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Question (11)

QN0029283

The difference between the squares of 31 and 30 is:

(A) 59
(B) 60
(C) 61
(D) 62

Correct Answer: C

Explanation:

31² − 30² = (31 − 30)(31 + 30) = 61.

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Question (12)

QN0029284

The smallest perfect square divisible by both 12 and 18 is:

(A) 36
(B) 72
(C) 144
(D) 324

Correct Answer: C

Explanation:

144 is divisible by both 12 and 18 and is a perfect square.

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Question (13)

QN0029285

A number has exactly one unpaired factor. The number must be:

(A) Prime
(B) Composite but not a square
(C) A perfect square
(D) Even

Correct Answer: C

Explanation:

Only perfect squares have one unpaired factor and therefore an odd number of factors.

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Question (14)

QN0029286

The least number that must be multiplied by 500 to make it a perfect cube is:

(A) 2
(B) 4
(C) 5
(D) 20

Correct Answer: A

Explanation:

500 = 2² × 5³. Multiply by 2 to get 2³ × 5³ = 1000 = 10³.

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Question (15)

QN0029287

Which of the following statements is true?

(A) Every perfect square is a perfect cube.
(B) Every perfect cube is a perfect square.
(C) Every perfect square has an odd number of factors.
(D) Every perfect cube has an even number of factors.

Correct Answer: C

Explanation:

Only perfect squares have an odd number of factors.

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Question (16)

QN0029288

Which of the following is the best estimate of √500?

(A) 20
(B) 21
(C) 22
(D) 23

Correct Answer: C

Explanation:

22² = 484 and 23² = 529. Since 500 is closer to 484, √500 ≈ 22.

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Question (17)

QN0029289

The sum of the first 10 odd natural numbers is:

(A) 90
(B) 99
(C) 100
(D) 110

Correct Answer: C

Explanation:

The sum of the first n odd numbers is n². Therefore, 10² = 100.

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Question (18)

QN0029290

If the edge of a cube is doubled, its volume becomes:

(A) Double
(B) Four times
(C) Six times
(D) Eight times

Correct Answer: D

Explanation:

Volume is proportional to the cube of the edge. Doubling the edge increases the volume by 2³ = 8 times.

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Question (19)

QN0029291

The smallest natural number that should be added to 990 to make it a perfect square is:

(A) 30
(B) 32
(C) 34
(D) 36

Correct Answer: C

Explanation:

The next perfect square after 990 is 32² = 1024. Hence, 1024 − 990 = 34.

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Question (20)

QN0029292

A number has prime factorisation 2³ × 3³ × 5³. Its cube root is:

(A) 30
(B) 60
(C) 90
(D) 120

Correct Answer: A

Explanation:

Cube root = 2 × 3 × 5 = 30.

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Question (11)

The difference between the squares of 31 and 30 is:

Explanation:

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Question (12)

The smallest perfect square divisible by both 12 and 18 is:

Explanation:

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Question (13)

A number has exactly one unpaired factor. The number must be:

Explanation:

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Question (14)

The least number that must be multiplied by 500 to make it a perfect cube is:

Explanation:

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Question (15)

Which of the following statements is true?

Explanation:

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Question (16)

Which of the following is the best estimate of √500?

Explanation:

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Question (17)

The sum of the first 10 odd natural numbers is:

Explanation:

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Question (18)

If the edge of a cube is doubled, its volume becomes:

Explanation:

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Question (19)

The smallest natural number that should be added to 990 to make it a perfect square is:

Explanation:

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Question (20)

A number has prime factorisation 2³ × 3³ × 5³. Its cube root is:

Explanation:

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