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Maths Exploring Algebraic Identities - Chapter 4 Class 9 (Ganita Manjari I) Assertion and Reason Questions

Assertion Reasoning Quiz · Class 9 · Maths · CBSE

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Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I) | 6 questions | about 5 minutes

Practise Exploring Algebraic Identities - Chapter 4 Class 9 (Ganita Manjari I) with Teachoo's Assertion Reasoning Quiz (Class 9 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 6
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Question 1 of 6
Assertion (A): If \(x+y+z=0\), then \(x^{3}+y^{3}+z^{3}=3xyz\).
Reason (R): The identity is \(x^{3}+y^{3}+z^{3}-3xyz=(x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx)\).
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Question 2 of 6
Assertion (A): The product of \((x+2)\) and \((x+3)\) can be found visually using algebra tiles by arranging them into a rectangle.
Reason (R): The dimensions of the resulting rectangle will be \((x+3)\) and \((x-2)\).
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Question 3 of 6
Assertion (A): The factors of \(x^{2}+4x+4\) are \((x+2)\) and \((x+2)\).
Reason (R): The identity used to factorise it is \((a-b)^{2}=a^{2}-2ab+b^{2}\).
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Question 4 of 6
Assertion (A): The expansion of \((x-y)^{3}\) consists of entirely negative terms: \(x^{3}-3x^{2}y-3xy^{2}-y^{3}\).
Reason (R): The identity for \((x-y)^{3}\) can be found by substituting \(-y\) in place of \(y\) in \((x+y)^{3}\).
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Question 5 of 6
Assertion: \(x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})\).
Reason: \(x-y\) is also a factor of \(x^{4}-y^{4}\).
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Question 6 of 6
Assertion: \(n^{3}-n\) is divisible by \(6\) for every natural number \(n\).
Reason: \(n^{3}-n=n(n-1)(n+1)\), which is the product of three consecutive integers and is therefore divisible by both \(2\) and \(3\).
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