Teachoo MCQ Test

Assertion Reasoning Quiz

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

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 576
Question 1 of 6
Question 1 of 6
Assertion (A): For any two positive numbers \(a\) and \(b\), \((a+b)^{2}\) is always greater than \(a^{2}+b^{2}\).
Reason (R): The expansion of \((a+b)^{2}\) includes the term \(2ab\), which is positive when \(a\) and \(b\) are positive.
Select one option. Answers are shown after the test.
Question 2 of 6
Assertion (A): The product of \(104\times 96\) can be calculated as \(10000-16=9984\).
Reason (R): We can use the identity \((a+b)(a-b)=a^{2}-b^{2}\) where \(a=100\) and \(b=4\).
Select one option. Answers are shown after the test.
Question 3 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 \((x-2)\).
Select one option. Answers are shown after the test.
Question 4 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 \(x-4\ne 0\).
Select one option. Answers are shown after the test.
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 \(3\).
Select one option. Answers are shown after the test.
Question 6 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 \((x+y)^{3}\).
Select one option. Answers are shown after the test.