B.Arch Aptitude Test Practice Set 1

B.Arch Aptitude Test · 2026 · with answers and explanations

questions
30
Total marks
60
Duration
180 minutes
Negative marking
No

Subjects: Mathematics · Aptitude (Reasoning) · Art and Craft

Question 1

Mathematics · 2 marks

If x + 1/x = 3, then x² + 1/x² equals:

  1. A.5
  2. B.7
  3. C.9
  4. D.11

Correct answer: B

Explanation: Squaring both sides: (x + 1/x)² = 9 → x² + 2 + 1/x² = 9 → x² + 1/x² = 7.

Question 2

Mathematics · 2 marks

The HCF of 36 and 48 is:

  1. A.6
  2. B.12
  3. C.18
  4. D.24

Correct answer: B

Explanation: 36 = 2² × 3² and 48 = 2⁴ × 3. HCF = 2² × 3 = 12.

Question 3

Mathematics · 2 marks

The value of tan(45°) + cot(45°) is:

  1. A.0
  2. B.1
  3. C.2
  4. D.√2

Correct answer: C

Explanation: tan(45°) = 1 and cot(45°) = 1. Therefore tan(45°) + cot(45°) = 1 + 1 = 2.

Question 4

Mathematics · 2 marks

The period of the function y = sin(2x) is:

  1. A.π/2
  2. B.π
  3. C.2π
  4. D.4π

Correct answer: B

Explanation: The period of sin(Bx) is 2π/B. Here B = 2, so the period = 2π/2 = π.

Question 5

Mathematics · 2 marks

The length of the tangent from the point (5, 12) to the circle x² + y² = 25 is:

  1. A.5
  2. B.12
  3. C.13
  4. D.7

Correct answer: B

Explanation: Length of tangent = √(x₁² + y₁² − r²) = √(25 + 144 − 25) = √144 = 12.

Question 6

Mathematics · 2 marks

The area of the region enclosed between y = x² and y = x is:

  1. A.1/3
  2. B.1/4
  3. C.1/6
  4. D.1/2

Correct answer: C

Explanation: The curves intersect at x = 0 and x = 1. Area = ∫₀¹ (x − x²)dx = [x²/2 − x³/3]₀¹ = 1/2 − 1/3 = 1/6.

Question 7

Mathematics · 2 marks

The direction ratios of a line passing through (1, 2, 3) and (4, 6, 8) are:

  1. A.1, 2, 3
  2. B.3, 4, 5
  3. C.4, 6, 8
  4. D.5, 8, 11

Correct answer: B

Explanation: Direction ratios = (4−1, 6−2, 8−3) = (3, 4, 5).

Question 8

Mathematics · 2 marks

A die is thrown twice. The probability of getting a sum of 7 is:

  1. A.1/6
  2. B.1/9
  3. C.5/36
  4. D.7/36

Correct answer: A

Explanation: Total outcomes = 36. Favourable outcomes for sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6. Probability = 6/36 = 1/6.

Question 9

Mathematics · 2 marks

The median of the data set {3, 7, 2, 9, 5, 1, 8} is:

  1. A.3
  2. B.5
  3. C.7
  4. D.9

Correct answer: B

Explanation: Arranging in order: 1, 2, 3, 5, 7, 8, 9. The middle value (4th of 7) is 5.

Question 10

Mathematics · 2 marks

The equation of the line passing through (0, 0) with slope 3 is:

  1. A.y = 3x
  2. B.y = x + 3
  3. C.y = x/3
  4. D.y = 3x + 1

Correct answer: A

Explanation: Using y = mx + c with m = 3 and passing through origin (c = 0): y = 3x.

Question 11

Mathematics · 2 marks

The derivative of x³ − 3x² + 2x − 1 at x = 1 is:

  1. A.−1
  2. B.0
  3. C.1
  4. D.2

Correct answer: A

Explanation: f'(x) = 3x² − 6x + 2. At x = 1: f'(1) = 3 − 6 + 2 = −1.

Question 12

Mathematics · 2 marks

If the LCM of two numbers is 60 and their HCF is 5, and one number is 15, the other number is:

  1. A.12
  2. B.20
  3. C.25
  4. D.30

Correct answer: B

Explanation: Product of two numbers = LCM × HCF. So 15 × other = 60 × 5 = 300. Other number = 300/15 = 20.

Question 13

Aptitude (Reasoning) · 2 marks

In a clock, what is the angle between the minute hand and the hour hand at 3:30?

  1. A.60°
  2. B.75°
  3. C.90°
  4. D.105°

Correct answer: B

Explanation: At 3:30, minute hand is at 180° (pointing at 6). Hour hand moves 0.5° per minute, so at 3:30 it is at 90° + 15° = 105°. Angle = 180° − 105° = 75°.

Question 14

Aptitude (Reasoning) · 2 marks

Complete the series: ACE, FHJ, KMO, ?

  1. A.NPR
  2. B.OQS
  3. C.PRT
  4. D.QSU

Correct answer: C

Explanation: Each group consists of 3 alternate letters, and each new group starts 5 letters after the previous start: A(1), F(6), K(11), P(16). So next is P, R, T → PRT.

Question 15

Aptitude (Reasoning) · 2 marks

A cube is placed on a table. Which face is NOT visible from any single viewpoint standing in front of it?

  1. A.The front face
  2. B.The top face
  3. C.The back face
  4. D.The right side face

Correct answer: C

Explanation: When standing in front of a cube on a table, you can see the front, top, and one side (up to 3 faces). The bottom face resting on the table and the back face are never visible from the front.

Question 16

Aptitude (Reasoning) · 2 marks

Which of the following is considered the first planned city in India?

  1. A.Jaipur
  2. B.Chandigarh
  3. C.Bhubaneswar
  4. D.Gandhinagar

Correct answer: B

Explanation: Chandigarh is regarded as India's first planned city in the modern era, designed by Le Corbusier in the 1950s with a systematic grid layout, sectors, and zoned areas.

Question 17

Aptitude (Reasoning) · 2 marks

If WATER is coded as 23-1-20-5-18 (A=1, B=2, ...), then FIRE is coded as:

  1. A.6-9-18-5
  2. B.5-8-17-4
  3. C.7-10-19-6
  4. D.6-9-17-5

Correct answer: A

Explanation: F=6, I=9, R=18, E=5. So FIRE = 6-9-18-5.

Question 18

Aptitude (Reasoning) · 2 marks

An object is placed in front of two mirrors set at 90° to each other. How many images are formed?

  1. A.2
  2. B.3
  3. C.4
  4. D.Infinite

Correct answer: B

Explanation: Number of images = (360°/angle) − 1 = (360/90) − 1 = 4 − 1 = 3.

Question 19

Aptitude (Reasoning) · 2 marks

Statement: All architects are designers. Some designers are artists. Conclusion: Some architects are artists. The conclusion is:

  1. A.Definitely true
  2. B.Definitely false
  3. C.Does not necessarily follow
  4. D.True only if all artists are architects

Correct answer: C

Explanation: From 'all architects are designers' and 'some designers are artists,' we cannot conclude that the artists who are designers are also among the architects. The conclusion does not necessarily follow.

Question 20

Aptitude (Reasoning) · 2 marks

A water tank has the shape of an inverted cone. If its height is 12 m and base radius is 5 m, which view shows a triangle?

  1. A.Plan view (top)
  2. B.Front elevation (side view)
  3. C.Bottom view
  4. D.Section view through the axis of symmetry

Correct answer: B

Explanation: An inverted cone viewed from the side (front elevation) shows a triangle — the two slant sides and the base (top) form a triangular profile.

Question 21

Aptitude (Reasoning) · 2 marks

The Pritzker Architecture Prize is often called the:

  1. A.Pulitzer of Architecture
  2. B.Nobel Prize of Architecture
  3. C.Oscar of Architecture
  4. D.Grammy of Architecture

Correct answer: B

Explanation: The Pritzker Prize, established in 1979, is considered the most prestigious award in architecture, often referred to as the Nobel Prize of architecture.

Question 22

Art and Craft · 2 marks

In visual composition, 'symmetry' along a vertical axis means:

  1. A.The top and bottom halves are identical
  2. B.The left and right halves mirror each other
  3. C.All corners are the same
  4. D.The composition rotates around a point

Correct answer: B

Explanation: Vertical axis symmetry means the left and right halves of the composition are mirror images of each other, creating formal balance.

Question 23

Art and Craft · 2 marks

In a three-point perspective drawing, the third vanishing point is typically located:

  1. A.On the horizon line between the other two
  2. B.Above or below the horizon line
  3. C.Behind the viewer
  4. D.At the centre of the composition

Correct answer: B

Explanation: In three-point perspective, two vanishing points are on the horizon line (for horizontal receding lines) and the third is above or below the horizon (for vertical lines), creating the effect of looking up at or down on a subject.

Question 24

Art and Craft · 2 marks

The concept of 'negative space' in a 2D composition can be used to:

  1. A.Only fill backgrounds with dark colours
  2. B.Create meaningful secondary shapes and forms
  3. C.Eliminate all white space
  4. D.Make the composition appear crowded

Correct answer: B

Explanation: Negative space (the empty area around subjects) can be deliberately shaped to create secondary images or meaningful forms, as seen in the FedEx logo's hidden arrow.

Question 25

Art and Craft · 2 marks

Which of the following materials has the highest compressive strength?

  1. A.Wood
  2. B.Glass
  3. C.Concrete
  4. D.Bamboo

Correct answer: C

Explanation: Among common building materials, concrete has the highest compressive strength, which is why it is used for foundations, columns, and load-bearing elements. However, it has low tensile strength.

Question 26

Art and Craft · 2 marks

In creative design, the principle of 'unity' refers to:

  1. A.Using exactly one colour throughout
  2. B.All elements working together as a cohesive whole
  3. C.Making every element identical
  4. D.Removing all decorative elements

Correct answer: B

Explanation: Unity is the principle by which all elements of a design work together as a cohesive whole. It ensures that despite variety, the composition reads as a single, harmonious entity.

Question 27

Art and Craft · 2 marks

The 'figure-ground' relationship in composition refers to:

  1. A.The height of a building above the ground
  2. B.The perceptual distinction between a subject and its background
  3. C.A mathematical ratio used in design
  4. D.The relationship between a floor plan and its elevation

Correct answer: B

Explanation: Figure-ground is the perceptual relationship between a subject (figure) and its surrounding area (ground). Our visual system naturally separates foreground objects from their background.

Question 28

Art and Craft · 2 marks

The Modulor system of proportions was devised by:

  1. A.Frank Lloyd Wright
  2. B.Le Corbusier
  3. C.Alvar Aalto
  4. D.Louis Sullivan

Correct answer: B

Explanation: The Modulor is a system of proportional measurements based on the human body and the golden ratio, developed by Le Corbusier in the 1940s to guide architectural design at human scale.

Question 29

Aptitude (Reasoning) · 2 marks

A paper is folded twice and a hole is punched through all layers. When unfolded, how many holes will appear?

  1. A.2
  2. B.3
  3. C.4
  4. D.8

Correct answer: C

Explanation: Each fold doubles the number of layers. After two folds there are 4 layers. A single punch through all 4 layers creates 4 holes when the paper is unfolded.

Question 30

Art and Craft · 2 marks

In a composition, gradation refers to:

  1. A.Sudden contrast between two elements
  2. B.A gradual transition from one state to another
  3. C.The exact repetition of a pattern
  4. D.Placing the largest element at the centre

Correct answer: B

Explanation: Gradation is the gradual transition from one condition to another (dark to light, small to large, rough to smooth), creating a sense of movement and visual flow in a composition.

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