CBSE Class 8 Maths Chapter 13: Algebra Play — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 13: Algebra Play from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): Algebra can explain why a number trick gives a fixed result.
Reason (R): Representing the starting number by x reveals cancellations independent of x.
Reason (R): Representing the starting number by x reveals cancellations independent of x.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Symbolic simplification proves the result for every allowed starting value.
2
Assertion (A): If x is doubled, increased by 4, halved, and then x is subtracted, the result is 2.
Reason (R): Number pyramids can be represented with variables.
Reason (R): Number pyramids can be represented with variables.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the pyramid fact does not explain this particular trick.
3
Assertion (A): The expression (2x + 4)/2 equals x + 2.
Reason (R): Dividing the numerator by 2 gives 2x + 2.
Reason (R): Dividing the numerator by 2 gives 2x + 2.
Answer: (c)
A is true, but R is false. Both terms must be divided, producing x + 2.
4
Assertion (A): Testing a trick for one starting number proves it for all numbers.
Reason (R): An algebraic identity can establish a result for every permitted value.
Reason (R): An algebraic identity can establish a result for every permitted value.
Answer: (d)
A is false, but R is true. Examples suggest a pattern, while algebra provides the general proof.
5
Assertion (A): A number pyramid can be represented using variables.
Reason (R): Relations between neighbouring entries can be translated into algebraic expressions.
Reason (R): Relations between neighbouring entries can be translated into algebraic expressions.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The rule of the pyramid then applies generally.
6
Assertion (A): Equivalent expressions give the same value for every allowed substitution.
Reason (R): The expressions 2(x + 3) and 2x + 6 are equivalent.
Reason (R): The expressions 2(x + 3) and 2x + 6 are equivalent.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the example illustrates rather than defines all equivalence.
7
Assertion (A): The expression 3(x + 2) equals 3x + 6.
Reason (R): The distributive law gives 3x + 2.
Reason (R): The distributive law gives 3x + 2.
Answer: (c)
A is true, but R is false. The factor 3 multiplies both terms.
8
Assertion (A): Like terms such as 3x and 4 can always be combined as 7x.
Reason (R): Only terms with the same variable part can be combined by adding coefficients.
Reason (R): Only terms with the same variable part can be combined by adding coefficients.
Answer: (d)
A is false, but R is true. A variable term and a constant are unlike terms.
9
Assertion (A): Algebraic grid patterns can reveal constant row or column sums.
Reason (R): Assigning variables helps compare the sums without checking every numerical example.
Reason (R): Assigning variables helps compare the sums without checking every numerical example.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Symbolic relations expose why the pattern holds.
10
Assertion (A): A counterexample can disprove a universal algebraic rule.
Reason (R): A two-digit number with digits a and b is 10a + b.
Reason (R): A two-digit number with digits a and b is 10a + b.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but place value does not explain the logic of a counterexample.
11
Assertion (A): For a fixed positive sum, the product is largest when the two numbers are equal or as close as possible.
Reason (R): The product is always largest when one number is zero.
Reason (R): The product is always largest when one number is zero.
Answer: (c)
A is true, but R is false. Balancing the two factors maximises their product.
12
Assertion (A): The product of two numbers with fixed sum increases without limit.
Reason (R): A fixed sum restricts the possible pairs and therefore their products.
Reason (R): A fixed sum restricts the possible pairs and therefore their products.
Answer: (d)
A is false, but R is true. The product has a finite maximum.
13
Assertion (A): A two-digit number with tens digit a and units digit b is 10a + b.
Reason (R): Place value assigns ten times the tens digit plus the units digit.
Reason (R): Place value assigns ten times the tens digit plus the units digit.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The algebraic form follows directly from decimal notation.
14
Assertion (A): Reversing the digits of 10a + b gives 10b + a.
Reason (R): Their difference is 9(a - b).
Reason (R): Their difference is 9(a - b).
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the difference formula does not explain the reversed-number representation.
15
Assertion (A): Not every two-digit number is divisible by the sum of its digits.
Reason (R): Every two-digit number passes that divisibility test.
Reason (R): Every two-digit number passes that divisibility test.
Answer: (c)
A is true, but R is false. For example, 23 is not divisible by 5.
16
Assertion (A): A number is divisible by 9 only when its last digit is 9.
Reason (R): Divisibility by 9 is determined by whether the sum of digits is divisible by 9.
Reason (R): Divisibility by 9 is determined by whether the sum of digits is divisible by 9.
Answer: (d)
A is false, but R is true. The last-digit test is not the rule for 9.
17
Assertion (A): A divisibility trick can be proved using place-value algebra.
Reason (R): Powers of 10 have predictable remainders modulo numbers such as 3, 9 or 11.
Reason (R): Powers of 10 have predictable remainders modulo numbers such as 3, 9 or 11.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Those remainders connect the whole number with combinations of its digits.
18
Assertion (A): Every multiple of 6 is divisible by both 2 and 3.
Reason (R): A number divisible by 2 and 3 is divisible by 6.
Reason (R): A number divisible by 2 and 3 is divisible by 6.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the converse statement does not explain the forward implication.
19
Assertion (A): The expression x - x equals 0 for every x.
Reason (R): It equals x for all values of x.
Reason (R): It equals x for all values of x.
Answer: (c)
A is true, but R is false. A quantity subtracted from itself is zero.
20
Assertion (A): Algebra is useful only for finding one missing number and cannot explain patterns.
Reason (R): Variables and identities can model puzzles, grids and divisibility rules.
Reason (R): Variables and identities can model puzzles, grids and divisibility rules.
Answer: (d)
A is false, but R is true. Algebra is a tool for general reasoning as well as solving equations.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 13 Algebra Play?
This chapter covers all key topics from Algebra Play as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Algebra Play online for free?
Yes, complete Assertion & Reason for Algebra Play is available free at eBookPublisher. Study online directly — no download needed.
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