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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: ...
Explanation:
Assertion:
- The assertion states that n^2 - n is divisible by 4 for every positive integer n.
- This can be proven by factoring out n from the expression: n(n-1).
- Since n and n-1 are consecutive integers, one of them must be even.
- Therefore, the product of n and n-1 is always divisible by 2.
- Since one of the factors is always even, the product is also divisible by 4.
- Hence, n^2 - n is indeed divisible by 4 for every positive integer n.
Reason:
- The reason states that √2 is not a rational number.
- A rational number is a number that can be expressed as a ratio of two integers.
- However, the square root of 2 cannot be expressed as a fraction of two integers.
- This can be proven by assuming that √2 can be expressed as a fraction a/b where a and b are integers.
- By squaring both sides of the equation, we get 2 = a^2/b^2, which leads to a contradiction.
- Therefore, √2 is not a rational number.
Explanation:
- Both the assertion and reason are correct in this case.
- The reason provided does not directly explain why n^2 - n is divisible by 4 for every positive integer.
- It is true that √2 is not a rational number, but this fact is not directly related to the divisibility of n^2 - n by 4.
- Hence, option 'B' is the correct choice as both the assertion and reason are correct, but the reason is not the correct explanation for the assertion.
Assertion:
- The assertion states that n^2 - n is divisible by 4 for every positive integer n.
- This can be proven by factoring out n from the expression: n(n-1).
- Since n and n-1 are consecutive integers, one of them must be even.
- Therefore, the product of n and n-1 is always divisible by 2.
- Since one of the factors is always even, the product is also divisible by 4.
- Hence, n^2 - n is indeed divisible by 4 for every positive integer n.
Reason:
- The reason states that √2 is not a rational number.
- A rational number is a number that can be expressed as a ratio of two integers.
- However, the square root of 2 cannot be expressed as a fraction of two integers.
- This can be proven by assuming that √2 can be expressed as a fraction a/b where a and b are integers.
- By squaring both sides of the equation, we get 2 = a^2/b^2, which leads to a contradiction.
- Therefore, √2 is not a rational number.
Explanation:
- Both the assertion and reason are correct in this case.
- The reason provided does not directly explain why n^2 - n is divisible by 4 for every positive integer.
- It is true that √2 is not a rational number, but this fact is not directly related to the divisibility of n^2 - n by 4.
- Hence, option 'B' is the correct choice as both the assertion and reason are correct, but the reason is not the correct explanation for the assertion.
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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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