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Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.
Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.
- a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- b)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- c)Assertion is correct but Reason is incorrect
- d)Assertion is incorrect but Reason is correct
Correct answer is option 'D'. Can you explain this answer?
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Assertion - If the pair of lines are coincident, then we say that pai...
If the pair of lines are coincident, then it has an infinite number of solutions. Thus, the assertion is false. If the given pair of lines are parallel, then the pair of equations is inconsistent and it has no solution. Thus, reason is correct. Hence, option (d).
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Assertion - If the pair of lines are coincident, then we say that pai...
Assertion: If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.
Reason: If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.
To understand why option D is the correct answer, let's examine the concepts of coincident lines, consistent pairs, and parallel lines.
Coincident Lines:
- When two lines lie on top of each other and have the same slope and y-intercept, they are called coincident lines.
- Coincident lines represent the same line and have infinitely many points of intersection.
Consistent Pair of Equations:
- A pair of linear equations is said to be consistent if it has at least one solution.
- In the case of coincident lines, the pair of equations is consistent as they have infinitely many solutions represented by the points on the coincident line.
Parallel Lines:
- When two lines have the same slope but different y-intercepts, they are called parallel lines.
- Parallel lines never intersect and have no common points of intersection.
- When a pair of lines is parallel, the pair of equations is inconsistent, meaning it has no solution.
Explanation of the Assertion:
The assertion states that if the pair of lines are coincident, then the pair is consistent and has a unique solution. This is correct because coincident lines represent the same line and have infinitely many points of intersection. Therefore, any point on the coincident line satisfies both equations, making the pair consistent with a unique solution.
Explanation of the Reason:
The reason states that if the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations. This is also correct because parallel lines never intersect and have no common points of intersection. Therefore, there is no solution that satisfies both equations simultaneously, making the pair inconsistent.
Conclusion:
Both the assertion and reason are correct statements. However, the reason does not provide a correct explanation for the assertion. The reason states the condition for an inconsistent pair (parallel lines), but it does not explain why coincident lines result in a consistent pair with a unique solution. Hence, option D is the correct answer.
Reason: If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.
To understand why option D is the correct answer, let's examine the concepts of coincident lines, consistent pairs, and parallel lines.
Coincident Lines:
- When two lines lie on top of each other and have the same slope and y-intercept, they are called coincident lines.
- Coincident lines represent the same line and have infinitely many points of intersection.
Consistent Pair of Equations:
- A pair of linear equations is said to be consistent if it has at least one solution.
- In the case of coincident lines, the pair of equations is consistent as they have infinitely many solutions represented by the points on the coincident line.
Parallel Lines:
- When two lines have the same slope but different y-intercepts, they are called parallel lines.
- Parallel lines never intersect and have no common points of intersection.
- When a pair of lines is parallel, the pair of equations is inconsistent, meaning it has no solution.
Explanation of the Assertion:
The assertion states that if the pair of lines are coincident, then the pair is consistent and has a unique solution. This is correct because coincident lines represent the same line and have infinitely many points of intersection. Therefore, any point on the coincident line satisfies both equations, making the pair consistent with a unique solution.
Explanation of the Reason:
The reason states that if the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations. This is also correct because parallel lines never intersect and have no common points of intersection. Therefore, there is no solution that satisfies both equations simultaneously, making the pair inconsistent.
Conclusion:
Both the assertion and reason are correct statements. However, the reason does not provide a correct explanation for the assertion. The reason states the condition for an inconsistent pair (parallel lines), but it does not explain why coincident lines result in a consistent pair with a unique solution. Hence, option D is the correct answer.
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Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer?
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Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer?.
Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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ample number of questions to practice Assertion - If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution.Reason - If the pair of lines are parallel, then the pair has no solution and is called an inconsistent pair of equations.a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertionb)Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionc)Assertion is correct but Reason is incorrectd)Assertion is incorrect but Reason is correctCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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