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Assertion: n2 - n is divisible by for every positive integer.
Reason: √2 is not a rational number.
- 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 'B'. Can you explain this answer?
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Assertion: n2 - n is divisible by for every positive integer.Reason: ...
n2 - n = n(n - 1) If n is odd, n - 1 will be even.
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Assertion: n2 - n is divisible by for every positive integer.Reason: ...
Assertion and Reasoning questions are designed to test the analytical and logical reasoning abilities of students. In such questions, a statement or assertion is given followed by a reason which justifies the assertion. The student is required to evaluate both the statement and the reason and determine if they are correct or not.
Explanation:
Assertion: n2 - n is divisible by for every positive integer.
Reason: √2 is not a rational number.
Let's evaluate both the assertion and reason to determine if they are correct or not.
Assertion:
n2 - n is divisible by for every positive integer.
To evaluate the assertion, we can use mathematical induction.
Base case: For n = 1, n2 - n = 1 - 1 = 0, which is divisible by any positive integer.
Inductive step: Assume that n2 - n is divisible by any positive integer k. We need to show that (n+1)2 - (n+1) is also divisible by k.
Expanding (n+1)2 - (n+1), we get:
(n+1)2 - (n+1) = n2 + 2n + 1 - n - 1 = n2 + n
Since we assumed that n2 - n is divisible by k, we can write:
n2 - n = kq
Adding kq to both sides of the above equation, we get:
n2 + n = kq + n
Substituting this in the expression for (n+1)2 - (n+1), we get:
(n+1)2 - (n+1) = kq + n + 2n + 1 - n - 1 = kq + 2n = kq' (where q' = q + 2)
Thus, (n+1)2 - (n+1) is also divisible by k. This completes the proof by mathematical induction.
Thus, the assertion is correct.
Reason:
√2 is not a rational number.
This is also correct. A rational number is defined as a number that can be expressed in the form of p/q, where p and q are integers and q ≠ 0. However, √2 cannot be expressed in this form as it is an irrational number.
The reason correctly justifies why the assertion is true, but it is not a direct explanation. The two statements are related, but not directly connected.
Conclusion:
Hence, option (B) is the correct answer as both Assertion and Reason are correct, but the Reason is not the correct explanation for the Assertion.
Explanation:
Assertion: n2 - n is divisible by for every positive integer.
Reason: √2 is not a rational number.
Let's evaluate both the assertion and reason to determine if they are correct or not.
Assertion:
n2 - n is divisible by for every positive integer.
To evaluate the assertion, we can use mathematical induction.
Base case: For n = 1, n2 - n = 1 - 1 = 0, which is divisible by any positive integer.
Inductive step: Assume that n2 - n is divisible by any positive integer k. We need to show that (n+1)2 - (n+1) is also divisible by k.
Expanding (n+1)2 - (n+1), we get:
(n+1)2 - (n+1) = n2 + 2n + 1 - n - 1 = n2 + n
Since we assumed that n2 - n is divisible by k, we can write:
n2 - n = kq
Adding kq to both sides of the above equation, we get:
n2 + n = kq + n
Substituting this in the expression for (n+1)2 - (n+1), we get:
(n+1)2 - (n+1) = kq + n + 2n + 1 - n - 1 = kq + 2n = kq' (where q' = q + 2)
Thus, (n+1)2 - (n+1) is also divisible by k. This completes the proof by mathematical induction.
Thus, the assertion is correct.
Reason:
√2 is not a rational number.
This is also correct. A rational number is defined as a number that can be expressed in the form of p/q, where p and q are integers and q ≠ 0. However, √2 cannot be expressed in this form as it is an irrational number.
The reason correctly justifies why the assertion is true, but it is not a direct explanation. The two statements are related, but not directly connected.
Conclusion:
Hence, option (B) is the correct answer as both Assertion and Reason are correct, but the Reason is not the correct explanation for the Assertion.
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Community Answer
Assertion: n2 - n is divisible by for every positive integer.Reason: ...
Both statements are true but the reason is not the correct explanation for assertion its reason will be that n^2 -n = n(n-1) => n is either odd or even no .
if n is odd then n-1 will be even. and if n is even then n-1 is ped
-> odd no. × even no. = even no.
if n is odd then n-1 will be even. and if n is even then n-1 is ped
-> odd no. × even no. = even no.
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Assertion: n2 - n is divisible by for every positive integer.Reason: √2 is not a rational number.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 'B'. Can you explain this answer?
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Assertion: n2 - n is divisible by for every positive integer.Reason: √2 is not a rational number.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 'B'. 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: n2 - n is divisible by for every positive integer.Reason: √2 is not a rational number.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 'B'. 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: n2 - n is divisible by for every positive integer.Reason: √2 is not a rational number.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 'B'. Can you explain this answer?.
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