1. The sum of the angles of a triangle is always:
A) 90°
B) 180°
C) 270°
D) 360°
Answer: B) 180°
Explanation: According to Euclidean geometry, the sum of the interior angles of any triangle is 180°.
2. The sum of all exterior angles of any polygon is:
A) 90°
B) 180°
C) 270°
D) 360°
Answer: D) 360°
Explanation: No matter how many sides a polygon has, the sum of its exterior angles is always 360°.
3. A triangle having two sides equal is called:
A) Scalene
B) Equilateral
C) Isosceles
D) Right-angled
Answer: C) Isosceles
Explanation: In an isosceles triangle, two sides and two angles are equal.
4. In an equilateral triangle, each angle measures:
A) 45°
B) 60°
C) 90°
D) 120°
Answer: B) 60°
Explanation: All three angles in an equilateral triangle are equal and add up to 180°, hence each = 60°.
5. The area of a rectangle is given by:
A) 2(l + b)
B) l × b
C) l² + b²
D) ½ × l × b
Answer: B) l × b
Explanation: Area = length × breadth for a rectangle.
6. The perimeter of a square is 40 cm. Find its side.
A) 8 cm
B) 10 cm
C) 12 cm
D) 14 cm
Answer: B) 10 cm
Explanation: Perimeter = 4 × side → 40 = 4 × side → side = 10 cm.
7. The area of a circle is πr². If radius = 7 cm, area = ?
A) 154 cm²
B) 44 cm²
C) 77 cm²
D) 308 cm²
Answer: A) 154 cm²
Explanation: Area = 22/7 × 7 × 7 = 154 cm².
8. The number of diagonals in a pentagon is:
A) 5
B) 6
C) 8
D) 10
Answer: B) 5
Explanation: Formula for diagonals = n(n−3)/2 = 5×2/2 = 5.
9. The radius of a circle is doubled. Its area becomes:
A) Double
B) Triple
C) Four times
D) Half
Answer: C) Four times
Explanation: Area ∝ r² → (2r)² = 4r².
10. The sum of all angles of a quadrilateral is:
A) 90°
B) 180°
C) 270°
D) 360°
Answer: D) 360°
Explanation: A quadrilateral can be divided into two triangles → 2×180° = 360°.
11. In a right-angled triangle, the side opposite the right angle is called:
A) Base
B) Altitude
C) Hypotenuse
D) Median
Answer: C) Hypotenuse
Explanation: The longest side opposite to the right angle is called the hypotenuse.
12. Pythagoras Theorem is applicable only to:
A) Acute-angled triangle
B) Obtuse-angled triangle
C) Right-angled triangle
D) Equilateral triangle
Answer: C) Right-angled triangle
Explanation: For a right triangle, hypotenuse² = base² + height².
13. The area of a triangle = ½ × base × height. If base = 10 cm, height = 8 cm, area = ?
A) 80 cm²
B) 40 cm²
C) 60 cm²
D) 48 cm²
Answer: B) 40 cm²
Explanation: ½ × 10 × 8 = 40 cm².
14. The sum of angles in a hexagon = ?
A) 540°
B) 720°
C) 900°
D) 1080°
Answer: B) 720°
Explanation: Sum = (n−2)×180 = (6−2)×180 = 720°.
15. A circle is a collection of all points which are ______ from a fixed point.
A) Equidistant
B) Variable
C) Unequal
D) Constant
Answer: A) Equidistant
Explanation: The fixed point is the centre; all points on circle are equidistant from it.
16. The number of sides of a regular polygon whose each interior angle is 120° is:
A) 5
B) 6
C) 8
D) 9
Answer: B) 6
Explanation: (n−2)×180/n = 120 → n = 6.
17. If all sides of a triangle are different, it is called:
A) Scalene
B) Isosceles
C) Equilateral
D) Right-angled
Answer: A) Scalene
Explanation: No equal sides → Scalene.
18. The longest chord in a circle is:
A) Diameter
B) Radius
C) Tangent
D) Arc
Answer: A) Diameter
Explanation: Diameter passes through the centre; longest chord.
19. The perimeter of an equilateral triangle of side 6 cm = ?
A) 12 cm
B) 18 cm
C) 24 cm
D) 36 cm
Answer: B) 18 cm
Explanation: 3 × side = 18 cm.
20. The distance around a circle is called:
A) Radius
B) Diameter
C) Circumference
D) Chord
Answer: C) Circumference
Explanation: Circumference = 2πr.
21. The area of a square is 64 cm². Find its side.
A) 4 cm
B) 6 cm
C) 8 cm
D) 10 cm
Answer: C) 8 cm
Explanation: Area = side² → side = √64 = 8 cm.
22. The perimeter of an equilateral triangle is 45 cm. Find each side.
A) 10 cm
B) 12 cm
C) 15 cm
D) 18 cm
Answer: C) 15 cm
Explanation: Perimeter = 3 × side → side = 45 ÷ 3 = 15 cm.
23. The diagonals of a rectangle are always:
A) Equal and bisect each other
B) Unequal
C) Perpendicular
D) Equal but do not bisect
Answer: A) Equal and bisect each other
Explanation: In a rectangle, both diagonals are equal in length and bisect each other.
24. The diagonals of a rhombus are:
A) Equal
B) Perpendicular and bisect each other
C) Unequal and parallel
D) None
Answer: B) Perpendicular and bisect each other
Explanation: Rhombus has diagonals that bisect at 90°.
25. The number of sides of a polygon having 9 diagonals is:
A) 5
B) 6
C) 7
D) 8
Answer: A) 5
Explanation: n(n−3)/2 = 9 → n² − 3n − 18 = 0 → n = 6 (wrong roots check),
Actually for n=5, diagonals = 5×2/2=5; for n=6, diagonals=9 ✅.
So Answer: B) 6 (correction).
26. The sum of interior angles of an octagon = ?
A) 900°
B) 1080°
C) 1260°
D) 1440°
Answer: B) 1080°
Explanation: Sum = (n−2)×180 = (8−2)×180 = 1080°.
27. The total number of faces in a cube is:
A) 4
B) 5
C) 6
D) 8
Answer: C) 6
Explanation: A cube has 6 equal square faces.
28. The total number of edges in a cuboid is:
A) 8
B) 10
C) 12
D) 16
Answer: C) 12
Explanation: A cuboid has 12 edges, 8 vertices, and 6 faces.
29. Volume of a cube of side ‘a’ = ?
A) a²
B) 2a³
C) 3a²
D) a³
Answer: D) a³
Explanation: Volume = side × side × side = a³.
30. Area of a parallelogram = ?
A) base × height
B) ½ × base × height
C) 2 × base × height
D) side × side
Answer: A) base × height
Explanation: Area of a parallelogram is the product of its base and the perpendicular height.
31. A line that touches a circle at only one point is called:
A) Chord
B) Secant
C) Tangent
D) Diameter
Answer: C) Tangent
Explanation: Tangent touches the circle at exactly one point.
32. The number of right angles in a rectangle is:
A) 1
B) 2
C) 3
D) 4
Answer: D) 4
Explanation: Each corner of a rectangle forms a 90° angle.
33. The radius of a circle is 14 cm. Find its circumference.
A) 44 cm
B) 88 cm
C) 154 cm
D) 176 cm
Answer: D) 176 cm
Explanation: Circumference = 2πr = 2 × 22/7 × 14 = 88 × 2 = 176 cm.
34. The diagonals of a square are:
A) Equal
B) Perpendicular
C) Bisect each other
D) All of the above
Answer: D) All of the above
Explanation: In a square, diagonals are equal, perpendicular, and bisect each other.
35. A triangle with one angle greater than 90° is called:
A) Acute-angled
B) Right-angled
C) Obtuse-angled
D) Equilateral
Answer: C) Obtuse-angled
Explanation: A triangle having one obtuse (>90°) angle is obtuse-angled.
36. If two angles of a triangle are 70° and 50°, the third angle = ?
A) 50°
B) 60°
C) 70°
D) 80°
Answer: D) 60°
Explanation: Sum = 180° → 180 − (70 + 50) = 60°.
37. The ratio of circumference to diameter of any circle is:
A) 2
B) 3
C) π
D) ½
Answer: C) π
Explanation: Circumference / Diameter = π ≈ 3.1416.
38. If each side of a square is doubled, its area becomes:
A) Double
B) Triple
C) Four times
D) Eight times
Answer: C) Four times
Explanation: Area ∝ side² → (2a)² = 4a².
39. The height of an equilateral triangle of side ‘a’ is:
A) a/2
B) a√3/2
C) a√2/2
D) a√5/2
Answer: B) a√3/2
Explanation: Height (h) = √(a² − (a/2)²) = a√3/2.
40. The sum of exterior and interior angle of a polygon is always:
A) 90°
B) 120°
C) 180°
D) 360°
Answer: C) 180°
Explanation: Each interior and its corresponding exterior angle form a linear pair (sum = 180°).
41. The point where the three medians of a triangle meet is called:
A) Orthocentre
B) Circumcentre
C) Centroid
D) Incentre
Answer: C) Centroid
Explanation: The centroid divides each median in the ratio 2:1 from the vertex.
42. The perpendicular drawn from the vertex of a triangle to the opposite side is called:
A) Median
B) Altitude
C) Bisector
D) Tangent
Answer: B) Altitude
Explanation: Altitude is the perpendicular distance from a vertex to the opposite side (base).
43. The line segment joining the midpoints of two sides of a triangle is called:
A) Median
B) Mid-segment
C) Altitude
D) Tangent
Answer: B) Mid-segment
Explanation: Mid-segment joins midpoints of two sides and is parallel to the third side.
44. The sum of three medians divides the triangle into ______ equal parts of equal area.
A) 2
B) 3
C) 4
D) 6
Answer: D) 6
Explanation: The three medians divide a triangle into six smaller triangles of equal area.
45. In a right triangle, if base = 9 cm and height = 12 cm, then hypotenuse = ?
A) 13 cm
B) 14 cm
C) 15 cm
D) 16 cm
Answer: A) 15 cm
Explanation: By Pythagoras theorem, √(9² + 12²) = √(81 + 144) = √225 = 15 cm.
46. The angle in a semicircle is always:
A) 30°
B) 45°
C) 60°
D) 90°
Answer: D) 90°
Explanation: The angle subtended by a semicircle at the circumference is always a right angle.
47. The perpendicular bisector of a chord passes through:
A) Centre of circle
B) Radius
C) Diameter
D) Tangent
Answer: A) Centre of circle
Explanation: The perpendicular drawn from the centre to a chord bisects it.
48. A line which divides an angle into two equal parts is called:
A) Median
B) Angle bisector
C) Altitude
D) Tangent
Answer: B) Angle bisector
Explanation: Angle bisector divides an angle into two equal halves.
49. The sum of all angles of a pentagon is:
A) 360°
B) 540°
C) 720°
D) 900°
Answer: B) 540°
Explanation: Sum = (n−2)×180 = (5−2)×180 = 540°.
50. In a parallelogram, opposite angles are:
A) Equal
B) Complementary
C) Supplementary
D) None
Answer: A) Equal
Explanation: Opposite angles of a parallelogram are always equal.
51. In a parallelogram, adjacent angles are:
A) Equal
B) Supplementary
C) Complementary
D) None
Answer: B) Supplementary
Explanation: Adjacent angles add up to 180°.
52. The diagonals of a rectangle are equal and ______ each other.
A) Perpendicular
B) Parallel
C) Bisect
D) Unequal
Answer: C) Bisect
Explanation: They bisect each other but are not perpendicular unless it is a square.
53. A trapezium has:
A) One pair of parallel sides
B) Two pairs of parallel sides
C) No parallel sides
D) Three equal sides
Answer: A) One pair of parallel sides
Explanation: Trapezium has exactly one pair of opposite sides parallel.
54. The area of a trapezium = ?
A) ½ × (sum of parallel sides) × height
B) base × height
C) side × height
D) ½ × base × height
Answer: A) ½ × (sum of parallel sides) × height
Explanation: Area = ½ × (a + b) × h where a and b are parallel sides.
55. A line having no common point with a circle is called:
A) Tangent
B) Secant
C) Chord
D) External line
Answer: D) External line
Explanation: A line not intersecting the circle at all is an external line.
56. The region enclosed by a circle is called:
A) Arc
B) Sector
C) Segment
D) Disk
Answer: D) Disk
Explanation: The whole area enclosed by a circle is called a circular region or disk.
57. A diameter divides a circle into how many equal parts?
A) 1
B) 2
C) 3
D) 4
Answer: B) 2
Explanation: Diameter divides a circle into two equal semicircles.
58. The total surface area of a cube of side ‘a’ = ?
A) 2a²
B) 4a²
C) 6a²
D) 8a²
Answer: C) 6a²
Explanation: A cube has 6 faces; each area = a² → total = 6a².
59. The volume of a cuboid = ?
A) l × b × h
B) 2(l + b + h)
C) l × b × 2h
D) l² + b² + h²
Answer: A) l × b × h
Explanation: Volume = product of length, breadth, and height.
60. The perimeter of a rectangle is 48 cm. If length = 14 cm, breadth = ?
A) 8 cm
B) 10 cm
C) 12 cm
D) 14 cm
Answer: A) 10 cm
Explanation: Perimeter = 2(l + b) → 48 = 2(14 + b) → 24 = 14 + b → b = 10 cm.
61. If two parallel lines are cut by a transversal, then alternate interior angles are:
A) Equal
B) Complementary
C) Supplementary
D) None
Answer: A) Equal
Explanation: When lines are parallel, corresponding and alternate interior angles are equal.
62. Two triangles are similar if:
A) All three sides are equal
B) Two angles of one are equal to two angles of another
C) Only one angle is equal
D) Their perimeters are equal
Answer: B) Two angles of one are equal to two angles of another
Explanation: AA (angle–angle) criterion proves triangle similarity.
63. In △ABC, if AB = AC, then ∠B = ∠C. This statement is:
A) True
B) False
C) True only for right triangles
D) Cannot say
Answer: A) True
Explanation: In an isosceles triangle, angles opposite equal sides are equal.
64. The measure of an interior angle of a regular 12-gon (12 sides) is:
A) 150°
B) 120°
C) 135°
D) 160°
Answer: C) 150°
Explanation: Interior angle = (n−2)×180/n = 10×180/12 = 1800/12 = 150°.
65. The area of a triangle with base 20 cm and altitude 9 cm is:
A) 90 cm²
B) 100 cm²
C) 180 cm²
D) 45 cm²
Answer: A) 90 cm²
Explanation: Area = ½ × base × height = 0.5 × 20 × 9 = 10 × 9 = 90 cm².
66. If two triangles are congruent, then:
A) Corresponding angles are equal and corresponding sides are proportional
B) Corresponding sides are equal and corresponding angles are equal
C) Only areas are equal
D) Only perimeters are equal
Answer: B) Corresponding sides are equal and corresponding angles are equal
Explanation: Congruence means exact equality of shape and size (SSS, SAS, ASA, RHS, etc.).
67. The length of the diagonal of a square whose area is 50 cm² is:
A) 5√2 cm
B) 10 cm
C) 5 cm
D) 25 cm
Answer: A) 5√2 cm
Explanation: Side = √area = √50 = 5√2; diagonal = side × √2 = 5√2 × √2 = 5×2 = 10.
Oops — corrected: diagonal = side × √2 = (5√2)×√2 = 5×2 = 10 cm.
So correct final numeric diagonal = 10 cm.
(Final Answer:) B) 10 cm.
68. In a right triangle, the altitude to the hypotenuse divides it into segments of lengths 9 and 16. Then the altitude length = ?
A) 12
B) 6
C) 7.2
D) 1
Answer: C) 12
Explanation: For right triangle with hypotenuse segments p and q, altitude h = √(p·q). Here √(9×16)=√144=12.
(So correct answer: A) 12 — option list corrected.)
(Final Answer:) A) 12.
69. The locus of points equidistant from two given points is:
A) A circle
B) The perpendicular bisector of the line segment joining them
C) A parabola
D) An ellipse
Answer: B) The perpendicular bisector of the line segment joining them
Explanation: Points equidistant from two fixed points lie on the perpendicular bisector.
70. The internal bisectors of the angles of a triangle meet at a point called:
A) Centroid
B) Circumcentre
C) Incentre
D) Orthocentre
Answer: C) Incentre
Explanation: Incentre is equidistant from all sides; intersection of angle bisectors.
71. The perpendicular distance from the centre of a circle to a chord that is equal to the radius is:
A) 0
B) r/2
C) r√3/2
D) r/√2
Answer: B) r/2
Explanation: Let chord length = r. Half-chord = r/2. In right triangle with hypotenuse r (radius) and half-chord r/2, perpendicular distance d = √(r² − (r/2)²) = √(r² − r²/4) = √(3r²/4) = (r√3)/2.
Wait — that yields (r√3)/2, not r/2. But the question asked: “perpendicular distance from centre to a chord that is equal to the radius” — chord length = r. Then d = √(r² − (r/2)²) = (r√3)/2.
(Final Answer:) C) r√3/2.
72. The measure of the exterior angle of a regular polygon with 9 sides is:
A) 40°
B) 60°
C) 80°
D) 100°
Answer: A) 40°
Explanation: Exterior angle = 360°/n = 360/9 = 40°.
73. If the coordinates of two points are (2, 3) and (8, 11), the distance between them is:
A) 10
B) √(52)
C) √(68)
D) √(100)
Answer: C) √(68)
Explanation: Distance = √[(8−2)² + (11−3)²] = √(6² + 8²) = √(36 + 64) = √100 = 10.
(Final Answer:) A) 10.
74. The side opposite the largest angle in a triangle is:
A) The shortest side
B) The longest side
C) Equal to median
D) None of these
Answer: B) The longest side
Explanation: Larger angle opposite larger side.
75. In triangle ABC, if ∠A = 90°, coordinates A(0,0), B(3,0), C(0,4). Area of triangle = ?
A) 6
B) 12
C) 24
D) 7
Answer: B) 6
Explanation: Area = ½×base×height = ½×3×4 = 6.
(Final Answer:) A) 6. — corrected mapping: option A) 6.
76. The segment joining the midpoints of two sides of a triangle equals:
A) Half the third side and parallel to it
B) Twice the third side
C) Equal to the third side
D) None of these
Answer: A) Half the third side and parallel to it
Explanation: Mid-segment theorem.
77. If a tangent and radius meet at point P on a circle, the angle between them is:
A) 0°
B) 45°
C) 90°
D) 180°
Answer: C) 90°
Explanation: A radius drawn to the point of contact is perpendicular to the tangent.
78. Sum of the squares of the sides of a parallelogram equals:
A) Sum of squares of diagonals
B) Twice the sum of squares of diagonals
C) Half the sum of squares of diagonals
D) Twice the sum of squares of the sides
Answer: D) Twice the sum of squares of the sides
Explanation: Actually, for parallelogram with sides a,b and diagonals p,q: p² + q² = 2(a² + b²). So p² + q² = 2(a² + b²). The question asked sum of squares of sides equals? It’s (a² + b²) = (p² + q²)/2.
(Final statement:) Correct relation is sum of squares of diagonals equals twice sum of squares of sides. So Answer: A) Sum of squares of diagonals (if question intended equality direction).
— To avoid ambiguity, interpret as: p² + q² = 2(a² + b²).
79. The inradius (r) of an equilateral triangle of side a is:
A) a/2
B) a√3/6
C) a√3/3
D) a√2/2
Answer: B) a√3/6
Explanation: Inradius r = (a√3)/6 for equilateral triangle.
80. The circumradius (R) of a right triangle with sides 6, 8, 10 is:
A) 5
B) 6
C) 10
D) 13
Answer: A) 5
Explanation: Circumradius of a right triangle = half the hypotenuse = 10/2 = 5.
81. The centroid divides each median of a triangle in the ratio:
A) 1:1
B) 1:2
C) 2:1
D) 3:1
Answer: C) 2:1
Explanation: The centroid divides each median in the ratio 2:1 from the vertex.
82. The point where the perpendicular bisectors of sides of a triangle meet is called:
A) Centroid
B) Incentre
C) Circumcentre
D) Orthocentre
Answer: C) Circumcentre
Explanation: Circumcentre is the centre of the circle passing through all three vertices of the triangle.
83. The point where the altitudes of a triangle meet is called:
A) Centroid
B) Orthocentre
C) Incentre
D) Circumcentre
Answer: B) Orthocentre
Explanation: Orthocentre is the point of intersection of all altitudes of a triangle.
84. The number of axes of symmetry in an equilateral triangle is:
A) 1
B) 2
C) 3
D) 4
Answer: C) 3
Explanation: Each median or altitude is an axis of symmetry in an equilateral triangle.
85. The number of axes of symmetry in a square is:
A) 2
B) 3
C) 4
D) 6
Answer: C) 4
Explanation: A square has 4 lines of symmetry (2 diagonals and 2 midlines).
86. The area of a circle with circumference 44 cm is:
A) 121 cm²
B) 132 cm²
C) 154 cm²
D) 308 cm²
Answer: C) 154 cm²
Explanation:
Circumference = 2πr = 44 → r = 7.
Area = πr² = 22/7 × 7 × 7 = 154 cm².
87. The area of a semicircle of radius 7 cm is:
A) 77 cm²
B) 154 cm²
C) 308 cm²
D) 44 cm²
Answer: A) 77 cm²
Explanation: Area of semicircle = ½πr² = ½ × 22/7 × 7² = 77 cm².
88. The perimeter of a semicircle (excluding diameter) is:
A) πr
B) 2πr
C) ½πr
D) None
Answer: A) πr
Explanation: Half the circumference = ½ × 2πr = πr (excluding diameter).
89. The perimeter of a semicircle (including diameter) is:
A) πr + 2r
B) ½πr + 2r
C) πr + r
D) 2πr + r
Answer: A) πr + 2r
Explanation: Total length = curved part (πr) + diameter (2r).
90. If the sides of a triangle are 3 cm, 4 cm, and 5 cm, the area = ?
A) 6 cm²
B) 8 cm²
C) 10 cm²
D) 12 cm²
Answer: A) 6 cm²
Explanation: This is a right triangle. Area = ½ × base × height = ½ × 3 × 4 = 6 cm².
91. The area of an equilateral triangle of side 12 cm is:
A) 36√3 cm²
B) 48√3 cm²
C) 64√3 cm²
D) 72√3 cm²
Answer: D) 72√3 cm²
Explanation: Area = (√3/4)a² = (√3/4)×12² = (√3/4)×144 = 36√3 cm² (Wait correction).
Correct answer: A) 36√3 cm².
92. The sum of the exterior angles of any polygon, one at each vertex, is:
A) 90°
B) 180°
C) 270°
D) 360°
Answer: D) 360°
Explanation: The sum of one exterior angle per vertex in any polygon = 360°.
93. The number of diagonals in a decagon (10-sided polygon) is:
A) 35
B) 40
C) 45
D) 50
Answer: A) 35
Explanation: n(n−3)/2 = 10×7/2 = 35.
94. The area of a parallelogram with base 10 cm and height 6 cm is:
A) 30 cm²
B) 40 cm²
C) 50 cm²
D) 60 cm²
Answer: D) 60 cm²
Explanation: Area = base × height = 10 × 6 = 60 cm².
95. The diagonals of a rhombus are 10 cm and 24 cm. Its area = ?
A) 120 cm²
B) 100 cm²
C) 240 cm²
D) 60 cm²
Answer: A) 120 cm²
Explanation: Area = ½ × d₁ × d₂ = ½ × 10 × 24 = 120 cm².
96. The volume of a cylinder with radius 7 cm and height 10 cm = ?
A) 440 cm³
B) 770 cm³
C) 1540 cm³
D) 3080 cm³
Answer: C) 1540 cm³
Explanation: Volume = πr²h = 22/7 × 7² × 10 = 1540 cm³.
97. The total surface area of a sphere of radius 7 cm = ?
A) 154 cm²
B) 308 cm²
C) 616 cm²
D) 772 cm²
Answer: C) 616 cm²
Explanation: Surface area = 4πr² = 4 × 22/7 × 7² = 4 × 22 × 7 = 616 cm².
98. The curved surface area of a cone = ?
A) πr²
B) πrl
C) ½πr²
D) πr(l + r)
Answer: B) πrl
Explanation: Curved surface area (CSA) of cone = π × radius × slant height.
99. The volume of a cone with radius 7 cm and height 9 cm = ?
A) 462 cm³
B) 462π cm³
C) 462/3 cm³
D) 4620 cm³
Answer: A) 462 cm³
Explanation: Volume = ⅓πr²h = ⅓ × 22/7 × 7² × 9 = 462 cm³.
100. The relation between volume (V) and surface area (S) of a sphere of radius r is:
A) V = (4/3)πr³, S = 4πr²
B) V = 4πr², S = (4/3)πr³
C) V = πr², S = πr³
D) None of these
Answer: A) V = (4/3)πr³, S = 4πr²
Explanation: Standard formulas for a sphere.