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Question (1)

QN0030828

What is meant by tiling?

(A) Covering a region with circles only
(B) Covering a region using shapes without gaps or overlaps
(C) Drawing repeated patterns using colours only
(D) Dividing a figure into equal parts

Correct Answer: B

Explanation:

Tiling means covering a region completely without leaving gaps or overlaps.

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Question (2)

QN0030829

Which of the following conditions must always be satisfied in a tiling?

(A) Shapes must overlap slightly
(B) Gaps between shapes are allowed
(C) There should be neither gaps nor overlaps
(D) Only regular polygons can be used

Correct Answer: C

Explanation:

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Question (3)

QN0030830

Which of the following puzzles uses seven pieces obtained by dividing a square?

(A) Sudoku
(B) Tangram
(C) Chess
(D) Rubik's Cube

Correct Answer: B

Explanation:

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Question (4)

QN0030831

A 4 × 6 grid contains how many unit squares?

(A) 10
(B) 20
(C) 24
(D) 28

Correct Answer: C

Explanation:

Total unit squares = 4 × 6 = 24.

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Question (5)

QN0030832

How many 2 × 1 tiles are required to completely tile a 4 × 6 grid?

(A) 10
(B) 12
(C) 14
(D) 24

Correct Answer: B

Explanation:

Total unit squares = 24. Each tile covers 2 unit squares, so 24 ÷ 2 = 12 tiles.

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Question (6)

QN0030833

Can a 4 × 7 grid be tiled completely using 2 × 1 tiles?

(A) Yes
(B) No
(C) Only if diagonal placement is allowed
(D) Only with square tiles

Correct Answer: A

Explanation:

A 4 × 7 grid has 28 unit squares, which is an even number.

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Question (7)

QN0030834

A 5 × 7 grid has how many unit squares?

(A) 30
(B) 32
(C) 35
(D) 40

Correct Answer: C

Explanation:

Total unit squares = 5 × 7 = 35.

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Question (8)

QN0030835

Why cannot a 5 × 7 grid be completely tiled using 2 × 1 tiles?

(A) The grid is too large
(B) The number of unit squares is odd
(C) The tiles are too small
(D) Rotation is not allowed

Correct Answer: B

Explanation:

Since there are 35 unit squares, an odd number, complete tiling is impossible.

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Question (9)

QN0030836

An m × n grid can always be tiled using 2 × 1 tiles if

(A) both m and n are odd
(B) at least one of m or n is even
(C) m = n only
(D) m is a prime number

Correct Answer: B

Explanation:

If one dimension is even, the total number of unit squares is even and a complete tiling is possible.

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Question (10)

QN0030837

Which arrangement can always tile a grid having an even number of rows?

(A) Vertical placement of all 2 × 1 tiles
(B) Diagonal placement only
(C) Circular arrangement
(D) Random placement

Correct Answer: A

Explanation:

Each column can be completely covered using vertical tiles.

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Question (1)

What is meant by tiling?

Explanation:

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Question (2)

Which of the following conditions must always be satisfied in a tiling?

Explanation:

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Question (3)

Which of the following puzzles uses seven pieces obtained by dividing a square?

Explanation:

Link:

Question (4)

A 4 × 6 grid contains how many unit squares?

Explanation:

Link:

Question (5)

How many 2 × 1 tiles are required to completely tile a 4 × 6 grid?

Explanation:

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Question (6)

Can a 4 × 7 grid be tiled completely using 2 × 1 tiles?

Explanation:

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Question (7)

A 5 × 7 grid has how many unit squares?

Explanation:

Link:

Question (8)

Why cannot a 5 × 7 grid be completely tiled using 2 × 1 tiles?

Explanation:

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Question (9)

An m × n grid can always be tiled using 2 × 1 tiles if

Explanation:

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Question (10)

Which arrangement can always tile a grid having an even number of rows?

Explanation:

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