10 Question MCQ (including Assertion)

Question 1 of 10

A triangular logo is enlarged so that every side becomes twice as long. What is the minimum number of congruent copies of the original logo that can exactly cover the enlarged logo?

A \(2\) B \(3\) C \(4\) D \(8\)

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Question 2 of 10

An isosceles triangle has a base of 10 cm and an area of \( 60 \text{ cm}^2 \). What is the length of one of its equal sides?

A 12 cm B 13 cm C 15 cm D 17 cm

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Question 3 of 10

Find the area of a triangle whose side lengths are \(8\text{ cm}\), \(11\text{ cm}\), and \(13\text{ cm}\).

A \(4\sqrt{30}\text{ cm}^2\) B \(8\sqrt{30}\text{ cm}^2\) C \(16\sqrt{15}\text{ cm}^2\) D \(24\sqrt5\text{ cm}^2\)

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Question 4 of 10

Consider all rectangles having perimeter \(40\) units. Which statement is correct?

A The maximum area is \(100\) square units, and the minimum is \(20\) B The maximum area is \(100\) square units, but there is no smallest positive area C The maximum area is \(80\) square units D All such rectangles have equal area

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Question 5 of 10

The ratio of the perimeters of two circles is 5:4. What is the ratio of their areas?

A 5:4 B 25:16 C \( \sqrt{5}:\sqrt{4} \) D 10:8

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Question 6 of 10

Assertion: Two parallelograms having the same pair of adjacent side lengths must have equal areas.
Reason: The area of a parallelogram is the product of a base and its corresponding perpendicular height.

A Both are true, and the reason correctly explains the assertion. B Both are true, but the reason does not correctly explain the assertion. C The assertion is true, but the reason is false. D The assertion is false, but the reason is true.

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Question 7 of 10

Assertion (A):
The exact area of an equilateral triangle of side \( a \) is \( \frac{\sqrt{3}}{4}a^2 \).
Reason (R):
Heron's formula can only be used for scalene triangles and fails for equilateral triangles because all sides are identical.

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 8 of 10

A circular lawn has radius \(14\text{ m}\). A \(60^\circ\) sector is used as a flower bed. What area remains as grass? Use \(\pi=\dfrac{22}{7}\).

A \(\dfrac{308}{3}\text{ m}^2\) B \(\dfrac{770}{3}\text{ m}^2\) C \(\dfrac{1540}{3}\text{ m}^2\) D \(616\text{ m}^2\)

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Question 9 of 10

Assertion: In the same circle, an arc subtending \(120^\circ\) at the centre is twice as long as an arc subtending \(60^\circ\).
Reason: The length of an arc of radius \(r\) and central angle \(\theta\) is \[l=2\pi r\times\frac{\theta}{360^\circ}.\]

A Both are true, and the reason correctly explains the assertion. B Both are true, but the reason does not correctly explain the assertion. C The assertion is true, but the reason is false. D The assertion is false, but the reason is true.

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Question 10 of 10

A circular pond of radius \(7\text{ m}\) lies inside a circular park of radius \(14\text{ m}\). What area of the park lies outside the pond? Use \(\pi=\dfrac{22}{7}\).

A \(154\text{ m}^2\) B \(308\text{ m}^2\) C \(462\text{ m}^2\) D \(616\text{ m}^2\)

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10 Question MCQ (including Assertion)