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A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the second point and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?
- a)10
- b)12
- c)14
- d)16
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A straight line segment is 36 cm long. Points are to be marked on the ...
This can again be solved manually as well as using a scale diagram.
Technique 1: (Manual)
First point is at a distance of 1 cm, 2nd at 2 cm and so on – therefore, the distance of each point from the left edge of the scale will be
1st point – 1 cm
2nd – 3 cm
3rd – 6 cm
4th – 10 cm
5th – 15 cm
6th – 21 cm
7th – 28 cm
8th – 36 cm
Similarily from the right edge too, the same story repeats. So we have totally 8+8 = 16 points.
But, common points are to be counted as one and end points not to be counted. End points are the 8th point drawn from both the sides. So reduce 2 points from 16 which becomes 14.
Now common points – so 5th point from the left; and 6th point from the right are common and will repeat twice. So they have to be counted only once. Reduce 2 more points from 14 which becomes 12 as the answer.
Technique 2: (Using a scale - or diagram) Draw a rectangle 36 cm long with some width on the rough side of your notebook and mark 1 to 36 cm on it roughly.
Similarily from the right edge too, the same story repeats. So we have totally 8+8 = 16 points.
But, common points are to be counted as one and end points not to be counted. End points are the 8th point drawn from both the sides. So reduce 2 points from 16 which becomes 14.
Now common points – so 5th point from the left; and 6th point from the right are common and will repeat twice. So they have to be counted only once. Reduce 2 more points from 14 which becomes 12 as the answer.
Technique 2: (Using a scale - or diagram) Draw a rectangle 36 cm long with some width on the rough side of your notebook and mark 1 to 36 cm on it roughly.
Start putting points on the top and bottom of the rectangle from both left and right hand sides. You will be easily able to see the total number of points as 16 and; out of which 2 points will be overlapping; and 2 as end points. So the final answer will be 12.
In the exam you can follow any of the above techniques. Both will take almost the same time.
In the exam you can follow any of the above techniques. Both will take almost the same time.
Most Upvoted Answer
A straight line segment is 36 cm long. Points are to be marked on the ...
Given:
- Length of straight line segment = 36 cm
- From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the second point and so on.
To find:
- The total number of points on the line (excluding the end points and counting the common points as one)
Solution:
- From each end, the first point is at a distance of 1 cm from the end. Therefore, there are 2 points at a distance of 1 cm from each end.
- From each end, the second point is at a distance of 2 cm from the first point. Therefore, there are 2 points at a distance of 2 cm from each end.
- Similarly, there are 2 points at a distance of 3 cm from each end, and so on.
- The last point that can be marked on the line segment will be at a distance of 18 cm from each end (as 1+2+3+...+n = n(n+1)/2, where n is the number of points from each end). Therefore, there are 2 points at a distance of 18 cm from each end.
- To find the total number of points, we need to add the number of points at each distance from each end.
- So, the total number of points = 2 + 2 + 2 + ... + 2 (18 times)
- This is an arithmetic series with first term = 2, common difference = 0, and number of terms = 18.
- Therefore, the sum of this series = (number of terms) x (average of first and last term)
- Sum = 18 x (2+2)/2 = 18 x 2 = 36
- However, we have counted the common points twice (once from each end). Therefore, we need to subtract the number of common points from the total.
- The number of common points = number of points at a distance of 1 cm from each end = 2
- Therefore, the total number of points (excluding the end points and counting the common points as one) = 36 - 2 = 34
- Hence, the correct option is (B) 12.
- Length of straight line segment = 36 cm
- From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the second point and so on.
To find:
- The total number of points on the line (excluding the end points and counting the common points as one)
Solution:
- From each end, the first point is at a distance of 1 cm from the end. Therefore, there are 2 points at a distance of 1 cm from each end.
- From each end, the second point is at a distance of 2 cm from the first point. Therefore, there are 2 points at a distance of 2 cm from each end.
- Similarly, there are 2 points at a distance of 3 cm from each end, and so on.
- The last point that can be marked on the line segment will be at a distance of 18 cm from each end (as 1+2+3+...+n = n(n+1)/2, where n is the number of points from each end). Therefore, there are 2 points at a distance of 18 cm from each end.
- To find the total number of points, we need to add the number of points at each distance from each end.
- So, the total number of points = 2 + 2 + 2 + ... + 2 (18 times)
- This is an arithmetic series with first term = 2, common difference = 0, and number of terms = 18.
- Therefore, the sum of this series = (number of terms) x (average of first and last term)
- Sum = 18 x (2+2)/2 = 18 x 2 = 36
- However, we have counted the common points twice (once from each end). Therefore, we need to subtract the number of common points from the total.
- The number of common points = number of points at a distance of 1 cm from each end = 2
- Therefore, the total number of points (excluding the end points and counting the common points as one) = 36 - 2 = 34
- Hence, the correct option is (B) 12.
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A straight line segment is 36 cm long. Points are to be marked on the ...
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A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer?
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A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer?.
A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer?.
Solutions for A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
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A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the secondpoint and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?a)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice UPSC tests.
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