CBSE Class 10 · Section A practice

Class 10 Maths assertion–reason questions, chapter-wise

One original assertion–reason question for every chapter, in the board paper's format (1 mark each, in Section A). Try each one, then open its worked answer on the chapter page; a free account opens it, no card.

14 chapters
14 questions
Worked answers with a free account

How to answer an assertion–reason question

Every question has the same four options:

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Decide first whether the assertion is true, then whether the reason is true, each on its own. Only when both are true do you ask the third question: does the reason explain why the assertion is true? A reason can be a true fact and still not be the explanation.

Questions by chapter

Chapter 1·Real Numbers·1 mark

Assertion (A): For no natural number $n$ does $15^{n}$ end with the digit $0$ .

Reason (R): A natural number ends with the digit $0$ only if its prime factorisation contains both $2$ and $5$ .

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 2·Polynomials·1 mark

Assertion (A): The polynomial $x^{2} - 6 x + 9$ has two equal zeroes.

Reason (R): Every quadratic polynomial has two distinct real zeroes.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 3·Pair of Linear Equations in Two Variables·1 mark

Assertion (A): The lines $3 x - y = 5$ and $6 x - 2 y = 7$ are parallel.

Reason (R): Lines $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ are parallel when $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ .

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 4·Quadratic Equations·1 mark

Assertion (A): The roots of $2 x^{2} - 7 x + 3 = 0$ are $3$ and $\frac{1}{2}$ .

Reason (R): The roots of $a x^{2} + b x + c = 0$ always add up to $\frac{b}{a}$ .

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 5·Arithmetic Progressions·1 mark

Assertion (A): $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \dots$ is an arithmetic progression.

Reason (R): Every term of an arithmetic progression must be a rational number.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 6·Triangles·1 mark

Assertion (A): A triangle with sides $3$ cm, $4$ cm, $5$ cm is similar to a triangle with sides $6$ cm, $8$ cm, $10$ cm.

Reason (R): All equilateral triangles are similar.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 7·Coordinate Geometry·1 mark

Assertion (A): The point $(0, - 7)$ lies on the $y$ -axis.

Reason (R): Every point on the $x$ -axis has $y$ -coordinate $0$ .

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 8·Introduction to Trigonometry·1 mark

Assertion (A): There is an acute angle $θ$ with $\sin θ = \frac{4}{3}$ .

Reason (R): For every acute angle $θ$ , $0 < \sin θ < 1$ .

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 9·Some Applications of Trigonometry·1 mark

Assertion (A): As you walk in a straight line towards the foot of a tower, the angle of elevation of its top increases.

Reason (R): For angles between $0^{\circ}$ and $90^{\circ}$ , $\tan θ$ increases as $θ$ increases.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 10·Circles·1 mark

Assertion (A): The tangents drawn at the two ends of a diameter of a circle are parallel.

Reason (R): A tangent to a circle is perpendicular to the radius through the point of contact.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 11·Areas Related to Circles·1 mark

Assertion (A): A circle whose circumference is $44$ cm has area $154 {cm}^{2}$ (take $π = \frac{22}{7}$ ).

Reason (R): The area of a sector of angle $θ$ in a circle of radius $r$ is $\frac{θ}{360^{\circ}} \times π r^{2}$ .

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 12·Surface Areas and Volumes·1 mark

Assertion (A): Two identical cubes of edge $a$ are joined face to face. The total surface area of the cuboid formed is $10 a^{2}$ .

Reason (R): When two solids are joined, the surface area of the new solid is the sum of their surface areas.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 13·Statistics·1 mark

Assertion (A): For any grouped data, the assumed-mean method gives the same mean as the direct method.

Reason (R): The assumed-mean method subtracts the same number $a$ from every class mark and adds $a$ back at the end.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

Chapter 14·Probability·1 mark

Assertion (A): When two dice are thrown, the probability that the sum of the numbers is $13$ is $0$ .

Reason (R): The probability of an impossible event is $0$ .

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

Worked answer →

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