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Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let α be the number of triangles having these points from different sides as vertices and β be the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:
- a)795
- b)1173
- c)1890
- d)717
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of ...
Us assume that the points inside the line segment AB divide it into 6 smaller line segments, and similarly for the other line segments.
Let's consider the line segment AB. It is divided into 6 smaller line segments by the 5 points in its interior. This means that there are 6 + 1 = 7 line segments in total. Similarly, there are 8 line segments in the line segment CD, 7 line segments in BC, and 10 line segments in DA.
Now, let's consider the interior of the rectangle ABCD. It is divided into two parts - the interior of the line segment AB and the interior of the line segment CD. The interior of the line segment AB has 5 points and 7 smaller line segments, while the interior of the line segment CD has 6 points and 8 smaller line segments.
Therefore, the total number of points in the interior of the rectangle ABCD is 5 + 6 = 11, and the total number of smaller line segments is 7 + 8 = 15.
Hence, the total number of points and smaller line segments in the interior of the rectangle ABCD is 11 + 15 = 26.
Let's consider the line segment AB. It is divided into 6 smaller line segments by the 5 points in its interior. This means that there are 6 + 1 = 7 line segments in total. Similarly, there are 8 line segments in the line segment CD, 7 line segments in BC, and 10 line segments in DA.
Now, let's consider the interior of the rectangle ABCD. It is divided into two parts - the interior of the line segment AB and the interior of the line segment CD. The interior of the line segment AB has 5 points and 7 smaller line segments, while the interior of the line segment CD has 6 points and 8 smaller line segments.
Therefore, the total number of points in the interior of the rectangle ABCD is 5 + 6 = 11, and the total number of smaller line segments is 7 + 8 = 15.
Hence, the total number of points and smaller line segments in the interior of the rectangle ABCD is 11 + 15 = 26.
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Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of ...
α = Number of triangles
α = 6C1 7C1 9C1 + 5C1 7C1 9C1 + 5C1 6C1 9C1 + 5C1 6C1 7C1
= 6.7.9 + 5.7.9 + 5.6.9 + 5.6.7
= 378 + 315 + 270 + 210
= 1173
β = Number of quadrilaterals
β = 5.6.7.9 = 1890
β - α = 1890 - 1173 = 717
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Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer?
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Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer?.
Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer?.
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Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA, respectively. Let αbe the number of triangles having these points from different sides as vertices and βbe the number of quadrilaterals having these points from different sides as vertices. Then (β - α) is equal to:a)795b)1173c)1890d)717Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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