10 Question MCQ (including Assertion)

Question 1 of 10

Find \(\sqrt{7056}\).

A 86 B 84 C 74 D 82

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Question 2 of 10

Assertion (A): 121 has an odd number of positive factors.
Reason (R): The product of two perfect squares is a perfect square.

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.

Select one option. Answers are shown after the test.

Question 3 of 10

Assertion (A): The smallest natural number that must multiply 245 to make a perfect square is 5.
Reason (R): In a perfect square, every prime factor has an even exponent.

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.

Select one option. Answers are shown after the test.

Question 4 of 10

Two square parks have consecutive whole-number side lengths. Their areas differ by \(85\text{ m}^2\). What is the larger side length?

A 42 m B 44 m C 43 m D 41 m

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Question 5 of 10

A square courtyard has side 25 m. A uniform border 3 m wide runs inside it. How many square metres does the border cover?

A 361 m² B 264 m² C 150 m² D 225 m²

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Question 6 of 10

For a natural number \(n\), the difference \(n^2-(n-1)^2\) is 57. Find \(n\).

A 29 B 28 C 30 D 57

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Question 7 of 10

Which two decompositions show that 4104 is a taxicab number?

A \(2^3+15^3\) and \(9^3+16^3\) B \(2^3+16^3\) and \(9^3+15^3\) C \(1^3+16^3\) and \(8^3+15^3\) D \(4^3+16^3\) and \(10^3+14^3\)

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Question 8 of 10

Assertion (A): It is not true that a negative integer can have a negative perfect cube.
Reason (R): The smallest natural number that must multiply 150 to make a perfect square is 6.

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.

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Question 9 of 10

In the 1-to-200 locker experiment, only lockers with square numbers remain open. How many lockers remain open?

A 15 B 20 C 14 D 13

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Question 10 of 10

Find \(\sqrt[3]{10648}\).

A 18 B 21 C 24 D 22

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10 Question MCQ (including Assertion)