CBSE Class 8 Maths Chapter 11: Exploring Some Geometric Themes — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 11: Exploring Some Geometric Themes 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): A fractal exhibits self-similarity at different scales.
Reason (R): A similar pattern reappears as one examines smaller parts of the figure.
Reason (R): A similar pattern reappears as one examines smaller parts of the figure.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Repeated structure across scales defines the self-similar behaviour.
2
Assertion (A): Ferns and branching trees suggest fractal-like patterns in nature.
Reason (R): Mathematical fractals can be generated by repeating a rule.
Reason (R): Mathematical fractals can be generated by repeating a rule.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the iterative rule does not explain every natural growth process.
3
Assertion (A): In the first Sierpinski carpet step, the central one of nine equal squares is removed.
Reason (R): The remaining area is 1/9 of the original.
Reason (R): The remaining area is 1/9 of the original.
Answer: (c)
A is true, but R is false. Eight of the nine equal squares remain, so the area is 8/9.
4
Assertion (A): A Sierpinski triangle is formed by repeatedly keeping the central subtriangle and removing the corner triangles.
Reason (R): The usual construction removes the central triangle and repeats on the three corner triangles.
Reason (R): The usual construction removes the central triangle and repeats on the three corner triangles.
Answer: (d)
A is false, but R is true. The assertion reverses the construction.
5
Assertion (A): At each Sierpinski triangle step, each retained triangle produces three smaller retained triangles.
Reason (R): The number of retained triangles is multiplied by 3 at every iteration.
Reason (R): The number of retained triangles is multiplied by 3 at every iteration.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The repeated replacement rule gives powers of 3.
6
Assertion (A): Fractal iteration can continue conceptually without end.
Reason (R): A finite drawing shows only a finite number of steps.
Reason (R): A finite drawing shows only a finite number of steps.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but drawing limitations do not define the mathematical continuation.
7
Assertion (A): A net of a solid is a flat arrangement of faces that can fold into the solid.
Reason (R): Every connected arrangement of six squares is a cube net.
Reason (R): Every connected arrangement of six squares is a cube net.
Answer: (c)
A is true, but R is false. Only certain arrangements fold without overlap to form a cube.
8
Assertion (A): A cube has only one possible net up to rotation and reflection.
Reason (R): A cube has 11 distinct net structures under the usual equivalence.
Reason (R): A cube has 11 distinct net structures under the usual equivalence.
Answer: (d)
A is false, but R is true. The variety is larger than one.
9
Assertion (A): A regular tetrahedron has four congruent equilateral triangular faces.
Reason (R): A valid net joins four such triangles so that they fold into the tetrahedron.
Reason (R): A valid net joins four such triangles so that they fold into the tetrahedron.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The face structure determines the pieces of its net.
10
Assertion (A): A cube has 6 faces, 12 edges and 8 vertices.
Reason (R): A regular tetrahedron has 4 faces.
Reason (R): A regular tetrahedron has 4 faces.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the tetrahedron count does not explain the cube count.
11
Assertion (A): A projection can distort some actual lengths or angles of a solid.
Reason (R): Every planar drawing preserves all three-dimensional measurements exactly.
Reason (R): Every planar drawing preserves all three-dimensional measurements exactly.
Answer: (c)
A is true, but R is false. Representing three dimensions on a plane generally requires distortion.
12
Assertion (A): The same solid looks identical from every viewpoint.
Reason (R): Front, top and side views can have different profiles.
Reason (R): Front, top and side views can have different profiles.
Answer: (d)
A is false, but R is true. A change of viewpoint changes the visible outline and faces.
13
Assertion (A): An isometric drawing uses three directions to suggest three-dimensional form.
Reason (R): Equal steps along its coordinate directions are represented consistently.
Reason (R): Equal steps along its coordinate directions are represented consistently.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The equal-scale convention creates an interpretable solid drawing.
14
Assertion (A): A shadow is a type of projection.
Reason (R): Parallel projection can preserve parallelism in suitable conditions.
Reason (R): Parallel projection can preserve parallelism in suitable conditions.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but preservation of parallelism does not explain every shadow.
15
Assertion (A): A solid cannot always be identified uniquely from one silhouette.
Reason (R): One profile always determines a unique solid.
Reason (R): One profile always determines a unique solid.
Answer: (c)
A is true, but R is false. Different solids may share the same profile from a particular direction.
16
Assertion (A): An impossible figure must correspond to a physically buildable solid.
Reason (R): Local parts of a drawing can be arranged to create a globally inconsistent visual object.
Reason (R): Local parts of a drawing can be arranged to create a globally inconsistent visual object.
Answer: (d)
A is false, but R is true. Impossible figures exploit conflicting depth cues.
17
Assertion (A): Visualising a net requires reasoning about which faces become adjacent.
Reason (R): Edges that meet after folding must be compatible without unwanted overlap.
Reason (R): Edges that meet after folding must be compatible without unwanted overlap.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Adjacency and orientation determine whether the net closes.
18
Assertion (A): A dodecahedron has pentagonal faces.
Reason (R): An octahedron has eight triangular faces.
Reason (R): An octahedron has eight triangular faces.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true properties, but the octahedron does not explain the dodecahedron.
19
Assertion (A): The area remaining in a Sierpinski construction decreases with repeated removal.
Reason (R): Each step increases the remaining area.
Reason (R): Each step increases the remaining area.
Answer: (c)
A is true, but R is false. Each iteration removes additional positive area.
20
Assertion (A): Self-similarity requires every natural object to match an exact mathematical fractal at infinitely small scales.
Reason (R): Natural objects may show approximate rather than perfect self-similarity.
Reason (R): Natural objects may show approximate rather than perfect self-similarity.
Answer: (d)
A is false, but R is true. Mathematical and natural fractals need not behave identically.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 11 Exploring Some Geometric Themes?
This chapter covers all key topics from Exploring Some Geometric Themes 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 Exploring Some Geometric Themes online for free?
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