Teachoo Quiz

Assertion Reasoning Quiz

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

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Question 1 of 6
Question 1 of 6
Assertion: A rectangular pool of area \(96\text{m}^{2}\), whose breadth is \(4\) m less than its length, has dimensions \(12\) m by \(8\) m.
Reason: The equation \(x(x-4)=96\) factors as \((x-12)(x+8)=0\), and the negative value is rejected for a length.
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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 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 4 of 6
Assertion (A): To factorise \(x^{2}+7x+12\) by splitting the middle term, we split \(7x\) into \(3x\) and \(4x\).
Reason (R): We need two numbers \(a\) and \(b\) such that \(a+b=7\) and \(ab=12\).
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Question 5 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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Question 6 of 6
Assertion (A): The binomial \((x-y)\) is a factor of the expression \(x^{3}-y^{3}\).
Reason (R): The expansion of \(x^{3}-y^{3}\) is \((x-y)(x^{2}+xy+y^{2})\).
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