JEE Main Paper 2 Practice Set 1

JEE Main · 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 A is a 3×3 matrix such that |A| = 5, then |adj(A)| is equal to:

  1. A.5
  2. B.25
  3. C.125
  4. D.10

Correct answer: B

Explanation: For an n×n matrix A, |adj(A)| = |A|^(n−1). Here n = 3, so |adj(A)| = 5^(3−1) = 5² = 25.

Question 2

Mathematics · 2 marks

The value of sin²(15°) + sin²(75°) is:

  1. A.0
  2. B.1/2
  3. C.1
  4. D.2

Correct answer: C

Explanation: sin(75°) = cos(15°), so sin²(15°) + sin²(75°) = sin²(15°) + cos²(15°) = 1.

Question 3

Mathematics · 2 marks

The number of ways to arrange the letters of the word 'DESIGN' such that the two vowels are always together is:

  1. A.120
  2. B.240
  3. C.360
  4. D.480

Correct answer: B

Explanation: DESIGN has 6 letters with vowels E and I. Treating EI as one unit gives 5 units to arrange in 5! = 120 ways. The two vowels can swap within the unit in 2! = 2 ways. Total = 120 × 2 = 240.

Question 4

Mathematics · 2 marks

The coefficient of x³ in the expansion of (1 + x)^10 is:

  1. A.45
  2. B.90
  3. C.120
  4. D.210

Correct answer: C

Explanation: Using the binomial theorem, the coefficient of x³ in (1 + x)^10 is C(10,3) = 10!/(3!·7!) = 120.

Question 5

Mathematics · 2 marks

The sum of the first 20 terms of the arithmetic progression 3, 7, 11, 15, ... is:

  1. A.780
  2. B.820
  3. C.860
  4. D.900

Correct answer: B

Explanation: First term a = 3, common difference d = 4. S₂₀ = (20/2)[2(3) + (20−1)(4)] = 10[6 + 76] = 10 × 82 = 820.

Question 6

Mathematics · 2 marks

If f(x) = |x − 2| + |x − 5|, then the minimum value of f(x) is:

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

Correct answer: B

Explanation: The minimum of |x − a| + |x − b| occurs for any x in [a, b] and equals |b − a| = |5 − 2| = 3.

Question 7

Mathematics · 2 marks

The area bounded by the curve y = x², the x-axis, and the lines x = 1 and x = 3 is:

  1. A.8
  2. B.26/3
  3. C.9
  4. D.28/3

Correct answer: B

Explanation: Area = ∫₁³ x² dx = [x³/3]₁³ = 27/3 − 1/3 = 26/3.

Question 8

Mathematics · 2 marks

The order and degree of the differential equation d²y/dx² + (dy/dx)³ + y = 0 are respectively:

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

Correct answer: B

Explanation: The highest order derivative is d²y/dx² (order 2). Its power is 1, so the degree is 1.

Question 9

Mathematics · 2 marks

The distance between the points (3, 4, 5) and (1, 2, 3) in three-dimensional space is:

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

Correct answer: B

Explanation: Distance = √[(3−1)² + (4−2)² + (5−3)²] = √[4 + 4 + 4] = √12 = 2√3.

Question 10

Mathematics · 2 marks

If vectors a = 2i + 3j − k and b = i − j + 2k, then a · b equals:

  1. A.−3
  2. B.3
  3. C.−1
  4. D.7

Correct answer: A

Explanation: a · b = (2)(1) + (3)(−1) + (−1)(2) = 2 − 3 − 2 = −3.

Question 11

Mathematics · 2 marks

The equation of the circle with center (2, −3) and radius 5 is:

  1. A.x² + y² − 4x + 6y − 12 = 0
  2. B.x² + y² + 4x − 6y − 12 = 0
  3. C.x² + y² − 4x − 6y + 12 = 0
  4. D.x² + y² + 4x + 6y + 12 = 0

Correct answer: A

Explanation: The standard form is (x − h)² + (y − k)² = r². Substituting: (x − 2)² + (y + 3)² = 25, which expands to x² + y² − 4x + 6y − 12 = 0.

Question 12

Mathematics · 2 marks

The probability that a leap year has 53 Sundays is:

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

Correct answer: B

Explanation: A leap year has 366 days = 52 weeks + 2 extra days. The two extra days can be (Sun-Mon), (Mon-Tue), ..., (Sat-Sun). Out of 7 equally likely pairs, 2 contain Sunday. So probability = 2/7.

Question 13

Aptitude (Reasoning) · 2 marks

The Lotus Temple in New Delhi is inspired by which natural form?

  1. A.A seashell
  2. B.A lotus flower
  3. C.A banyan tree
  4. D.A mountain peak

Correct answer: B

Explanation: The Lotus Temple, a Bahá'í House of Worship designed by Fariborz Sahba, is shaped like a lotus flower with 27 free-standing marble-clad petals arranged in clusters of three.

Question 14

Aptitude (Reasoning) · 2 marks

A cube has 6 faces painted in 6 different colours. How many distinct ways can you orient the cube so that a specific colour faces up?

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

Correct answer: B

Explanation: Once a specific colour is fixed on top, the bottom face is fixed too. The 4 remaining side faces can be rotated into 4 orientations. So there are 4 distinct orientations with a given colour on top.

Question 15

Aptitude (Reasoning) · 2 marks

Which material is traditionally used for the dome of the Taj Mahal?

  1. A.Red sandstone
  2. B.White Makrana marble
  3. C.Granite
  4. D.Limestone

Correct answer: B

Explanation: The Taj Mahal's dome and entire exterior is clad in white Makrana marble, quarried from Rajasthan.

Question 16

Aptitude (Reasoning) · 2 marks

An isometric drawing of a cube shows how many faces simultaneously?

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

Correct answer: C

Explanation: An isometric view is an axonometric projection that shows three faces of a cube — the top, front, and side — simultaneously with equal foreshortening.

Question 17

Aptitude (Reasoning) · 2 marks

In a sequence: 2, 6, 12, 20, 30, ... the next term is:

  1. A.36
  2. B.40
  3. C.42
  4. D.44

Correct answer: C

Explanation: The pattern is n(n+1): 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30. The next term is 6×7 = 42.

Question 18

Aptitude (Reasoning) · 2 marks

Which of the following best describes a 'cantilever' in building construction?

  1. A.A vertical support column
  2. B.A beam fixed at one end and free at the other
  3. C.A curved arch spanning an opening
  4. D.A foundation resting on bedrock

Correct answer: B

Explanation: A cantilever is a structural element that extends horizontally and is supported at only one end, with the other end projecting freely. Examples include balconies and canopies.

Question 19

Aptitude (Reasoning) · 2 marks

Which texture would feel smoothest to touch?

  1. A.Exposed brick
  2. B.Rough-cut stone
  3. C.Polished marble
  4. D.Unfinished concrete

Correct answer: C

Explanation: Polished marble has an extremely smooth surface finish achieved through progressive grinding and buffing, making it the smoothest among the given options.

Question 20

Aptitude (Reasoning) · 2 marks

If a solid is viewed from the front and appears as a circle, and from the top also appears as a circle, the solid is most likely a:

  1. A.Cylinder
  2. B.Cone
  3. C.Sphere
  4. D.Cube

Correct answer: C

Explanation: A sphere appears as a circle from every viewing direction — front, top, and side. A cylinder would appear as a circle from one end but as a rectangle from the side.

Question 21

Aptitude (Reasoning) · 2 marks

A person facing North turns 90° clockwise, then 180° anticlockwise, then 45° clockwise. Which direction is the person now facing?

  1. A.South-West
  2. B.North-West
  3. C.West
  4. D.North-East

Correct answer: B

Explanation: Starting at North (0°): +90° clockwise = East (90°); −180° (anticlockwise) = 90° − 180° = −90° = West (270°); +45° clockwise = 270° + 45° = 315° = North-West.

Question 22

Aptitude (Reasoning) · 2 marks

The Gateway of India in Mumbai was built in which architectural style?

  1. A.Neo-Gothic
  2. B.Art Deco
  3. C.Indo-Saracenic
  4. D.Baroque

Correct answer: C

Explanation: The Gateway of India, designed by George Wittet, is built in the Indo-Saracenic style, combining elements of Hindu, Muslim, and Western architecture. It was completed in 1924.

Question 23

Art and Craft · 2 marks

In a two-dimensional composition, the principle of 'visual balance' is best achieved by:

  1. A.Placing all elements on the left side
  2. B.Distributing visual weight evenly across the composition
  3. C.Using only geometric shapes
  4. D.Making all elements the same size

Correct answer: B

Explanation: Visual balance in 2D composition is achieved by distributing visual weight evenly across the composition, considering factors like size, colour, and placement of elements.

Question 24

Art and Craft · 2 marks

In three-dimensional composition, which element creates a sense of depth and volume?

  1. A.Flat colour fills
  2. B.Overlapping of forms
  3. C.Uniform line thickness
  4. D.Repetition of identical shapes

Correct answer: B

Explanation: Overlapping forms create visual depth by showing one object partially concealing another, establishing a front-to-back spatial relationship that produces the illusion of volume.

Question 25

Art and Craft · 2 marks

In a one-point perspective drawing, all receding lines converge at:

  1. A.Two vanishing points on the horizon
  2. B.A single vanishing point on the horizon line
  3. C.The bottom of the picture plane
  4. D.The centre of the paper

Correct answer: B

Explanation: In one-point perspective, all lines receding into depth converge at a single vanishing point located on the horizon line.

Question 26

Art and Craft · 2 marks

A building plan drawn at a scale of 1:100 means that 1 cm on the drawing represents:

  1. A.10 cm in reality
  2. B.100 cm (1 m) in reality
  3. C.1000 cm (10 m) in reality
  4. D.1 cm in reality

Correct answer: B

Explanation: A scale of 1:100 means every unit on the drawing equals 100 units in reality. So 1 cm on the drawing represents 100 cm = 1 metre in actual size.

Question 27

Art and Craft · 2 marks

Which principle of design refers to the arrangement of elements to create a sense of movement in a composition?

  1. A.Emphasis
  2. B.Unity
  3. C.Rhythm
  4. D.Proportion

Correct answer: C

Explanation: Rhythm in design is the visual flow created by repeating or alternating elements in a pattern, guiding the viewer's eye through the composition in a way that suggests movement.

Question 28

Art and Craft · 2 marks

The 'Golden Ratio' (approximately 1:1.618) is widely used in architecture and art because it:

  1. A.Minimises material usage in construction
  2. B.Produces proportions perceived as aesthetically pleasing
  3. C.Ensures structural stability
  4. D.Maximises the floor area

Correct answer: B

Explanation: The Golden Ratio produces proportions perceived as naturally pleasing. It appears throughout nature and has been used in the Parthenon, the Great Pyramid, and many Renaissance artworks.

Question 29

Mathematics · 2 marks

If A and B are two sets such that n(A) = 20, n(B) = 30, and n(A ∩ B) = 10, then n(A ∪ B) is:

  1. A.30
  2. B.40
  3. C.50
  4. D.60

Correct answer: B

Explanation: By the inclusion-exclusion principle: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 20 + 30 − 10 = 40.

Question 30

Art and Craft · 2 marks

In a factual drawing, the term 'foreshortening' refers to:

  1. A.Drawing an object larger than its actual size
  2. B.The visual compression of an object as it recedes from the viewer
  3. C.Removing unnecessary details from a drawing
  4. D.Using only horizontal lines in a composition

Correct answer: B

Explanation: Foreshortening is a technique where an object or form appears shorter than it actually is because it is angled toward the viewer, creating a sense of depth and three-dimensionality.

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