Exams › JEE Main › Maths

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?

1. 5C3 − 3
2. 5C3 − 1
3. 5C3
4. 5C3 − 2

Correct answer: 5C3 − 3

Solution

From {2,3,4,5,6} choose 3: 5C3=10 ways. Triangle inequality fails for (2,3,5),(2,3,6),(2,4,6) (3 cases). Valid triangles = 10-3 = 5C3 - 3 = 7.

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?
• 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?
• In a prediction contest, the outcomes of 10 football matches must each be guessed as win, draw, or loss. The number of possible entries that have at least 5 correct predictions is:

⚔️ Practice JEE Main Maths free + battle 1v1 →