1. The sum of the interior angles of a triangle is:
a) 90°
b) 180°
c) 270°
d) 360°
Answer: b) 180°
Explanation: In Euclidean geometry, the interior angles of a triangle always add up to 180°.
2. The sum of exterior angles of any polygon is always:
a) 90°
b) 180°
c) 270°
d) 360°
Answer: d) 360°
Explanation: No matter how many sides, the sum of all exterior angles = 360°.
3. In a right triangle, the side opposite the right angle is called:
a) Base
b) Perpendicular
c) Hypotenuse
d) Median
Answer: c) Hypotenuse
Explanation: Hypotenuse is always the longest side in a right triangle.
4. A polygon with 8 sides is called:
a) Heptagon
b) Octagon
c) Nonagon
d) Decagon
Answer: b) Octagon
Explanation: 8-sided polygon = Octagon.
5. The sum of the interior angles of a quadrilateral is:
a) 180°
b) 270°
c) 360°
d) 540°
Answer: c) 360°
Explanation: For an n-sided polygon, sum = (n−2)×180°. For n=4 → 360°.
6. The number of diagonals in a hexagon is:
a) 6
b) 7
c) 9
d) 12
Answer: d) 9
Explanation: Formula: 
. For n=6, 
.
7. If each interior angle of a regular polygon is 120°, the polygon is:
a) Pentagon
b) Hexagon
c) Octagon
d) Decagon
Answer: b) Hexagon
Explanation: Interior angle = 
. Solve for n = 6.
8. The area of an equilateral triangle with side ‘a’ is:
a) 
b) 
c)
d) 
Answer: c)
Explanation: Formula: .
9. The angle in a semicircle is always:
a) 30°
b) 45°
c) 60°
d) 90°
Answer: d) 90°
Explanation: Angle subtended by diameter at circumference is a right angle.
10. In a parallelogram, opposite sides are:
a) Unequal
b) Equal and parallel
c) Equal but not parallel
d) Perpendicular
Answer: b) Equal and parallel
Explanation: This is the defining property of a parallelogram.
11. The diagonals of a rhombus:
a) Are equal
b) Bisect each other at right angles
c) Are perpendicular bisectors
d) Both b and c
Answer: d) Both b and c
Explanation: Diagonals of a rhombus bisect each other at right angles.
12. If the radius of a circle is r, its area is:
a) 
b) 
c) 
d) 
Answer: b)
Explanation: Formula of circle’s area.
13. The perimeter of a rectangle with length l and breadth b is:
a) l+b
b) 2(l+b)
c) lb
d) 2(lb)
Answer: b) 2(l+b)
Explanation: Perimeter = 2×(length+breadth).
14.The area of a square of diagonal d is:
a) 
b) 
c)
d) 
Answer: b)
Explanation: Side = . Area = side² = 
.
15. The volume of a cube of side a is:
a) a
b) a²
c) a³
d) 6a²
Answer: c) a³
Explanation: Volume of cube = side³.
16. The surface area of a sphere of radius r is:
a)
b)
c)
d)
Answer: c)
Explanation: Formula = 4πr².
17. The number of faces in a cube is:
a) 4
b) 6
c) 8
d) 12
Answer: b) 6
Explanation: Cube has 6 equal square faces.
18. The line joining the center of a circle to a point on the circle is:
a) Diameter
b) Radius
c) Chord
d) Secant
Answer: b) Radius
Explanation: Distance from center to boundary = radius.
19. The longest chord of a circle is:
a) Radius
b) Diameter
c) Tangent
d) Secant
Answer: b) Diameter
Explanation: Diameter = 2r, longest chord.
20. If two sides of a triangle are equal, it is called:
a) Scalene
b) Isosceles
c) Equilateral
d) Right triangle
Answer: b) Isosceles
Explanation: Isosceles has 2 equal sides.
21. If all sides and all angles are equal, the triangle is:
a) Right
b) Scalene
c) Equilateral
d) Isosceles
Answer: c) Equilateral
Explanation: All angles 60° and all sides equal.
22. A quadrilateral with one pair of parallel sides is called:
a) Rhombus
b) Parallelogram
c) Trapezium
d) Kite
Answer: c) Trapezium
Explanation: Only one pair parallel = trapezium.
23. The height of an equilateral triangle of side a is:
a) a
b) 
c) 
d) 
Answer: c)
Explanation: Height formula = √3/2 × side.
24. If the circumference of a circle is 2πr, its diameter is:
a) r
b) 2r
c) πr
d) r/2
Answer: b) 2r
Explanation: Diameter = 2r.
25. The sum of all angles in a pentagon is:
a) 360°
b) 540°
c) 720°
d) 900°
Answer: b) 540°
Explanation: (n−2)×180 = (5−2)×180 = 540°.
26. The sum of the angles of a hexagon is:
a) 540°
b) 600°
c) 720°
d) 900°
Answer: c) 720°
Explanation: Formula = (n−2)×180. For n=6 → 4×180 = 720°.
27. The diagonal of a square of side 10 cm is:
a) 10 cm
b) 15 cm
c) cm
d) 20 cm
Answer: c) cm
Explanation: Diagonal = side × √2 = 10√2.
28. The number of diagonals in a polygon of 10 sides is:
a) 35
b) 40
c) 45
d) 50
Answer: a) 35
Explanation: Formula = n(n−3)/2. For n=10 → 10×7/2 = 35.
29. In an equilateral triangle, each angle is:
a) 30°
b) 45°
c) 60°
d) 90°
Answer: c) 60°
Explanation: All angles are equal, sum = 180°, each = 60°.
30. The perimeter of a circle is also called:
a) Area
b) Circumference
c) Diameter
d) Sector
Answer: b) Circumference
Explanation: Perimeter of a circle = 2πr, known as circumference.
31. A line segment joining two non-adjacent vertices of a polygon is called:
a) Chord
b) Diagonal
c) Radius
d) Median
Answer: b) Diagonal
Explanation: Non-adjacent vertex joining line = diagonal.
32. A triangle with all unequal sides is:
a) Isosceles
b) Equilateral
c) Scalene
d) Right-angled
Answer: c) Scalene
Explanation: Scalene triangle = no equal sides.
33. The centroid of a triangle divides each median in the ratio:
a) 1:1
b) 1:2
c) 2:1
d) 3:1
Answer: c) 2:1
Explanation: Centroid divides median 2:1 from vertex to midpoint.
34. The point where perpendicular bisectors of a triangle meet is called:
a) Centroid
b) Circumcenter
c) Incenter
d) Orthocenter
Answer: b) Circumcenter
Explanation: Circumcenter is the intersection of perpendicular bisectors.
35. The sum of the angles of an octagon is:
a) 900°
b) 1080°
c) 1200°
d) 1440°
Answer: b) 1080°
Explanation: (n−2)×180 = (8−2)×180 = 1080°.
36. The area of a rectangle with length l and breadth b is:
a) l+b
b) 2(l+b)
c) lb
d) l²+b²
Answer: c) lb
Explanation: Area = length × breadth.
37. The diagonals of a rectangle are:
a) Equal
b) Unequal
c) Perpendicular
d) Parallel
Answer: a) Equal
Explanation: Diagonals of a rectangle are equal in length.
38. The shape of the base of a cone is:
a) Triangle
b) Square
c) Circle
d) Rectangle
Answer: c) Circle
Explanation: Base of a cone is circular.
39. The perimeter of a square of side a is:
a) a²
b) 4a
c) 2a
d) 3a
Answer: b) 4a
Explanation: Perimeter = 4 × side.
40. The volume of a cuboid with length l, breadth b, height h is:
a) l+b+h
b) 2(lb+bh+hl)
c) lbh
d) (l+b+h)²
Answer: c) lbh
Explanation: Volume = l×b×h.
41. The number of vertices in a cube is:
a) 6
b) 8
c) 10
d) 12
Answer: b) 8
Explanation: Cube has 8 corners (vertices).
42. The number of edges in a cube is:
a) 6
b) 8
c) 10
d) 12
Answer: d) 12
Explanation: Cube has 12 edges.
43. The number of faces in a cuboid is:
a) 4
b) 6
c) 8
d) 12
Answer: b) 6
Explanation: A cuboid has 6 rectangular faces.
44. The radius of a circle is half its:
a) Chord
b) Diameter
c) Circumference
d) Area
Answer: b) Diameter
Explanation: Diameter = 2r.
45. The diagonals of a square are:
a) Equal and perpendicular
b) Equal and parallel
c) Unequal and perpendicular
d) Unequal and parallel
Answer: a) Equal and perpendicular
Explanation: Diagonals of a square bisect at right angles.
46. The point where altitudes of a triangle meet is:
a) Centroid
b) Circumcenter
c) Orthocenter
d) Incenter
Answer: c) Orthocenter
Explanation: Intersection of altitudes = orthocenter.
47. The point where angle bisectors of a triangle meet is:
a) Centroid
b) Incenter
c) Orthocenter
d) Circumcenter
Answer: b) Incenter
Explanation: Intersection of angle bisectors = incenter.
48. The perimeter of an equilateral triangle of side a is:
a) a
b) 2a
c) 3a
d) 4a
Answer: c) 3a
Explanation: Perimeter = sum of 3 sides = 3a.
49. The locus of all points equidistant from a fixed point is:
a) Line
b) Circle
c) Triangle
d) Parabola
Answer: b) Circle
Explanation: Circle is defined as set of points equidistant from center.
50. The radius of a sphere is doubled. Its volume becomes:
a) 2 times
b) 4 times
c) 6 times
d) 8 times
Answer: d) 8 times
Explanation: Volume ∝ r³. Doubling r → volume increases 2³ = 8 times.
51. A line which touches a circle at only one point is called:
a) Chord
b) Tangent
c) Secant
d) Diameter
Answer: b) Tangent
Explanation: A tangent touches the circle at exactly one point.
52. The distance around a rectangle is called its:
a) Area
b) Diagonal
c) Perimeter
d) Volume
Answer: c) Perimeter
Explanation: Perimeter = 2(l+b).
53. The number of sides in a decagon is:
a) 8
b) 9
c) 10
d) 12
Answer: c) 10
Explanation: A decagon has 10 sides.
54. The sum of the angles of a heptagon is:
a) 720°
b) 900°
c) 1080°
d) 1260°
Answer: d) 900° → Correction: Actually 900° belongs to pentagon. Correct is: (n−2)×180 = (7−2)×180 = 900°. So answer is b) 900°.
55. The volume of a sphere of radius r is:
a) 
b)
c)
d)
Answer: a)
Explanation: Formula for volume of sphere.
56. The area of a parallelogram with base b and height h is:
a) 2bh
b) bh
c) b+h
d) b²+h²
Answer: b) bh
Explanation: Area = base × height.
57. The diagonals of a parallelogram:
a) Are equal
b) Bisect each other
c) Are perpendicular
d) Are parallel
Answer: b) Bisect each other
Explanation: They bisect but are not necessarily equal.
58. In a trapezium, the line joining the midpoints of the non-parallel sides is:
a) Equal to the parallel sides
b) Parallel to the bases
c) Perpendicular to the bases
d) None
Answer: b) Parallel to the bases
Explanation: Mid-segment theorem of trapezium.
59. The sum of the angles in a quadrilateral is:
a) 90°
b) 180°
c) 270°
d) 360°
Answer: d) 360°
Explanation: (n−2)×180 = (4−2)×180 = 360°.
60. The point where medians of a triangle meet is called:
a) Centroid
b) Circumcenter
c) Incenter
d) Orthocenter
Answer: a) Centroid
Explanation: Medians intersect at centroid.
61. A regular polygon with each interior angle = 150° has how many sides?
a) 10
b) 12
c) 15
d) 18
Answer: b) 12
Explanation: Interior angle = . Solve → n=12.
62. The diagonal of a cube of side a is:
a) a
b) √2a
c) √3a
d) 2a
Answer: c) √3a
Explanation: Space diagonal = √(a²+a²+a²) = √3a.
63. The surface area of a cube of side a is:
a) 2a²
b) 4a²
c) 6a²
d) 8a²
Answer: c) 6a²
Explanation: Cube has 6 faces, each area = a².
64. A polygon with all sides and angles equal is called:
a) Regular polygon
b) Irregular polygon
c) Concave polygon
d) Convex polygon
Answer: a) Regular polygon
Explanation: Regular = equal sides and angles.
65. The base and height of a triangle are 10 cm and 12 cm. Its area is:
a) 50 cm²
b) 60 cm²
c) 70 cm²
d) 80 cm²
Answer: b) 60 cm²
Explanation: Area = ½ × base × height = ½×10×12 = 60.
66. The perimeter of a semicircle of radius r (without diameter) is:
a) πr
b) πr²
c) πr+2r
d) πr+r
Answer: d) πr+r
Explanation: Length of semicircle = half circumference + radius = πr + r.
67. The three medians of a triangle:
a) Meet at different points
b) Are parallel
c) Are concurrent
d) Are perpendicular
Answer: c) Are concurrent
Explanation: All medians meet at centroid.
68. The length of each side of a regular hexagon inscribed in a circle of radius r is:
a) r
b) 2r
c) √2r
d) √3r
Answer: a) r
Explanation: Side of inscribed hexagon = radius of circle.
69. The sum of the interior angles of a nonagon is:
a) 900°
b) 1080°
c) 1260°
d) 1440°
Answer: c) 1260°
Explanation: (n−2)×180 = (9−2)×180 = 1260°.
70. The diagonals of a kite:
a) Are equal
b) Are perpendicular
c) Bisect each other
d) Are parallel
Answer: b) Are perpendicular
Explanation: Diagonals of a kite intersect at right angles.
71. The exterior angle of a regular decagon is:
a) 30°
b) 36°
c) 45°
d) 60°
Answer: b) 36°
Explanation: Exterior angle = 360°/n = 360/10 = 36°.
72. The radius of a circle is 7 cm. Its circumference is:
a) 22 cm
b) 44 cm
c) 77 cm
d) 154 cm
Answer: c) 44 cm → Correction: Formula 2πr = 2×22/7×7 = 44. So correct is b) 44 cm.
73. The area of a rhombus with diagonals d1 and d2 is:
a) d1×d2
b) ½ d1×d2
c) (d1+d2)/2
d) (d1²+d2²)/2
Answer: b) ½ d1×d2
Explanation: Formula of rhombus area.
74. The lateral surface area of a cylinder of radius r and height h is:
a) 2πrh
b) πr²h
c) 2πr²
d) πrh²
Answer: a) 2πrh
Explanation: Curved surface area = 2πrh.
75. In a right triangle, if base = 6 cm, height = 8 cm, then hypotenuse = ?
a) 8 cm
b) 9 cm
c) 10 cm
d) 12 cm
Answer: c) 10 cm
Explanation: By Pythagoras: √(6²+8²) = √100 = 10.
76 .The radius of a circle is doubled. Its area becomes:
a) 2 times
b) 3 times
c) 4 times
d) 8 times
Answer: c) 4 times
Explanation: Area ∝ r². Doubling r → area increases 2² = 4 times.
77. The sum of exterior angles of a hexagon is:
a) 180°
b) 270°
c) 360°
d) 540°
Answer: c) 360°
Explanation: For any polygon, sum of exterior angles = 360°.
78. The longest diagonal of a cube of side a is:
a) a
b) √2a
c) √3a
d) 2a
Answer: c) √3a
Explanation: Space diagonal = √(a²+a²+a²) = √3a.
79. The total surface area of a cuboid is:
a) 2(lb+bh+hl)
b) lbh
c) 2(l+b+h)
d) (l+b+h)²
Answer: a) 2(lb+bh+hl)
Explanation: Formula for total surface area.
80. The incenter of a triangle is the center of:
a) Circumscribed circle
b) Inscribed circle
c) Median circle
d) None
Answer: b) Inscribed circle
Explanation: Incenter = intersection of angle bisectors → center of incircle.
81. The circumcircle of a triangle passes through:
a) Incenter
b) Orthocenter
c) All three vertices
d) Midpoints
Answer: c) All three vertices
Explanation: Circumcircle is drawn through vertices of triangle.
82. The locus of points equidistant from two fixed points is:
a) Angle bisector
b) Perpendicular bisector of the line joining them
c) Altitude
d) Median
Answer: b) Perpendicular bisector
Explanation: Any point equidistant from 2 points lies on perpendicular bisector.
83. The sum of interior and exterior angle at a vertex of a polygon is:
a) 90°
b) 120°
c) 150°
d) 180°
Answer: d) 180°
Explanation: Interior + exterior angle = 180°.
84. The volume of a right circular cone of radius r and height h is:
a) πr²h
b) ½πr²h
c) ⅓πr²h
d) 2πrh
Answer: c) ⅓πr²h
Explanation: Formula = (1/3)πr²h.
85. The surface area of a hemisphere of radius r is:
a) 2πr²
b) 3πr²
c) 4πr²
d) πr²
Answer: b) 3πr²
Explanation: CSA = 2πr², base area = πr², total = 3πr².
86. The altitude of an equilateral triangle of side a is:
a) a
b) √3a/2
c) a/2
d) √2a
Answer: b) √3a/2
Explanation: Height = (√3/2)×side.
87. The angle sum of a polygon with 12 sides is:
a) 1620°
b) 1800°
c) 1980°
d) 2160°
Answer: a) 1800°
Explanation: (n−2)×180 = (12−2)×180 = 1800°.
88 .The mid-point of the hypotenuse of a right-angled triangle is:
a) Centroid
b) Incenter
c) Equidistant from all vertices
d) Orthocenter
Answer: c) Equidistant from all vertices
Explanation: Midpoint of hypotenuse is circumcenter of right triangle.
89. The radius of the incircle of a square of side a is:
a) a
b) a/2
c) √2a
d) a/√2
Answer: b) a/2
Explanation: Incircle touches all sides → radius = half side.
90. A diagonal divides a parallelogram into:
a) Two trapeziums
b) Two rectangles
c) Two congruent triangles
d) Two squares
Answer: c) Two congruent triangles
Explanation: Diagonal splits parallelogram into equal triangles.
91. The area of a sector of a circle of radius r and angle θ (in degrees) is:
a)
b)
c)
d)
Answer: b) 
Explanation: Formula for area of a sector.
92. The perpendicular drawn from the center of a circle to a chord:
a) Bisects the chord
b) Doubles the chord
c) Equals radius
d) Is tangent
Answer: a) Bisects the chord
Explanation: Perpendicular from center bisects chord.
93. The number of sides of a polygon whose interior angle is 165° is:
a) 18
b) 20
c) 22
d) 24
Answer: c) 24
Explanation: Interior angle = (n−2)×180/n. Solve for n=24.
94. The volume of a right prism is:
a) Base area × height
b) ½ base area × height
c) ⅓ base area × height
d) None
Answer: a) Base area × height
Explanation: Volume = area of base × height.
95. The radius of a circle is 14 cm. Its area is:
a) 154 cm²
b) 308 cm²
c) 616 cm²
d) 704 cm²
Answer: c) 616 cm²
Explanation: Area = πr² = 22/7 × 14 × 14 = 616.
96. The diagonals of a rectangle are equal and:
a) Parallel
b) Perpendicular
c) Bisect each other
d) None
Answer: c) Bisect each other
Explanation: They are equal and bisect at midpoint.
97. The number of diagonals in a polygon with n sides is:
a) n(n−1)/2
b) n(n−3)/2
c) (n−2)(n−3)/2
d) n²
Answer: b) n(n−3)/2
Explanation: Standard formula for diagonals.
98. The area of a trapezium with parallel sides a, b and height h is:
a) (a+b)h
b) ½(a+b)h
c) (a−b)h
d) ab+h
Answer: b) ½(a+b)h
Explanation: Area = ½ × sum of parallel sides × height.
99. In a circle, equal chords are equidistant from:
a) Diameter
b) Radius
c) Center
d) Circumference
Answer: c) Center
Explanation: Equal chords are at equal distance from the center.
100. The angle in a major segment of a circle is always:
a) Acute
b) Obtuse
c) Right
d) Reflex
Answer: b) Obtuse
Explanation: Angle in a major segment > 90°.