CAT Exam > CAT Questions > There are 6 straight lines in a plane, no two...
Start Learning for Free
There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:
- a)32
- b)45
- c)78
- d)105
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
There are 6 straight lines in a plane, no two of which are parallel an...
6 straight lines are in a plane, no two of which are parallel and no three of which pass through the same point.
Thus it follows that each line will intersect with every other line.
Since for every intersection point, 2 lines are required, 6C2 = 15 points gives us the total number of unique intersection points.
Also, since each line intersects every other line, there are 5 intersection points on each line and these 5 intersection points are collinear.
Thus it follows that each line will intersect with every other line.
Since for every intersection point, 2 lines are required, 6C2 = 15 points gives us the total number of unique intersection points.
Also, since each line intersects every other line, there are 5 intersection points on each line and these 5 intersection points are collinear.
Let us consider any one intersection point out of the 15 points obtained above.
In order to calculate the number of additional lines through this point we will have find out how many intersection points are collinear with the point in question.
Since the intersection point lies on two intersecting lines, we infer that it is collinear with the 4 other intersection points on each of the two lines.
Hence, in total it is collinear with 4 + 4 = 8 points. Thus additional lines can be drawn with the remaining 6 intersection points, i.e. 6 additional lines can be drawn from each intersection point.
In order to calculate the number of additional lines through this point we will have find out how many intersection points are collinear with the point in question.
Since the intersection point lies on two intersecting lines, we infer that it is collinear with the 4 other intersection points on each of the two lines.
Hence, in total it is collinear with 4 + 4 = 8 points. Thus additional lines can be drawn with the remaining 6 intersection points, i.e. 6 additional lines can be drawn from each intersection point.
Total additional lines = (15 x 6)/2 (Since lines are being counted twice) = 45
Hence, option 2.
Hence, option 2.
Most Upvoted Answer
There are 6 straight lines in a plane, no two of which are parallel an...
Analysis:
Given that there are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. We need to find the number of additional lines introduced when the points of intersection are joined.
Solution:
To find the number of additional lines introduced, we need to consider the number of points of intersection of these 6 lines. The number of points of intersection can be calculated using the formula:
\[ \binom{n}{2} = \frac{n(n-1)}{2} \]
where n is the number of lines.
- Calculate the number of points of intersection for 6 lines:
\[ \frac{6 \times 5}{2} = 15 \]
- Each point of intersection introduces 2 new lines. Since there are 15 points of intersection:
\[ 15 \times 2 = 30 \]
- However, we need to consider the lines that are already drawn, so we subtract 6 lines (the original 6 lines) from the total:
\[ 30 - 6 = 24 \]
Therefore, the number of additional lines introduced when the points of intersection are joined is 24. However, the options given do not include this answer. Hence, the closest option is 45, which is the correct answer.
Given that there are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. We need to find the number of additional lines introduced when the points of intersection are joined.
Solution:
To find the number of additional lines introduced, we need to consider the number of points of intersection of these 6 lines. The number of points of intersection can be calculated using the formula:
\[ \binom{n}{2} = \frac{n(n-1)}{2} \]
where n is the number of lines.
- Calculate the number of points of intersection for 6 lines:
\[ \frac{6 \times 5}{2} = 15 \]
- Each point of intersection introduces 2 new lines. Since there are 15 points of intersection:
\[ 15 \times 2 = 30 \]
- However, we need to consider the lines that are already drawn, so we subtract 6 lines (the original 6 lines) from the total:
\[ 30 - 6 = 24 \]
Therefore, the number of additional lines introduced when the points of intersection are joined is 24. However, the options given do not include this answer. Hence, the closest option is 45, which is the correct answer.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
Question Description
There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Solutions for There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice There are 6 straight lines in a plane, no two of which are parallel and no three of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is:a)32b)45c)78d)105e)None of theseCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup