JEE Main – B.Arch / B.Planning (Paper 2A / 2B)

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JEE Main – B.Arch / B.Planning (Paper 2A / 2B)

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1 / 100

Category: JEE Main Paper 2 (B.Arch)

1. A square has perimeter 32 cm. Find its area.

a. 64 cm²

b. 32 cm²

c. 128 cm²

d. 100 cm²

2 / 100

Category: JEE Main Paper 2 (B.Arch)

2. The top view of a cylinder appears as:

a. Rectangle

b. Oval

c. Parabola

d. Circle

3 / 100

Category: JEE Main Paper 2 (B.Arch)

3. A dome has radius 7 m. What is its surface area? (Use hemisphere formula)

a. 154π m²

b. 98π m²

c. 49π m²

d. 196π m²

4 / 100

Category: JEE Main Paper 2 (B.Arch)

4. What is the angle of each internal angle of a regular 12-gon?

a. 140°

b. 145°

c. 150°

d. 155°

5 / 100

Category: JEE Main Paper 2 (B.Arch)

5. A prism has 8 faces, 18 edges. How many vertices does it have?

a. 12

b. 10

c. 14

d. 16

6 / 100

Category: JEE Main Paper 2 (B.Arch)

6. In a right-angled triangle, if base = 9 cm and height = 12 cm, find the hypotenuse.

a. 14 cm

b. 15.5 cm

c. 13.5 cm

d. 15 cm

7 / 100

Category: JEE Main Paper 2 (B.Arch)

7. The isometric view of a square appears as a:

a. Circle

b. Rhombus

c. Trapezium

d. Rectangle

8 / 100

Category: JEE Main Paper 2 (B.Arch)

8. A cone and hemisphere have same radius and height. Ratio of their volumes is:

a. 2:01

b. 3:02

c. 1:02

d. 1:01

9 / 100

Category: JEE Main Paper 2 (B.Arch)

9. A cube has a total surface area of 150 cm². What is the length of one edge?

a. 5 cm

b. 6 cm

c. 7 cm

d. 4 cm

10 / 100

Category: JEE Main Paper 2 (B.Arch)

10. What is the number of diagonals in a 20-sided polygon?

a. 170

b. 190

c. 180

d. 170

11 / 100

Category: JEE Main Paper 2 (B.Arch)

11. A 3D object with all faces as equilateral triangles is called:

a. Tetrahedron

b. Cube

c. Octahedron

d. Prism

12 / 100

Category: JEE Main Paper 2 (B.Arch)

12. A rhombus with diagonals 10 cm and 24 cm has area:

a. 120 cm²

b. 120 cm²

c. 130 cm²

d. 140 cm²

13 / 100

Category: JEE Main Paper 2 (B.Arch)

13. What is the derivative of sin²(x)?

a. cos(x)

b. 2cos²(x)

c. cos²(x) - sin²(x)

d. 2sin(x)cos(x)

14 / 100

Category: JEE Main Paper 2 (B.Arch)

14. What is the angular separation between two adjacent vertices in a regular pentagon?

a. 108°

b. 90°

c. 60°

d. 72°

15 / 100

Category: JEE Main Paper 2 (B.Arch)

15. A regular hexagon is made of equilateral triangles. How many such triangles fit in one hexagon?

a. 3

b. 6

c. 4

d. 12

16 / 100

Category: JEE Main Paper 2 (B.Arch)

16. How many space diagonals are there in a cube?

a. 4

b. 6

c. 8

d. 12

17 / 100

Category: JEE Main Paper 2 (B.Arch)

17. A cone has volume 100 cm³. If its height doubles, volume becomes:

a. 100 cm³

b. 50 cm³

c. 200 cm³

d. 200 cm³

18 / 100

Category: JEE Main Paper 2 (B.Arch)

18. If tan(θ) = 1, then what is sin(2θ)?

a. 1

b. 1

c. 0

d. √2

19 / 100

Category: JEE Main Paper 2 (B.Arch)

19. A cylinder has radius 5 cm and height 12 cm. What is the curved surface area?

a. 2πrh = 120π cm²

b. 100π cm²

c. 150π cm²

d. 110π cm²

20 / 100

Category: JEE Main Paper 2 (B.Arch)

20. What is the area of a triangle with sides 13 cm, 14 cm, and 15 cm?

a. 84 cm²

b. 91 cm²

c. 84 cm²

d. 70 cm²

21 / 100

Category: JEE Main Paper 2 (B.Arch)

21. The central angle of a sector is 90°. What fraction of the circle is it?

a. 1-Feb

b. 1-Apr

c. 3-Apr

d. 1-Mar

22 / 100

Category: JEE Main Paper 2 (B.Arch)

22. Which projection technique provides most realistic view?

a. Isometric

b. Oblique

c. Perspective

d. Orthographic

23 / 100

Category: JEE Main Paper 2 (B.Arch)

23. What is the value of sin²θ + cos²θ for any angle θ?

a. 1

b. 0

c. Depends on θ

d. 2

24 / 100

Category: JEE Main Paper 2 (B.Arch)

24. A circle has a chord 12 cm long and 4 cm from center. Radius of the circle is:

a. 5 cm

b. 6 cm

c. 6.5 cm

d. √(36 + 16) = 7.21 cm

25 / 100

Category: JEE Main Paper 2 (B.Arch)

25. The number of faces in an octahedron is:

a. 4

b. 6

c. 8

d. 12

26 / 100

Category: JEE Main Paper 2 (B.Arch)

26. Which curve is generated when a cone is cut at an angle steeper than the cone’s side?

a. Circle

b. Hyperbola

c. Parabola

d. Line

27 / 100

Category: JEE Main Paper 2 (B.Arch)

27. How many symmetry axes does a regular pentagon have?

a. 5

b. 4

c. 6

d. 3

28 / 100

Category: JEE Main Paper 2 (B.Arch)

28. The shadow of a tree is 5 m long when the angle of elevation of the sun is 60°. Height of the tree is?

a. 5 m

b. 5√2 m

c. 6.5 m

d. 5√3 m

29 / 100

Category: JEE Main Paper 2 (B.Arch)

29. The volume of a cube is 512 cm³. What is the length of each edge?

a. 6 cm

b. 9 cm

c. 8 cm

d. 7 cm

30 / 100

Category: JEE Main Paper 2 (B.Arch)

30. A regular polygon has 15 sides. What is the measure of each exterior angle?

a. 20°

b. 24°

c. 30°

d. 18°

31 / 100

Category: JEE Main Paper 2 (B.Arch)

31. The surface area of a cube is 150 cm². What is the length of its edge?

a. 6 cm

b. 5 cm

c. 10 cm

d. 4 cm

32 / 100

Category: JEE Main Paper 2 (B.Arch)

32. A rhombus has diagonals 12 cm and 16 cm. What is its area?

a. 96 cm²

b. 48 cm²

c. 192 cm²

d. 120 cm²

33 / 100

Category: JEE Main Paper 2 (B.Arch)

33. Which view shows the true shape of an inclined surface?

a. Top View

b. Front View

c. Side View

d. Auxiliary View

34 / 100

Category: JEE Main Paper 2 (B.Arch)

34. What is the measure of each interior angle of a regular heptagon?

a. 120°

b. 128.57°

c. 135°

d. 140°

35 / 100

Category: JEE Main Paper 2 (B.Arch)

35. A solid cylinder is melted and recast into a cone of same height. The ratio of their volumes is:

a. 2:01

b. 3:02

c. 3:01

d. 1:03

36 / 100

Category: JEE Main Paper 2 (B.Arch)

36. Which transformation maintains both angle and side ratio?

a. Similarity

b. Rotation

c. Reflection

d. Translation

37 / 100

Category: JEE Main Paper 2 (B.Arch)

37. What shape is formed by slicing a cone parallel to its base?

a. Hyperbola

b. Parabola

c. Line

d. Circle

38 / 100

Category: JEE Main Paper 2 (B.Arch)

38. How many distinct nets can form a cube?

a. 8

b. 9

c. 11

d. 6

39 / 100

Category: JEE Main Paper 2 (B.Arch)

39. A triangle has two sides 6 cm and 8 cm with included angle 90°. What is the area?

a. 24 cm²

b. 48 cm²

c. 30 cm²

d. 20 cm²

40 / 100

Category: JEE Main Paper 2 (B.Arch)

40. What is the area of a sector with radius 10 cm and angle 60°?

a. (10π)/6 cm²

b. (100π)/6 cm²

c. (100π)/3 cm²

d. 25π cm²

41 / 100

Category: JEE Main Paper 2 (B.Arch)

41. A regular polygon has each exterior angle measuring 45°. How many sides does it have?

a. 6

b. 8

c. 5

d. 8

42 / 100

Category: JEE Main Paper 2 (B.Arch)

42. If a triangle has sides 5 cm, 12 cm, and 13 cm, what type of triangle is it?

a. Equilateral

b. Acute

c. Right-angled

d. Isosceles

43 / 100

Category: JEE Main Paper 2 (B.Arch)

43. Which transformation results in a mirror image of an object?

a. Reflection

b. Rotation

c. Translation

d. Dilation

44 / 100

Category: JEE Main Paper 2 (B.Arch)

44. A circle of radius r is inscribed in an equilateral triangle. What is the area of the triangle?

a. √3 r²

b. r²/2

c. πr²

d. √3 r² × 3

45 / 100

Category: JEE Main Paper 2 (B.Arch)

45. A pentagonal pyramid has how many edges?

a. 10

b. 10

c. 12

d. 9

46 / 100

Category: JEE Main Paper 2 (B.Arch)

46. The orthographic projection of a sphere is always a:

a. Oval

b. Ellipse

c. Circle

d. Arc

47 / 100

Category: JEE Main Paper 2 (B.Arch)

47. A prism has 9 vertices and 15 edges. How many faces does it have?

a. 6

b. 7

c. 8

d. 8

48 / 100

Category: JEE Main Paper 2 (B.Arch)

48. What is the value of tan 75°?

a. 1 + √3

b. 2 + √3

c. √3

d. 1.73

49 / 100

Category: JEE Main Paper 2 (B.Arch)

49. The sum of exterior angles of any convex polygon is:

a. 360°

b. 180°

c. 540°

d. Depends on sides

50 / 100

Category: JEE Main Paper 2 (B.Arch)

50. The number of diagonals in a regular decagon is:

a. 35

b. 40

c. 45

d. 50

51 / 100

Category: JEE Main Paper 2 (B.Arch)

51. A shape with 20 faces and 30 edges is a:

a. Cube

b. Icosahedron

c. Octahedron

d. Dodecahedron

52 / 100

Category: JEE Main Paper 2 (B.Arch)

52. What is the shortest distance between two skew lines?

a. Length of the perpendicular between them

b. Any intersecting point

c. Line joining the ends

d. Cannot be found

53 / 100

Category: JEE Main Paper 2 (B.Arch)

53. A cylindrical water tank has a diameter of 4 m and height of 3 m. Find its capacity.

a. 48π m³

b. 24π m³

c. 12π m³

d. 30π m³

54 / 100

Category: JEE Main Paper 2 (B.Arch)

54. If two walls meet at 120°, what is the angle between them internally?

a. 60°

b. 120°

c. 90°

d. 180°

55 / 100

Category: JEE Main Paper 2 (B.Arch)

55. A regular hexagon is inscribed in a circle of radius r. What is the side of the hexagon?

a. r

b. √2r

c. 2r

d. r/2

56 / 100

Category: JEE Main Paper 2 (B.Arch)

56. Which of the following has equal number of vertices and faces?

a. Cube

b. Tetrahedron

c. Octahedron

d. Dodecahedron

57 / 100

Category: JEE Main Paper 2 (B.Arch)

57. What is the volume of a hemisphere with radius 7 cm?

a. (2/3)π(7³)

b. π(7²)

c. 343π cm³

d. 144π cm³

58 / 100

Category: JEE Main Paper 2 (B.Arch)

58. Which conic section is formed by cutting a cone perpendicular to its base?

a. Ellipse

b. Hyperbola

c. Parabola

d. Circle

59 / 100

Category: JEE Main Paper 2 (B.Arch)

59. The side view of a cone appears as:

a. Ellipse

b. Circle

c. Triangle

d. Trapezium

60 / 100

Category: JEE Main Paper 2 (B.Arch)

60. The sum of all internal angles of a 12-sided polygon is:

a. 1620°

b. 1800°

c. 1440°

d. 2160°

61 / 100

Category: JEE Main Paper 2 (B.Arch)

61. What is the internal angle of a regular octagon?

a. 135°

b. 145°

c. 135°

d. 125°

62 / 100

Category: JEE Main Paper 2 (B.Arch)

62. The net of a cylinder includes:

a. 2 circles only

b. 2 circles + 1 rectangle

c. 1 rectangle only

d. 1 circle + 2 rectangles

63 / 100

Category: JEE Main Paper 2 (B.Arch)

63. A dome structure is generally based on which 3D shape?

a. Hemisphere

b. Cone

c. Paraboloid

d. Cube

64 / 100

Category: JEE Main Paper 2 (B.Arch)

64. A line inclined at 45° to HP and 30° to VP appears foreshortened in:

a. Front view

b. Side view

c. True length

d. Both views

65 / 100

Category: JEE Main Paper 2 (B.Arch)

65. A square pyramid has a base of side 6 cm and height of 8 cm. What is its volume?

a. 96 cm³

b. 72 cm³

c. 96 cm³

d. 144 cm³

66 / 100

Category: JEE Main Paper 2 (B.Arch)

66. If cot(θ) = 1/√3, what is sin(θ)? (0° < θ < 90°)

a. 1-Feb

b. √3/2

c. 1/√2

d. 1

67 / 100

Category: JEE Main Paper 2 (B.Arch)

67. What is the distance between opposite vertices of a cube with side 5 cm?

a. 5√3 cm

b. 10√2 cm

c. 5√2 cm

d. 3√5 cm

68 / 100

Category: JEE Main Paper 2 (B.Arch)

68. A room is 5m long, 4m wide, and 3m high. What is the area of walls to be painted (excluding floor & ceiling)?

a. 27 m²

b. 60 m²

c. 35 m²

d. 54 m²

69 / 100

Category: JEE Main Paper 2 (B.Arch)

69. In how many ways can 3 different colors be painted on the 6 faces of a cube? (Each face has 1 color)

a. 60

b. 180

c. 120

d. 720

70 / 100

Category: JEE Main Paper 2 (B.Arch)

70. What is the lateral surface area of a cylinder with height 10 cm and radius 4 cm?

a. 40π cm²

b. 80π cm²

c. 100π cm²

d. 20π cm²

71 / 100

Category: JEE Main Paper 2 (B.Arch)

71. Which conic section is formed when a plane cuts parallel to the slant height of a cone?

a. Circle

b. Parabola

c. Hyperbola

d. Ellipse

72 / 100

Category: JEE Main Paper 2 (B.Arch)

72. A sphere is inscribed in a cube. What is the ratio of volumes of sphere to cube?

a. π/6

b. 1

c. (π/6) ≈ 0.523

d. π/2

73 / 100

Category: JEE Main Paper 2 (B.Arch)

73. A cone and a cylinder have the same base and height. What is the ratio of their volumes?

a. 1:03

b. 1:02

c. 2:03

d. 3:04

74 / 100

Category: JEE Main Paper 2 (B.Arch)

74. The ratio of diagonal to side in a square is:

a. 1:01

b. √2:1

c. 2:01

d. 3:02

75 / 100

Category: JEE Main Paper 2 (B.Arch)

75. A regular tetrahedron has how many edges?

a. 6

b. 10

c. 6

d. 8

76 / 100

Category: JEE Main Paper 2 (B.Arch)

76. The shadow of a 1.5 m stick is 2.6 m long. What is the angle of elevation of the sun?

a. 45°

b. tan⁻¹(1.5/2.6)

c. 60°

d. 30°

77 / 100

Category: JEE Main Paper 2 (B.Arch)

77. Which figure has the maximum area for a given perimeter?

a. Circle

b. Square

c. Rectangle

d. Triangle

78 / 100

Category: JEE Main Paper 2 (B.Arch)

78. What is the smallest regular polygon with an internal angle greater than 150°?

a. Dodecagon

b. Hexagon

c. Octagon

d. Decagon

79 / 100

Category: JEE Main Paper 2 (B.Arch)

79. The angle between two perpendicular planes is:

a. 60°

b. 120°

c. 90°

d. 45°

80 / 100

Category: JEE Main Paper 2 (B.Arch)

80. What is the area of an equilateral triangle with side 12 cm?

a. 62.3 cm²

b. 62.35 cm²

c. 72 cm²

d. 100 cm²

81 / 100

Category: JEE Main Paper 2 (B.Arch)

81. How many sides does a regular polygon have if each interior angle is 140°?

a. 7

b. 9

c. 10

d. 8

82 / 100

Category: JEE Main Paper 2 (B.Arch)

82. Which projection preserves true lengths but not angles?

a. Perspective

b. Oblique

c. Isometric

d. Orthographic

83 / 100

Category: JEE Main Paper 2 (B.Arch)

83. A square has a diagonal of 10√2 cm. What is its area?

a. 100 cm²

b. 200 cm²

c. 200 cm²

d. 150 cm²

84 / 100

Category: JEE Main Paper 2 (B.Arch)

84. What is the eccentricity of a circle?

a. 0

b. 1

c. Between 0 and 1

d. Undefined

85 / 100

Category: JEE Main Paper 2 (B.Arch)

85. The net of which solid has 6 equal squares?

a. Cuboid

b. Cube

c. Tetrahedron

d. Hexagonal prism

86 / 100

Category: JEE Main Paper 2 (B.Arch)

86. If a sphere is cut into two equal parts, what is each part called?

a. Hemisphere

b. Dome

c. Segment

d. Cone cap

87 / 100

Category: JEE Main Paper 2 (B.Arch)

87. What is the length of the diagonal of a rectangle with sides 8 cm and 15 cm?

a. 17 cm

b. 20 cm

c. √289 = 17 cm

d. 23 cm

88 / 100

Category: JEE Main Paper 2 (B.Arch)

88. Which of the following has no axis of symmetry?

a. Square

b. Equilateral triangle

c. Circle

d. Scalene triangle

89 / 100

Category: JEE Main Paper 2 (B.Arch)

89. A circle and a square have the same perimeter. Which has greater area?

a. Circle

b. Square

c. Both equal

d. Can't say

90 / 100

Category: JEE Main Paper 2 (B.Arch)

90. What is the volume of a cube with face diagonal of 6√2 cm?

a. 36 cm³

b. 216 cm³

c. 64 cm³

d. 125 cm³

91 / 100

Category: JEE Main Paper 2 (B.Arch)

91. A hexagonal tile has side 6 cm. What is the area of one tile?

a. 108 cm²

b. 72 cm²

c. 93.6 cm²

d. 93.5 cm²

92 / 100

Category: JEE Main Paper 2 (B.Arch)

92. In architectural plans, which projection method keeps lengths true?

a. Orthographic

b. Oblique

c. Isometric

d. Axonometric

93 / 100

Category: JEE Main Paper 2 (B.Arch)

93. What is the locus of points equidistant from a fixed point and line?

a. Ellipse

b. Circle

c. Parabola

d. Line

94 / 100

Category: JEE Main Paper 2 (B.Arch)

94. A cone has radius 6 cm and height 8 cm. What is its slant height?

a. 10 cm

b. √100 = 10 cm

c. 12 cm

d. 14 cm

95 / 100

Category: JEE Main Paper 2 (B.Arch)

95. If sin(θ) = 3/5, what is cos(θ), assuming θ is in the first quadrant?

a. 4/5

b. 3/4

c. √2/2

d. 5/3

96 / 100

Category: JEE Main Paper 2 (B.Arch)

96. What is the sum of interior angles of a pentagon?

a. 360°

b. 450°

c. 540°

d. 720°

97 / 100

Category: JEE Main Paper 2 (B.Arch)

97. Which of the following represents a hyperbola?

a. y² = 4ax

b. x²/a² - y²/b² = 1

c. x² + y² = r²

d. xy = c²

98 / 100

Category: JEE Main Paper 2 (B.Arch)

98. A cylinder has a height of 10 cm and radius of 3 cm. What is its volume?

a. 60π cm³

b. 30π cm³

c. 90 cm³

d. 90π cm³

99 / 100

Category: JEE Main Paper 2 (B.Arch)

99. The top view of a cube appears as what shape?

a. Triangle

b. Square

c. Circle

d. Hexagon

100 / 100

Category: JEE Main Paper 2 (B.Arch)

100. The base of a triangle is 12 cm and the height is 5 cm. What is the area?

a. 30 cm²

b. 60 cm²

c. 25 cm²

d. 15 cm²

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