L26 | Geometrical Problems in Permutations & Combinations | Line, Triangles | JEE Mains and Advanced

In this video, we cover Geometrical Problems in Permutations and Combinations for JEE Mains and Advanced. This is a crucial topic for Class 11th Maths and JEE Maths aspirants, focusing on detailed problem-solving and analysis.

About this Lecture: Welcome to Lecture 26 of our Permutations and Combinations series! In this session, we provide a proper analysis of important problems and Previous Year Questions (PYQs) related to geometry. You will get full problems discussed in detail, moving from basic concepts to advanced applications. We cover how to find the number of intersection points for lines and circles, and how to count triangles and quadrilaterals formed by collinear and non-collinear points.


📝 Assignment: You can download the assignment on this topic from the link provided in the pinned comment below!

🔥 Topics & Questions Discussed:

Maximum number of intersection points of lines (Conditions: No two parallel, No three concurrent).

Maximum number of intersection points of circles.

Number of straight lines and triangles formed from n points (General case vs. Collinear case).

Number of Quadrilaterals formed by joining vertices.

Counting the number of diagonals in an n-sided polygon.

Maximum number of intersection points of 16 lines (No two parallel, No three concurrent).

Finding the maximum intersection points of 10 circles.


Problem: Finding the number of straight lines, triangles, and quadrilaterals from 10 points where 4 are collinear.

Calculating the number of diagonals in a regular polygon with interior angles of 150 degrees.


JEE Mains 2015: Finding the number of sides of a polygon that has 54 diagonals.


Problem: Finding intersection points when n lines divide a plane into 67 parts.


JEE Mains pyq 2024: Maximum intersection points of 20 lines where sets are parallel or concurrent.


JEE Mains pyq 2025: Total number of triangles formed from 12 points where 5 are collinear.


JEE Mains pyq 2025: Triangles formed by points located on two intersecting lines with different slopes.


JEE Mains pyq 2013: Triangles constructed using distinct points chosen on the sides of a triangle.



Mixed Problem: Maximum intersection points of 5 straight lines and 4 circles.

🚀 Upcoming Lecture: Stay tuned for the next video where we will discuss Geometrical Problems on the Number of Rectangles and Squares!

▶️ Full Playlists:

Sets: [   • Sets Complete Lecture Series | JEE Mains a...  ]

Relations: [   • Relations | Class 11th & 12th | Complete L...  ]

Binomial Theorem: [   • Binomial Theorem Complete Series | JEE Mai...  ]

Permutations & Combinations: [   • Permutations and Combinations Complete Pla...  ]



Timestamps:
00:00 - Introduction & Analysis
01:29 - Intersection of Lines (Condition based)
06:58 - Problem1
09:33 - Intersection of Circles
11:43 - Problem 2
13:42 - Lines, Triangles & Quadrilaterals (Collinear Points)
22:23 - Problem 3
29:50 - Interior Angles & Diagonals
31:48 - Problems 4
33:24 - JEE Mains 2015 PYQ (Diagonals)
35:11 - Plane Division Problem (67 Parts)
41:55 - JEE Mains 2024 PYQ (Parallel & Concurrent)
44:07 - JEE Mains 2025 PYQ (12 Points)
45:01 - JEE Mains 2025 PYQ (Intersecting Lines)
50:30 - JEE Mains 2013 PYQ (Triangle Sides)
55:13 - Intersection of Lines & Circles Combined
56:56 - Summary and Next Lecture


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