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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: In \(\frac{x^{2}-7x+12}{5x^{2}+5x-100}\), the common factor \(x-4\) may be cancelled when the original denominator is non-zero.
Reason: The denominator factors as \(5(x-4)(x+5)\), so the non-zero-denominator condition ensures \(x-4\ne 0\).
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Question 2 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 3 of 6
Assertion (A): The expansion of \((a+b+c)^{2}\) is \(a^{2}+b^{2}+c^{2}+2ab+2bc+2ca\).
Reason (R): This can be derived by grouping \(b+c=d\) and applying the identity for \((a+d)^{2}\).
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Question 4 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 5 of 6
Assertion: A square playground of side \(40\) m with an outside path of uniform width \(s\) m has path area \(160s+4s^{2}\) square metres.
Reason: The side of the outer square is \(40+2s\), so the path area is \((40+2s)^{2}-40^{2}\).
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Question 6 of 6
Assertion (A): The rational expression \(\frac{x^{2}-9}{x-3}\) simplifies to \(x+3\) for all \(x\ne 3\).
Reason (R): Rational algebraic expressions cannot be simplified by cancelling common factors.
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