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Question (1)

QN0029473

In the Sierpinski Carpet, if Step 3 contains (8^3) remaining squares, how many squares remain in Step 4?

(A) 512
(B) 4096
(C) 1024
(D) 64

Correct Answer: B

Explanation:

Each remaining square produces 8 new squares. Therefore, (R_4 = 8^4 = 4096).

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Question (2)

QN0029474

A Sierpinski Triangle at Step 2 has 9 remaining triangles. How many triangles will remain at Step 4?

(A) 27
(B) 64
(C) 81
(D) 243

Correct Answer: C

Explanation:

The number of remaining triangles follows the pattern (3^n). Hence, at Step 4, the number is (3^4 = 81).

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Question (3)

QN0029475

The area of the initial square in a Sierpinski Carpet is 1 sq. unit. What is the area remaining after Step 2?

(A) (64/81) sq. unit
(B) (8/9) sq. unit
(C) (1/9) sq. unit
(D) (16/81) sq. unit

Correct Answer: A

Explanation:

Each step retains (8/9) of the previous area. Thus, area after Step 2 is ((8/9)^2 = 64/81) sq. unit.

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Question (4)

QN0029476

A Koch Snowflake starts with an equilateral triangle having 3 sides. How many sides does it have after Step 3?

(A) 48
(B) 64
(C) 192
(D) 81

Correct Answer: C

Explanation:

The number of sides becomes four times at each step. Hence, number of sides at Step 3 is (3 \times 4^3 = 192).

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Question (5)

QN0029477

A cube is viewed directly from the top. Which shape will its profile definitely have?

(A) Circle
(B) Square
(C) Triangle
(D) Pentagon

Correct Answer: B

Explanation:

When viewed from the top, a cube shows one of its square faces.

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Question (6)

QN0029478

Which solid can give both a circular profile and a rectangular profile from different viewpoints?

(A) Sphere
(B) Cylinder
(C) Cube
(D) Pyramid

Correct Answer: B

Explanation:

A cylinder gives a circular top view and a rectangular side view.

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Question (7)

QN0029479

A prism has an octagonal base. How many vertices does it have?

(A) 8
(B) 10
(C) 16
(D) 18

Correct Answer: C

Explanation:

An (n)-sided prism has (2n) vertices. For an octagonal prism, vertices (= 2 \times 8 = 16).

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Question (8)

QN0029480

A prism has 24 vertices. The base polygon has how many sides?

(A) 10
(B) 12
(C) 24
(D) 48

Correct Answer: B

Explanation:

Since a prism has (2n) vertices, (2n = 24). Therefore, (n = 12).

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Question (9)

QN0029481

A pyramid has a hexagonal base. How many faces does it have?

(A) 6
(B) 7
(C) 8
(D) 12

Correct Answer: B

Explanation:

A pyramid with an (n)-sided base has (n+1) faces. Thus, faces (= 6+1 = 7).

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Question (10)

QN0029482

A pyramid has 9 faces in total. What is the shape of its base?

(A) Hexagon
(B) Heptagon
(C) Octagon
(D) Nonagon

Correct Answer: C

Explanation:

If total faces are 9, then (n+1 = 9). Hence, (n = 8), so the base is an octagon.

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Question (1)

In the Sierpinski Carpet, if Step 3 contains (8^3) remaining squares, how many squares remain in Step 4?

Explanation:

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Question (2)

A Sierpinski Triangle at Step 2 has 9 remaining triangles. How many triangles will remain at Step 4?

Explanation:

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Question (3)

The area of the initial square in a Sierpinski Carpet is 1 sq. unit. What is the area remaining after Step 2?

Explanation:

Link:

Question (4)

A Koch Snowflake starts with an equilateral triangle having 3 sides. How many sides does it have after Step 3?

Explanation:

Link:

Question (5)

A cube is viewed directly from the top. Which shape will its profile definitely have?

Explanation:

Link:

Question (6)

Which solid can give both a circular profile and a rectangular profile from different viewpoints?

Explanation:

Link:

Question (7)

A prism has an octagonal base. How many vertices does it have?

Explanation:

Link:

Question (8)

A prism has 24 vertices. The base polygon has how many sides?

Explanation:

Link:

Question (9)

A pyramid has a hexagonal base. How many faces does it have?

Explanation:

Link:

Question (10)

A pyramid has 9 faces in total. What is the shape of its base?

Explanation:

Link:

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