10 Question MCQ (including Assertion)

Question 1 of 10

An arc of a circle of radius \(6.3\text{ m}\) subtends \(120^\circ\) at the centre. Find its length using \(\pi=\dfrac{22}{7}\).

A \(6.6\text{ m}\) B \(13.2\text{ m}\) C \(19.8\text{ m}\) D \(26.4\text{ m}\)

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Question 2 of 10

Find the area of the quadrant of a circle whose circumference is exactly 44 cm. (Use \( \pi = 22/7 \))

A \( 19.25 \text{ cm}^2 \) B \( 38.5 \text{ cm}^2 \) C \( 77 \text{ cm}^2 \) D \( 154 \text{ cm}^2 \)

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Question 3 of 10

An isosceles triangle has a perimeter of 40 cm, and its two equal sides are 15 cm each. What is its exact area?

A \( 25\sqrt{2} \text{ cm}^2 \) B \( 50\sqrt{2} \text{ cm}^2 \) C \( 75 \text{ cm}^2 \) D \( 100\sqrt{2} \text{ cm}^2 \)

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Question 4 of 10

A circular pizza of radius \(21\text{ cm}\) is divided into three equal slices. What is the area of each slice? Use \(\pi=\dfrac{22}{7}\).

A \(231\text{ cm}^2\) B \(308\text{ cm}^2\) C \(462\text{ cm}^2\) D \(1386\text{ cm}^2\)

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Question 5 of 10

If you use Heron's formula to find the area of an equilateral triangle with side \( a \), what is the resulting simplified expression?

A \( \frac{\sqrt{3}}{2}a^2 \) B \( \frac{\sqrt{3}}{4}a^2 \) C \( \frac{3}{4}a^2 \) D \( a^2\sqrt{3} \)

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Question 6 of 10

Assertion (A):
The perimeter of a circle is always strictly between the perimeters of an inscribed regular polygon and a circumscribed regular polygon.
Reason (R):
A straight-line chord is shorter than the circular arc connecting its endpoints, while tangential straight segments bounding the circle are longer than the arcs they enclose.

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 7 of 10

Semicircles are drawn on all three sides of a right-angled triangle as diameters. Let Area(A) and Area(B) be the areas of the semicircles on the legs, and Area(C) be the area of the semicircle on the hypotenuse. Which relationship holds true?

A Area(A) + Area(B) > Area(C) B Area(A) + Area(B) = Area(C) C Area(A)^2 + Area(B)^2 = Area(C)^2 D Area(C) = Area(A) \times Area(B)

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Question 8 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 9 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 10 of 10

A stadium boundary consists of two straight sections of \(80\text{ m}\) each and two semicircular ends whose common diameter is \(60\text{ m}\). Find the total boundary length. Use \(\pi=\dfrac{22}{7}\).

A \(\dfrac{1320}{7}\text{ m}\) B \(\dfrac{1880}{7}\text{ m}\) C \(\dfrac{2440}{7}\text{ m}\) D \(\dfrac{3560}{7}\text{ m}\)

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10 Question MCQ (including Assertion)