What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as circle and lines)? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
View all NDA Papers >
  1. 6
  2. 10
  3. 14
  4. 16

Answer (Detailed Solution Below)

Option 3 : 14
Free
BSF HC RO/RM All India Mega Live Test
5.4 K Users
100 Questions 200 Marks 120 Mins

Detailed Solution

Download Solution PDF

Explanation:

Since there are 4 lines, the maximum number of intersection points are 4C2 = 6.

The maximum number of intersections of the circle with 4 lines is 4 × 2 = 8.

Required intersection points = 6 + 8 = 14

∴ the correct answer is Option 3 ie 14

Latest NDA Updates

Last updated on May 30, 2025

->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.

-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

More Permutations and Combinations Questions

Get Free Access Now
Hot Links: teen patti real cash apk teen patti all teen patti gold download