Q.1 The sum of the interior angles of a polygon with 8 sides is:
1080°
900°
720°
1440°
Explanation - Sum of interior angles of a polygon = (n-2)×180° = (8-2)×180° = 6×180° = 1080°.
Correct answer is: 1080°
Q.2 The area of a circle whose radius is 7 cm is:
154 cm²
144 cm²
132 cm²
196 cm²
Explanation - Area of circle = πr² = 3.14×7×7 ≈ 153.86 ≈ 154 cm².
Correct answer is: 154 cm²
Q.3 A triangle has sides 7 cm, 24 cm and 25 cm. What type of triangle is it?
Acute
Right-angled
Obtuse
Equilateral
Explanation - Check using Pythagoras theorem: 7² + 24² = 25² ⇒ 49 + 576 = 625. Hence right-angled.
Correct answer is: Right-angled
Q.4 If a square and a circle have the same perimeter of 40 cm, the side of the square is:
10 cm
8 cm
12 cm
15 cm
Explanation - Perimeter of square = 4×side ⇒ 40 = 4×side ⇒ side = 10 cm.
Correct answer is: 10 cm
Q.5 The diagonal of a rectangle is 13 cm and one side is 5 cm. Find the other side.
12 cm
10 cm
8 cm
9 cm
Explanation - Using Pythagoras theorem: diagonal² = l² + b² ⇒ 13² = 5² + b² ⇒ 169 = 25 + b² ⇒ b²=144 ⇒ b=12 cm.
Correct answer is: 12 cm
Q.6 The area of a triangle with base 10 cm and height 8 cm is:
40 cm²
50 cm²
80 cm²
18 cm²
Explanation - Area = 1/2 × base × height = 1/2 × 10 × 8 = 40 cm².
Correct answer is: 40 cm²
Q.7 The circumference of a circle is 31.4 cm. Find the radius.
5 cm
7 cm
10 cm
6 cm
Explanation - Circumference = 2πr ⇒ 31.4 = 2×3.14×r ⇒ r ≈ 5 cm.
Correct answer is: 5 cm
Q.8 In a rhombus, the diagonals are 12 cm and 16 cm. The area is:
96 cm²
192 cm²
48 cm²
60 cm²
Explanation - Area of rhombus = (1/2)×d1×d2 = 1/2×12×16 = 96 cm².
Correct answer is: 96 cm²
Q.9 The length of each side of a regular hexagon inscribed in a circle of radius 10 cm is:
10 cm
5 cm
15 cm
20 cm
Explanation - In a regular hexagon inscribed in a circle, side = radius = 10 cm.
Correct answer is: 10 cm
Q.10 A sector of a circle has angle 90° and radius 14 cm. Find its area.
154 cm²
154 π cm²
308 cm²
49 cm²
Explanation - Area of sector = (θ/360)×πr² = (90/360)×3.14×14² ≈ 153.86 ≈ 154 cm².
Correct answer is: 154 cm²
Q.11 The sum of exterior angles of a polygon is always:
360°
180°
540°
Varies with sides
Explanation - Sum of exterior angles of any polygon = 360° regardless of number of sides.
Correct answer is: 360°
Q.12 A cylinder has radius 7 cm and height 10 cm. Find its volume.
1540 cm³
1538 cm³
154 cm³
700 cm³
Explanation - Volume = πr²h = 3.14×7²×10 ≈ 1538 cm³.
Correct answer is: 1538 cm³
Q.13 A right circular cone has height 12 cm and base radius 5 cm. Find its volume.
314 cm³
100 cm³
250 cm³
300 cm³
Explanation - Volume = 1/3 × πr²h = 1/3 × 3.14 × 25 × 12 ≈ 314 cm³.
Correct answer is: 314 cm³
Q.14 The side of a square is increased by 20%. The area increases by:
44%
40%
42%
48%
Explanation - Area increase % = (1.2² -1)×100% = (1.44-1)×100 = 44%.
Correct answer is: 44%
Q.15 A cuboid has length 10 cm, breadth 5 cm, and height 8 cm. Its surface area is:
340 cm²
400 cm²
260 cm²
280 cm²
Explanation - Surface area = 2(lb + bh + hl) = 2(50 + 40 + 80) = 2×170 = 340 cm².
Correct answer is: 340 cm²
Q.16 The base angles of an isosceles triangle are each 70°. The vertex angle is:
40°
50°
60°
70°
Explanation - Sum of angles = 180° ⇒ vertex = 180 - 70 - 70 = 40°.
Correct answer is: 40°
Q.17 The distance between the circumcenter and incenter of an equilateral triangle is:
Zero
Depends on side
Half of height
Cannot determine
Explanation - In an equilateral triangle, circumcenter, incenter, centroid, and orthocenter coincide ⇒ distance = 0.
Correct answer is: Zero
Q.18 The diagonal of a cube with side 5 cm is:
5√3 cm
5√2 cm
10 cm
5 cm
Explanation - Space diagonal = a√3 = 5√3 cm.
Correct answer is: 5√3 cm
Q.19 If two circles touch externally and their radii are 4 cm and 9 cm, the distance between their centers is:
13 cm
5 cm
9 cm
4 cm
Explanation - Distance between centers = sum of radii = 4 + 9 = 13 cm.
Correct answer is: 13 cm
Q.20 If the perimeter of a square is 48 cm, its diagonal is:
12√2 cm
24√2 cm
48√2 cm
12 cm
Explanation - Side = 48/4 = 12 cm. Diagonal = side√2 = 12√2 cm.
Correct answer is: 12√2 cm
Q.21 A triangle has sides 8 cm, 15 cm, and 17 cm. Its area is:
60 cm²
50 cm²
56 cm²
64 cm²
Explanation - Right triangle: area = 1/2 × base × height = 1/2 × 8 × 15 = 60 cm².
Correct answer is: 60 cm²
Q.22 A circle is inscribed in a square of side 14 cm. The radius of the circle is:
7 cm
14 cm
10 cm
5 cm
Explanation - Radius of inscribed circle = side/2 = 14/2 = 7 cm.
Correct answer is: 7 cm
Q.23 The perimeter of a rectangle is 50 cm. If length = 15 cm, breadth = ?
10 cm
20 cm
25 cm
12 cm
Explanation - Perimeter = 2(l+b) ⇒ 50 = 2(15+b) ⇒ b=10 cm.
Correct answer is: 10 cm
Q.24 The radius of a circle whose area is 154 cm² is approximately:
7 cm
14 cm
21 cm
10 cm
Explanation - Area = πr² ⇒ 154 = 3.14×r² ⇒ r² ≈ 49 ⇒ r ≈ 7 cm.
Correct answer is: 7 cm
Q.25 The number of diagonals in a polygon of 12 sides is:
54
66
60
72
Explanation - Number of diagonals = n(n-3)/2 = 12×9/2 = 54.
Correct answer is: 54