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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)...

exercise on permutation or arrangement

by | Aug 2, 2023 | Uncategorized

 1. In how many ways 15 students can be seated on 20 seats in a row ? 2. In how many ways 5 distinct volume of chemistry and 7 distinct volume of Botany book can be arranged on a bookshelf such that no two chemistry books are together ? 3. In how many ways 15 students...

Consider ‘n’ straight lines in a plane such that no two of which are parallel and no three of which pass through the same point. How many new straight lines can be drawn from the point of intersection of these straight lines

by | Jun 15, 2023 | Uncategorized

(Q). Consider ‘n’ straight lines in a plane such that no two of which are parallel and no three of which pass through the same point. How many new straight lines can be drawn from the point of intersection of these straight lines?Solution:-Since each line...

Consider a polygon of n sides. what is the number of triangles that can be drawn taking vertices of these polygons as vertices of triangles and no side of triangles is common with any side of the polygon

by | Jun 6, 2022 | Uncategorized

(Q). Consider a polygon of n sides. what is the number of triangles that can be drawn taking vertices of these polygons as vertices of triangles and no side of triangles is common with any side of the polygon?Solution:-Without any restriction number of tiangle formed...

Consider a polygon of k sides with n points on each side (no point on the vertices)
(i) How many straight lines can be drawn from these ‘kn’ points such that each line passes through exactly 2 of the given points.
(ii) if ‘T’ is the maximum number of triangles that can be drawn from these kn points as vertices then find the value of ‘T’.
(iii) if ‘Q’ is the maximum number of quadrilaterals that can be drawn from these ‘kn’ points as vertices then find the value of Q

by | May 30, 2022 | Uncategorized

(Q). Consider a polygon of k sides with n points on each side (no point on the vertices)(i) How many straight lines can be drawn from these ‘kn’ points such that each line passes through exactly 2 of the given points.(ii) if ‘T’ is the maximum...