100+ Free JEE B.Arch Practice Questions

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JEE Main Paper 2B — B.Planning (National Testing Agency, India)

Practice Questions100 questions

2026 Statistics

Key Facts: JEE B.Arch Exam

400

Total Marks

NTA Exam Pattern

Total Questions

NTA Syllabus

+4 / -1

Marking Scheme

MCQ Sections

3 hours

Exam Duration

NTA

₹1,000

Male General Fee

NTA Registration

50%

Min PCM marks in 12th

Eligibility Criteria

JEE Main Paper 2A (B.Arch) is the gateway to premier architecture colleges in India. It is a 400-mark hybrid exam: Part I (Mathematics, 100 marks) and Part II (Aptitude, 200 marks) are computer-based with +4/-1 marking, while Part III (Drawing, 100 marks) is offline. General registration fee is ₹1,000 for males, ₹800 for females, and ₹500 for reserved categories. Admission is highly competitive, based on national JoSAA/CSAB percentile rankings.

Sample JEE B.Arch Practice Questions

Try these sample questions to test your JEE B.Arch exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A surveyor standing on the bank of a river observes that the angle of elevation of the top of a monument standing on the opposite bank is 60°. When he retires 40 meters away from the bank in a straight line, he finds the angle of elevation to be 30°. What is the height of the monument?

A.20 meters

B.20√3 meters

C.40 meters

D.40√3 meters

Explanation: Let the height of the monument be h and the width of the river be x. From the first position, tan(60°) = h/x, which gives x = h/√3. From the second position, tan(30°) = h/(x + 40), which gives x + 40 = h√3. Substituting x, we get h/√3 + 40 = h√3. Solving for h, we get h(3 - 1)/√3 = 40, which simplifies to 2h = 40√3, or h = 20√3 meters.

2If the system of linear equations x + y + z = 6, x + 2y + 3z = 10, and x + 2y + λz = μ has infinitely many solutions, what are the values of λ and μ?

A.λ = 3, μ = 10

B.λ = 3, μ ≠ 10

C.λ ≠ 3, μ = 10

D.λ ≠ 3, μ ≠ 10

Explanation: For a system of linear equations to have infinitely many solutions, the determinant of the coefficients (D) must be zero, which gives λ = 3. Additionally, the determinants Dx, Dy, and Dz must also be zero. Expanding Dz with the constant vector replacing the z-column yields μ = 10. Thus, λ = 3 and μ = 10.

3What is the scalar projection of the vector a = 2ı + 3ȷ + 2k on the direction of the vector b = ı + 2ȷ + k?

A.5/√6

B.10/√6

C.10/√3

D.5/√3

Explanation: The scalar projection of vector a on vector b is given by the formula (a • b) / |b|. The dot product a • b is 2(1) + 3(2) + 2(1) = 2 + 6 + 2 = 10. The magnitude of b, |b|, is √(1² + 2² + 1²) = √6. Therefore, the scalar projection is 10/√6.

4What is the eccentricity of the hyperbola represented by the equation 9x² - 16y² = 144?

A.5/4

B.4/3

C.5/3

D.3/4

Explanation: Dividing the equation 9x² - 16y² = 144 by 144 gives the standard form x²/16 - y²/9 = 1, where a² = 16 and b² = 9. The eccentricity e of a hyperbola is calculated using e = √(1 + b²/a²) = √(1 + 9/16) = √(25/16) = 5/4.

5Find the value of the limit: lim (x → 0) [ (e^(x²) - cos(x)) / x² ].

A.1/2

B.1

C.3/2

D.2

Explanation: Using Taylor series expansions around x = 0, we know e^(x²) = 1 + x² + O(x⁴) and cos(x) = 1 - x²/2 + O(x⁴). Substituting these into the limit expression gives lim (x → 0) [ (1 + x² - 1 + x²/2) / x² ] = lim (x → 0) [ (3x²/2) / x² ] = 3/2.

6Determine the sum of the infinite geometric series: 1 + 1/3 + 1/9 + 1/27 + ...

A.1.5

B.2.0

C.3.0

D.1.33

Explanation: This is an infinite geometric progression with the first term a = 1 and common ratio r = 1/3. Since |r| < 1, the sum to infinity exists and is given by S = a / (1 - r) = 1 / (1 - 1/3) = 1 / (2/3) = 3/2 = 1.5.

7What is the angle between the two planes represented by the equations 2x - y + z = 6 and x + y + 2z = 3?

A.30°

B.45°

C.60°

D.90°

Explanation: The angle θ between two planes is the angle between their normal vectors, n1 = (2, -1, 1) and n2 = (1, 1, 2). Using the dot product formula, cos(θ) = |n1 • n2| / (|n1| * |n2|) = |2(1) + (-1)(1) + 1(2)| / (√6 * √6) = (2 - 1 + 2) / 6 = 3/6 = 1/2. Therefore, θ = 60°.

8If two fair six-sided dice are rolled simultaneously, what is the probability that the sum of the numbers shown on their top faces is a prime number?

A.5/12

B.7/12

C.1/2

D.5/18

Explanation: The total number of outcomes when rolling two dice is 36. The prime sums possible are 2, 3, 5, 7, and 11. The number of ways to get these sums are: 2 (1 way), 3 (2 ways), 5 (4 ways), 7 (6 ways), and 11 (2 ways). The total number of favorable outcomes is 1 + 2 + 4 + 6 + 2 = 15. The probability is 15/36, which simplifies to 5/12.

9How many distinct four-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 without repetition, such that the resulting number is divisible by 5?

A.60

B.120

C.24

D.48

Explanation: For a number to be divisible by 5, its units digit must be either 0 or 5. Since only 5 is available in the set, the units place is fixed (1 choice). The remaining three places can be filled by selecting and arranging 3 digits from the remaining 5 digits, which can be done in P(5, 3) = 5 * 4 * 3 = 60 ways.

10If the roots of the quadratic equation x² - px + q = 0 differ by unity, which of the following relations is correct?

A.p² = 4q + 1

B.p² = 4q - 1

C.q² = 4p + 1

D.q² = 4p - 1

Explanation: Let the roots of the equation be α and β. From the properties of quadratic equations, sum of roots α + β = p and product of roots αβ = q. We are given that |α - β| = 1. Squaring both sides, we get (α - β)² = 1, which expands to (α + β)² - 4αβ = 1. Substituting the sum and product, we obtain p² - 4q = 1, or p² = 4q + 1.

About the JEE B.Arch Exam

JEE Main Paper 2A is the national-level entrance examination conducted by the National Testing Agency (NTA) for admission to undergraduate Bachelor of Architecture (B.Arch) programs in premier Indian institutes like School of Planning and Architecture (SPAs) and NITs. The exam follows a hybrid structure of 3 hours, featuring online sections for Mathematics (30 questions, 100 marks) and an Aptitude Test (50 questions, 200 marks), combined with an offline pen-and-paper Drawing Test (2 questions, 100 marks) for a total of 400 marks. The online sections carry a marking scheme of +4 for correct answers and -1 for wrong answers. JEE Main is held twice a year, and scores are used for JoSAA/CSAB counseling.

Questions

77 scored questions

Time Limit

3 hours (180 minutes)

Passing Score

Percentile-based cut-off

Exam Fee

₹1,000 (National Testing Agency (NTA), India)

JEE B.Arch Exam Content Outline

50%

Aptitude Test (Part II)

Architectural awareness, famous buildings, key construction materials, 3D visualization from 2D nets, block counting, perspective concepts, and color harmony.

25%

Mathematics (Part I)

Calculus, coordinate geometry, 3D geometry, matrices and determinants, vectors, probability, and trigonometry.

25%

Drawing Test (Part III)

Offline sketching questions testing perspective, scale, proportion, shading, composition, and visual creativity.

How to Pass the JEE B.Arch Exam

What You Need to Know

Passing score: Percentile-based cut-off
Exam length: 77 questions
Time limit: 3 hours (180 minutes)
Exam fee: ₹1,000

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

JEE B.Arch Study Tips from Top Performers

1Master high-yield Aptitude topics: Architectural awareness, 3D visualization, and orthographic projections make up 50% of the total marks (200 marks). Memorizing famous buildings, Indian and global architects, and structural terms provides easy scoring opportunities.

2Understand perspective principles: Learn how one-point, two-point, and three-point perspective drawings are constructed, and understand vanishing points and horizon levels. This knowledge is crucial for both Part II MCQs and Part III sketching.

3Practice 3D block counting and unfolding nets: These spatial reasoning questions are highly scoring and require speed. Practice rotating 3D shapes mentally and identifying top/front/side views.

4Revise Class 11 and 12 Mathematics: Focus on Coordinate Geometry, Vectors, 3D Geometry, and Matrices. These chapters are relatively direct compared to Calculus and form a major portion of Part I.

5Develop sketching speed and proportions: For the offline Drawing test, practice sketching everyday scenes (like a railway station, a market place, or a room interior) in two-point perspective. Focus on correct human proportions, texture, and light/shade effects.

6Avoid negative marks: With a penalty of -1 for every wrong MCQ, do not guess blindly. Only attempt questions where you can confidently eliminate at least two options.

Frequently Asked Questions

What is the structure of the JEE Main Paper 2A (B.Arch) exam?

JEE Main Paper 2A consists of three parts: Part I is Mathematics (30 questions: 20 MCQs and 10 Numerical Value questions where candidates answer any 5), Part II is the Aptitude Test (50 MCQs), and Part III is the Drawing Test (2 subjective sketching questions). The total marks are 400.

How are the marks distributed in the JEE Main B.Arch exam?

The total of 400 marks is divided as: Mathematics has 100 marks (25 questions evaluated), the Aptitude Test has 200 marks (50 questions), and the Drawing Test has 100 marks (2 questions of 50 marks each).

What is the marking scheme for the online MCQs?

For both Mathematics and Aptitude MCQs, you receive +4 marks for each correct answer and -1 mark for each incorrect answer. Unattempted questions receive 0 marks.

How can I register and what is the fee for JEE Main B.Arch?

Registration is done online on the official NTA JEE Main website (jeemain.nta.ac.in). The registration fee for a single paper (B.Arch) is ₹1,000 for General/OBC-NCL Male candidates, ₹800 for General/OBC-NCL Female candidates, and ₹500 for SC/ST/PwD/Third Gender candidates.

Which colleges accept JEE Main Paper 2A scores?

Scores are accepted for admission to B.Arch programs at NITs, School of Planning and Architecture (SPAs - located in Delhi, Bhopal, and Vijayawada), IIEST Shibpur, and various other Centrally Funded Technical Institutions (CFTIs) and state universities through JoSAA/CSAB counseling.

Do I need to take NATA if I clear JEE Main Paper 2A?

No. JEE Main Paper 2A and NATA (National Aptitude Test in Architecture) are two separate exams. SPAs and NITs admit students solely through JEE Main Paper 2A rankings via JoSAA. Other architecture colleges (including private and state colleges under COA) accept NATA or JEE Main scores, depending on their individual admission rules.

What are the eligibility requirements for JEE Main B.Arch?

Candidates must have passed their 10+2 (Class 12) or equivalent exam with Physics, Chemistry, and Mathematics (PCM) as compulsory subjects, obtaining a minimum of 50% marks in aggregate and also 50% in each of these three subjects.