tₙ = 10, then what will be the value of n? Solution:-  As per the given conditionⁿ⁺¹C₃ – ⁿC₃ = 10we know that  ⁿCᵣ + ⁿCᵣ ₋ ₁ = ⁿ...

The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them.The number of triangles that can be constructed using these interior points as vertices will be?

by | Aug 3, 2023 | Uncategorized

we have following cases in this question:-case (i): if one point is selected from each side then number of triangle is = 3×4×5 = 60case (ii):  if one point is selected from one side and 2 points from another side then number of ways is= ³C₂×(4 + 5) + ⁴C₂×(5+3)...