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Question (11)

QN0020022

If Rn = 8ⁿ, then R₄ is:

(A) 2048
(B) 4096
(C) 1024
(D) 8192

Correct Answer: B

Explanation:

R₄ = 8⁴ = 4096.

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Question (12)

QN0020023

The number of holes in the Sierpinski Carpet at Step 2 is:

(A) 8
(B) 9
(C) 10
(D) 11

Correct Answer: B

Explanation:

H₂ = 1 + 8 = 9.

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Question (13)

QN0020024

The number of holes in the Sierpinski Carpet at Step 3 is:

(A) 64
(B) 72
(C) 73
(D) 81

Correct Answer: C

Explanation:

H₃ = 1 + 8 + 64 = 73.

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Question (14)

QN0020025

Which relation is correct for the Sierpinski Carpet?

(A) Rn+1 = 9Rn
(B) Rn+1 = 8Rn
(C) Rn+1 = 7Rn
(D) Rn+1 = 4Rn

Correct Answer: B

Explanation:

Each remaining square produces 8 new remaining squares.

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Question (15)

QN0020026

In the Sierpinski Triangle, an equilateral triangle is divided into ________ identical equilateral triangles.

(A) 3
(B) 4
(C) 6
(D) 9

Correct Answer: B

Explanation:

Joining the midpoints divides it into 4 equal equilateral triangles.

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Question (16)

QN0020027

During each step of constructing a Sierpinski Triangle, the ________ triangle is removed.

(A) top
(B) corner
(C) central
(D) largest

Correct Answer: C

Explanation:

The central triangle is removed at every step.

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Question (17)

QN0020028

The number of remaining triangles at Step 1 of the Sierpinski Triangle is:

(A) 2
(B) 3
(C) 4
(D) 5

Correct Answer: B

Explanation:

Three corner triangles remain after removing the center.

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Question (18)

QN0020029

The number of remaining triangles at Step 2 of the Sierpinski Triangle is:

(A) 6
(B) 8
(C) 9
(D) 12

Correct Answer: C

Explanation:

3² = 9 triangles remain.

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Question (19)

QN0020030

The number of remaining triangles at Step 3 of the Sierpinski Triangle is:

(A) 18
(B) 27
(C) 36
(D) 81

Correct Answer: B

Explanation:

3³ = 27 triangles remain.

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Question (20)

QN0020031

If the area of the original square in a Sierpinski Carpet is 1 sq. unit, then the area remaining after Step 1 is:

(A) 7/9
(B) 8/9
(C) 1/9
(D) 2/9

Correct Answer: B

Explanation:

One of the 9 equal parts is removed, leaving 8/9 area.

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Question (11)

If Rn = 8ⁿ, then R₄ is:

Explanation:

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Question (12)

The number of holes in the Sierpinski Carpet at Step 2 is:

Explanation:

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Question (13)

The number of holes in the Sierpinski Carpet at Step 3 is:

Explanation:

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Question (14)

Which relation is correct for the Sierpinski Carpet?

Explanation:

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Question (15)

In the Sierpinski Triangle, an equilateral triangle is divided into ________ identical equilateral triangles.

Explanation:

Link:

Question (16)

During each step of constructing a Sierpinski Triangle, the ________ triangle is removed.

Explanation:

Link:

Question (17)

The number of remaining triangles at Step 1 of the Sierpinski Triangle is:

Explanation:

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Question (18)

The number of remaining triangles at Step 2 of the Sierpinski Triangle is:

Explanation:

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Question (19)

The number of remaining triangles at Step 3 of the Sierpinski Triangle is:

Explanation:

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Question (20)

If the area of the original square in a Sierpinski Carpet is 1 sq. unit, then the area remaining after Step 1 is:

Explanation:

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