JEE Main 2027 Sample Paper B.Arch

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

JEE Main B.Arch 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

75 300 180 Min +4 / −1

GENERAL INSTRUCTIONS

1. This paper contains 75 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 4 marks; 1 mark is deducted for each wrong answer.

4. Total time allowed is 180 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

JEE Main B.Arch 2027
SAMPLE QUESTION PAPER

Questions 75 Max Marks 300 Time 180 Min Marking +4 / −1

Attempt all questions. Choose the one correct option for each.

MATHEMATICS

1. An urn contains 5 red, 4 black and 3 white marbles. 2. If 2α is a root of ax² + bx + c=0, β is a root of ax²-2bx-
Then the number of ways in which 4 marbles can be c=0, and the real numbers a, b, c (a>0), are such that βα;
drawn from it so that at most 3 of them are red, is : then a root Y of ax²+4bx+2c=0 always satisfies:

(A) 455 (A) βүα

(B) 460 (B) βαү

(C) 490 (C) үβα

(D) 495 (D) αү2β

3. The area (in sq. units) of the region bounded by the 4. √(x+6)- (x-3)-3(x-3) (x-3) is equal to :
x arrow 3
curve √( x ) + √( y ) = 1 , x, y >=0, and the tangent to it
(A) 5/6
at the point ( 1/4, 1/4 ) is:
(B) 1/6
(A) 1/24
(C) -2/3
(B) 1/36
(D) -5/6
(C) 1/12

(D) ⅛

5. The distance of the point (1, 2, 3) from the plane 6. The equation of the circle, which is the mirror image
x+y+z=2 measured parallel to the line ( x + 1 )/( - 1 ) = ( of the circle, x²+y²−2x=0, in the line, y=3−x is :
y )/( - 2 ) = ( z - 3 )/( 1 ) is :
(A) x²+y²−6x−8y+24=0
(A) √( 23 ) (B) x²+y²−8x−6y+24=0
(B) √( 22 ) (C) x²+y²−4x−6y+12=0
(C) √( 24 ) (D) x²+y²−6x−4y+12=0
(D) √( 21 )

7. Three vectors a, b and c are such that |a|=1,|b|=2,|c|=4 8. Let f be a continuous function defined by equation
and a+b+c=0 Then the value of 4 a · b+3 b · c+3 c · a is f(x)=\arrayrlr (a 2 x-b x)/((π)/(2)-x) & , & x>(π)/(2) \\
equal to : (π)/(2)-x & , & x=(π)/(2) \\ (2 b x)/((π)/(2)-x) & , & x(π)/(2)
array. equation , Then the value of a+b is:
(A) −68

(B) −26 (A) 1

(C) −34 (B) 4

(D) 27 (C) 5

(D) 8

9. If three vectors v =α i+j+k , V =i+β j-2 k , and V =i+j 10. If λ1 and λ2 are the two values of λ such that the
1 2 3
are coplanar, v and v are perpendicular, then the roots α and β of the quadratic equation aligned &
1 3
vector v × V is: equation, λ(x2-x)+x+5=0 satisfy \\
1 2
&(α)/(β)+(β)/(α)+(4)/(5)=0, then λ λ 2+λ λ 2 is equal
(A) -i+j+2 k 1 2 2 1
aligned equation :
(B) i-j+2 k
(A) 536
(C) i+j
(B) 512
(D) 2 i-2 j+k
(C) 504

(D) 488

11. If m and n are the lengths of the perpendicular from 12. The product of the perpendiculars drawn from the
the origin to the straight lines whose equations are xcotθ foci of the ellipse, x29+y225=1 upon the tangent to it at
- y = 2cosθ and 4x + 3y = -√5 cos2θ, (θ є (0,π)), the point ((3)/(2), 5 √(3)2) is :
respectively, then the value of m² +5n² is:
(A) 9
(A) 5 (B) 189/13
(B) 1 (C) 18
(C) 7 (D) 3 √(13)
(D) 3

13. If the sum of the first 15 terms of the series 14. The order and the degree of the differential equation
3+7+14+24+37+ . . . . . is 15 k, then k is equal to : of all ellipses with centre at the origin, major axis along
x-axis and eccentricity √(3)2 are, respectively :
(A) 122

(B) 81 (A) 1, 1

(C) 119 (B) 2, 1

(D) 126 (C) 1, 2

(D) 2, 2

15. Let the tangent drawn at any point P(x, y) on a curve 16. Let S be the set of all real values of ‘a’ for which the
intersect x and y axes at two distinct points A and B following system of linear equations ax+2y+5z=1
respectively. If AP : PB= 5 : 1, and the curve passes 2x+y+3z=1 3y+7z=1 is consistent. Then the set S is :
through the point (2, 2) then an equation Of the curve is :
(A) equal to R
(A) x y5=26 (B) equal to R−{1}
(B) x y4=25 (C) equal to {1}
(C) x4 y=25 (D) an empty set
(D) x5 y=26

17. A real valued function f ( x ) = Clog _ e | x | + D x ^ 3 18. Let A(l, 3) and C(5, 1) be two opposite vertices of a
+ x , x ≠ 0 , where C and D are constants, has critical rectangle. The other two vertices B(a, b) and D(c, d) lie
points at x = -1 and x=2. Then the ordered pair (C,D) is: on the line y—2x+k for some k. Then the value of (a+b)
(c+d) is:
(A) (⅔ , -1/9)

(B) (-⅔, 1/9) (A) 8

(C) (-1/9, 2/3) (B) 16

(D) (1/9, -2/3) (C) 24

(D) 32

19. Two numbers are selected at random (without 20. ( ( 7 x+ 7 x))/( 3 x) equals :
x arrow 0
replacement) from the first six positive integers. If X
(A) 7/3
denotes the smaller of the two numbers, then the
(B) 14/3
expectation of X, is :
(C) 1/3
(A) 14/3
(D) ⅓ log 7
(B) 13/3

(C) 7/3

(D) 5/3

21. A and B try to hit a target. The probability that A hits 22. The value of the integral ∫ _ π / 2 ^ π ( ( 3 x / 2 ) )/( (
the target is 7/10 and the probability that B hits the x / 2 ) ) d x is:
target is 4/10. If these two events are independent, the
(A) π/2
probability that B hits the target, given that the target is
(B) π/2 - 2
hit, is:
(C) π/2 - 1
(A) 17/41
(D) π/2 + 2
(B) 18/41

(C) 20/41

(D) 19/41

23. For f(x)=\arraycc x e1 / x-e-1 / xe1 / x+e-1 / x, & x ≠ 0 \ 24. The set of all real values of ∝ for which the equation,
0 & , x=0 array. |x+2|*|x-2|= ∝2-2∝ has real solutions for x is:

(A) f'(0) = 1 (A) ([-∞,0]∪[2,∞])

(B) f is not continuous at 0 (B) ([-∞,0]∪[2, 1+√5])

(C) f'(0) = 0 (C) ([-1-√5, 1-√5]∪[1+√5, ∞])

(D) f is not differentiable at 0 (D) ([1-√5,0], ∪[2, 1+√5])

25. If an ellipse has its foci at (2,0) and (-2,0) and its
length of the latus rectum is 6, then the equation of the
ellipse is:

(A) x ^ 2 16 + y ^ 2 12 = 1

(B) x ^ 2 24 + y ^ 2 64 = 1

(C) x ^ 2 64 + y ^ 2 24 = 1

(D) x ^ 2 36 + y ^ 2 18 = 1

APTITUDE TEST

26. Which one of the answer figures is the correct mirror 27. Which one of the following is not a planned city ?
image of the problem figure with respect to X - X ?
(A) Gandhi nagar
(A) (B) Kanpur
(B) (C) Bhubaneshwar
(C) (D) Chandigarh
(D)

28. Green buildings are associated with which of the 29. Directions: The problem figure shows the top view of
following: an object. Identify the correct elevation from amongst
the answer figures looking in the direction of the arrow.
(A) Location

(B) Landscape (A)

(C) Environmental suitability (B)

(D) Beauty (C)

(D)

30. Directions : The 3-D figure shows the view of an 31. The problem figure shows the top view of an object.
object. Identify the correct top view from amongst the Identify the correct elevation from amongst the answer
answer figures. figures looking in the direction of the arrow.

(A) (A)

(B) (B)

(C) (C)

(D) (D)

32. One of the following answer figures is hidden in the 33. The problem figure shows the top view of objects.
problem figure in the same size and direction. Select the Looking in the direction of the arrow, identify the correct
correct one. elevation, from amongst the answer figures.

(A) (A)

(B) (B)

(C) (C)

(D) (D)

34. Problem Figures 35. Which one of the answer figures is the correct mirror
image of the problem figure with respect to X - X ?
(A)

(B) (A)

(C) (B)

(D) (C)

(D)

36. A byte is which one of the following ? 37. Directions: One of the following answer figure is
hidden in the problem figure in the same size and
(A) A unit of digital memory
direction Select the correct one.
(B) An act of an acrobat
(A)
(C) A group of stars
(B)
(D) A unit of sound
(C)

(D)

38. Directions : The 3D figure shows the view of an 39. Directions : The 3-D figure shows the view of an
object. Identify the correct side view looking in the object. Identify the correct front view in the direction of
direction of the arrow, from amongst the answer figures. the arrow, from amongst the answer figures.

(A) (A)

(B) (B)

(C) (C)

(D) (D)

40. The problem figure shows the top view of an object. 41. Big Ben is a :
Identify the correct elevation from amongst the answer
(A) Clock Tower
figures looking in the direction of the arrow.
(B) Palace
(A)
(C) Mosque
(B)
(D) Temple
(C)

(D)

42. An escalator moves in which of the following 43. Which one of the following is not a load bearing
direction ? component in a building ?

(A) Only Vertically (A) Column

(B) Only Horizontally (B) Beam

(C) Vertically and Horizontally (C) Partition wall

(D) In Steps (D) Concrete floor slab

44. Problem Figures 45. From the top view given in the problem figure
identify the correct 3-D figure from amongst the answer
(A)
figures.
(B)
(A)
(C)
(B)
(D)
(C)

(D)

46. The problem figure shows the elevation of an object. 47. Directions : The 3D figure shows the view of an
Identify the correct top view from amongst the answer object. Identify the correct front view looking in the
figures. direction of the arrow, from amongst the answer figures.

(A) (A)

(B) (B)

(C) (C)

(D) (D)

48. The 3-D problem figure shows a view of an object. 49. Directions : The 3D figure shows the view of an
Identify the correct front view, from amongst the answer object. Identify the correct front view looking in the
figures, looking in the direction of arrow. direction of the arrow, from amongst the answer figures.

(A) (A)

(B) (B)

(C) (C)

(D) (D)

50. Which one of die following is a UNESCO World 51. Directions : Which one of the answer figure is the
Heritage Site ? correct mirror image of the problem figure with respect
to X-X?
(A) Kochi

(B) Hampi (A)

(C) Bijnor (B)

(D) Bijapur (C)

(D)

52. Directions : The problem figure shows a top view of 53. Directions : Find the odd figure out of the answer
an object. Identify the correct elevation from amongst figures given below:
the answer figures looking in the direction of the arrow.
(A)
(A) (B)
(B) (C)
(C) (D)
(D)

54. The problem figure shows the top view of objects. 55. Chajjas above windows are meant to protect the
Looking in the direction of the arrow, identify the correct building from which of the following ?
elevation, from amongst the answer figures.
(A) Sun
(A) (B) Birds
(B) (C) Typhoon
(C) (D) Wind
(D)

56. Directions : The 3D figure shows the view of an 57. Salim Chisti mosque is located in :
object. Identify the correct side view looking in the
(A) Gwalior
direction of the arrow, from amongst the answer figures.
(B) Fatehpur Sikri
(A)
(C) Hyderabad
(B)
(D) Delhi
(C)

(D)

58. Directions: The 3-D figure shows the view of an 59. The problem figure shows the top view of objects.
object. Identify the correct top view from amongst the Looking in the direction of the arrow, identify the correct
answer figures. elevation, from amongst the answer figures.

(A) (A)

(B) (B)

(C) (C)

(D) (D)

60. Zaha Hadid was born in which country amongst the 61. Directions : The 3-D figure shows the view of an
following ? object. Identify the correct front view in the direction of
the arrow, from amongst the answer figures.
(A) Iran

(B) Iraq (A)

(C) Afghanistan (B)

(D) Turkistan (C)

(D)

62. Directions : The 3-D figure shows the view of an 63. The Lotus Temple is located in which one of the
object. Identify the correct front view in the direction of following city ?
the arrow, from amongst the answer figures.
(A) New Delhi
(A) (B) Nagpur
(B) (C) Kanpur
(C) (D) Lucknow
(D)

64. In the Northern Hemisphere the winter sun rises 65. Directions : The 3-D figure shows the view of an
from which direction amongst the following ? object. Identify the correct top view from amongst the
answer figures.
(A) North East

(B) South West (A)

(C) South East (B)

(D) North West (C)

(D)

66. Directions : One of the following answer figures is 67. Which one of the following is a horizontal element
hidden in the problem figure in the same size and that supports the loads above openings in walls in a
direction. Select the correct one. building ?

(A) (A) Column

(B) (B) Pillar

(C) (C) Lintel

(D) (D) Foundation

68. Buland Darwaza is located in : 69. Which one of the answer figures shows the correct
view of the 3–D problem figure after the problem figure is
(A) Fatehpur Sikri
opened up ?
(B) Red Fort
(A)
(C) Agra Fort
(B)
(D) Golconda
(C)

(D)

70. Directions: Find the odd figure out of the answer 71. Directions : The 3-D figure shows the view of an
figures given below: object. Identify the correct front view in the direction of
the arrow', from amongst the answer figures.
(A)

(B) (A)

(C) (B)

(D) (C)

(D)

72. Directions: Which one of the answer figure is the 73. Identify the correct 3-D figure from amongst the
correct mirror image of the problem figure with respect answer figures, which has the same elevation, as given in
to X-X? the problem figure on the left.

(A) (A)

(B) (B)

(C) (C)

(D) (D)

74. Ellora temples are : 75. Find the odd figure out of the problem figures given
below.
(A) Made in marble

(B) Built in sandstone (A)

(C) Cut out of rock (B)

(D) Built in wood (C)

(D)

ANSWER KEY

1. (C) 2. (A) 3. (A) 4. (D) 5. (C) 6. (D) 7. (B)

8. (C) 9. (B) 10. (D) 11. (B) 12. (A) 13. (A) 14. (A)

15. (A) 16. (A) 17. (A) 18. (B) 19. (C) 20. (A) 21. (C)

22. (B) 23. (D) 24. (D) 25. (A) 26. (A) 27. (B) 28. (C)

29. (D) 30. (C) 31. (A) 32. (B) 33. (C) 34. (B) 35. (B)

36. (A) 37. (A) 38. (A) 39. (C) 40. (B) 41. (A) 42. (C)

43. (C) 44. (A) 45. (B) 46. (B) 47. (A) 48. (A) 49. (B)

50. (B) 51. (B) 52. (C) 53. (B) 54. (B) 55. (A) 56. (C)

57. (B) 58. (B) 59. (A) 60. (B) 61. (D) 62. (A) 63. (A)

64. (A) 65. (A) 66. (A) 67. (C) 68. (A) 69. (B) 70. (A)

71. (B) 72. (D) 73. (B) 74. (C) 75. (C)