Exams › JEE Main › Maths
Let Tₙ denote the total number of triangles that can be formed by choosing vertices of a regular polygon with n sides. If Tₙ₊₁ - Tₙ = 10, then what is the value of n?
- 7
- 5
- 10
- 8
Correct answer: 5
Solution
The number of triangles that can be formed from the vertices of a regular polygon with n sides is given by the combination formula C(n, 3). The difference Tₙ₊₁ - Tₙ represents the additional triangles formed when adding one more vertex, which is calculated as C(n+1, 3) - C(n, 3). Setting this equal to 10 and solving for n reveals that n must be 5.
Related JEE Main Maths questions
- ABCD is a convex quadrilateral. Points numbered 3, 4, 5, and 6 are placed on sides AB, BC, CD, and DA respectively. How many triangles can be formed if each triangle must have its three vertices on three different sides of the quadrilateral?
- Let Tₙ represent the count of triangles that can be formed from the vertices of a regular polygon with n sides. If Tₙ₊₁ - Tₙ = 28, then the value of n is
- Let a be the number of permutations of x + 2 objects taken all at once, b be the number of permutations of x objects taken 11 at a time, and c be the number of permutations of x − 11 objects taken all at once. If a = 182bc, then what is the value of x?
- Five line segments have lengths 2, 3, 4, 5, and 6 units. How many triangles can be formed by choosing any three of these segments and joining them as sides?
- Three parallel lines lie in the same plane. If each line contains n marked points, what is the greatest possible number of triangles that can be formed using these points as vertices?
- Five speakers A, B, C, D and E are to speak at a meeting. How many different orders are possible if B is not allowed to come before A, whether directly or at any earlier position?
⚔️ Practice JEE Main Maths free + battle 1v1 →