GATE DA (Data Science and Artificial Intelligence) has only three official papers so far, so each previous year question deserves careful use. This page shows where IIT Madras publishes those papers and keys, sets out the official paper pattern, explains how to use the papers section by section, and ends with 12 original practice questions with full solutions. For structured practice afterwards, the Myndaq GATE DA course follows the same seven syllabus sections.
The GATE DA paper pattern as officially published
The official GATE website gives this frame for DA:
- 65 questions in 3 hours - 10 General Aptitude questions plus 55 subject questions
- 100 marks in total - General Aptitude carries 15 marks and the DA subject part carries 85 marks
- No separate Engineering Mathematics block - most papers split their subject part into 72 marks plus 13 of Engineering Mathematics, but DA is listed with 85 subject marks
- Every question is worth 1 mark or 2 marks
Since every question is worth 1 or 2 marks, the counts fix the split: 10 questions for 15 marks means five 1-mark and five 2-mark questions, and 55 questions for 85 marks means 25 one-mark and 30 two-mark questions. More than half the DA part is 2-mark work.
Question types and marking
- MCQ (multiple choice) - one correct option. A wrong answer loses 1/3 mark on a 1-mark MCQ and 2/3 mark on a 2-mark MCQ.
- MSQ (multiple select) - one or more options can be correct; no negative marking and no partial marking.
- NAT (numerical answer type) - you type a number. There is no negative marking.
Attempt decisions under these rules are worked out in the GATE marking guide, and NAT entry in the NAT and virtual calculator guide.
Where the official previous year papers are
The Download page of the official GATE website offers question papers with answer keys year by year for 2021 to 2026. DA appears only from 2024:
- GATE 2026 DA - question paper and answer key, also listed on the IIT Guwahati GATE 2026 page of master question papers and answer keys
- GATE 2025 DA - question paper and answer key
- GATE 2024 DA - question paper and final answer key
Direct links to all six PDFs are in Official sources below. Use the official files rather than reposted copies; this page reproduces no official question.
One caution: the official GATE site has published revised syllabi, while the 2024 to 2026 papers followed earlier versions. Check each old question against the GATE DA syllabus guide and the official PDF before relying on it.
How to use the DA papers section by section
Three papers are too few to predict weightage. Use them for style and depth, and the current syllabus for coverage.
- Probability and Statistics - separate multi-step conditioning and Bayes items from named-distribution and hypothesis-test items, and redo each against the clock.
- Linear Algebra - sort items into rank and nullity, eigenvalues, projections and decompositions; many fall quickly to properties rather than long calculation.
- Calculus and Optimization - the current syllabus PDF covers functions of a single variable only, up to Taylor series and maxima and minima; always check interval endpoints.
- Programming, Data Structures and Algorithms - the language is Python; trace code on paper, especially aliasing, slicing and recursion.
- Database Management and Warehousing - redo functional-dependency and normal-form items from scratch, and write the SQL yourself before reading the options.
- Machine Learning - split numerical items, such as regression fits and distances, from statement-judging items.
- AI - write out every step of search, logic and inference items.
Score each paper with the official key, total it with the GATE score calculator, and log every miss by section and format.
12 original practice questions with solutions
These are original practice questions written by Myndaq in the official formats, not official past-paper questions.
Question 1 - Probability, MCQ, 1 mark
Two fair dice are rolled and the sum is 8. What is the probability that at least one die shows 3? (A) 1/5 (B) 2/5 (C) 1/3 (D) 2/9
Answer: (B). Sum 8 has five equally likely outcomes: (2,6), (3,5), (4,4), (5,3), (6,2). Two contain a 3, so the probability is 2/5.
Question 2 - Bayes theorem, NAT, 2 marks
A condition affects 1% of a population. A test detects it in 90% of affected people and gives a false positive for 5% of unaffected people. Find P(condition | positive), rounded off to three decimal places.
Answer: 0.154. P(positive) = 0.01 × 0.90 + 0.99 × 0.05 = 0.009 + 0.0495 = 0.0585. Then 0.009 / 0.0585 = 0.15385, which rounds to 0.154.
Question 3 - Statistics, MSQ, 2 marks
Select all correct statements. (A) If X and Y are independent, Cov(X, Y) = 0. (B) If Cov(X, Y) = 0, then X and Y are independent. (C) For a standard normal Z, P(Z ≤ 0) = 0.5. (D) Var(X + Y) = Var(X) + Var(Y) for any X and Y.
Answer: (A) and (C). (A) holds because E(XY) = E(X)E(Y) under independence. (B) fails: take X uniform on {−1, 0, 1} and Y = X², where the covariance is 0 but Y depends on X. (C) holds by symmetry. (D) needs Cov(X, Y) = 0, since in general Var(X + Y) = Var(X) + Var(Y) + 2Cov(X, Y).
Question 4 - Linear algebra, NAT, 1 mark
A is the 2 × 2 matrix with rows (2, 1) and (1, 2). Find the sum of the eigenvalues of A².
Answer: 10. (2 − λ)² − 1 = 0 gives λ = 1 and 3, so A² has eigenvalues 1 and 9, which sum to 10. Check: A² has rows (5, 4) and (4, 5), and its trace is 10.
Question 5 - Linear algebra, MCQ, 2 marks
M is the 3 × 4 matrix with rows (1, 2, 0, 1), (2, 4, 1, 3) and (3, 6, 1, 4). The dimension of the null space of M is (A) 0 (B) 1 (C) 2 (D) 3
Answer: (C). Row 3 = row 1 + row 2. Row 2 − 2 × row 1 = (0, 0, 1, 1), which is non-zero, so rows 1 and 2 are independent and the rank is 2. Nullity = 4 − 2 = 2.
Question 6 - Optimization, NAT, 2 marks
Find the maximum value of f(x) = x³ − 6x² + 9x + 1 on the interval 0 ≤ x ≤ 4.
Answer: 5. f′(x) = 3(x − 1)(x − 3), so the critical points are 1 and 3. f(0) = 1, f(1) = 5, f(3) = 1 and f(4) = 5. The maximum is 5, reached both at x = 1 and at the endpoint x = 4.
Question 7 - Python, NAT, 1 mark
The code runs a = [1, 2, 3], then b = a, then b.append(4), then c = a[:], then c.append(5), then print(len(a) + len(c)). What is printed?
Answer: 9. b is another name for the same list, so a becomes [1, 2, 3, 4]. The slice a[:] makes a new copy, so appending to c does not change a. The lengths are 4 and 5.
Question 8 - Data structures, NAT, 2 marks
The keys 50, 30, 70, 20, 40, 60, 80, 35 are inserted in that order into an empty binary search tree. Taking height as the number of edges on the longest root-to-leaf path, find the height.
Answer: 3. 50 is the root, 30 and 70 are its children, and 20, 40, 60, 80 form the next level. 35 goes left of 50, right of 30, then left of 40. The path 50-30-40-35 has 3 edges.
Question 9 - Databases, MCQ, 2 marks
R(A, B, C, D) has the functional dependencies A → B and B → C. The highest normal form R satisfies is (A) 1NF (B) 2NF (C) 3NF (D) BCNF
Answer: (A). A and D never appear on a right-hand side, and the closure of AD is ABCD, so AD is the only candidate key. B depends on A alone, which is a proper part of the key. That partial dependency breaks 2NF.
Question 10 - Machine learning, NAT, 2 marks
Fit a least-squares line to (1, 2), (2, 3), (3, 5), (4, 6) and give the predicted y at x = 5, rounded off to one decimal place.
Answer: 7.5. The means are 2.5 and 4. The sum of cross-deviations is 3 + 0.5 + 0.5 + 3 = 7 and the sum of squared x-deviations is 5, so the slope is 1.4 and the intercept is 4 − 1.4 × 2.5 = 0.5. The prediction is 0.5 + 1.4 × 5 = 7.5.
Question 11 - Machine learning, MSQ, 2 marks
Select all correct statements. (A) In k-nearest neighbour classification, increasing k generally lowers variance and raises bias. (B) Ridge regression adds an L2 penalty that shrinks coefficients towards zero. (C) k-means always reaches the global minimum of the within-cluster sum of squares. (D) For centred data, the first principal component is the direction of maximum projected variance.
Answer: (A), (B) and (D). (C) is false because k-means converges to a local optimum that depends on the starting centres.
Question 12 - Adversarial search, NAT, 2 marks
A MAX root has three MIN children. Reading from left to right, their leaves are (4, 9, 6), (7, 1, 8) and (3, 10, 5). With alpha-beta pruning from left to right, how many leaves are never evaluated?
Answer: 3. The first MIN node gives 4, so alpha = 4. In the second node, leaf 1 makes its value at most 1, which is not above 4, so leaf 8 is pruned. In the third node, leaf 3 is already not above 4, so leaves 10 and 5 are pruned. That makes 1 + 2 = 3 pruned leaves, and the root value is 4.
Quick answers
How many official GATE DA previous year papers exist
Three: 2024, 2025 and 2026, each with an answer key on the official GATE download page.
Does GATE DA have negative marking
Only on wrong MCQ answers: 1/3 mark for 1-mark MCQs and 2/3 mark for 2-mark MCQs. MSQ and NAT have none.
Are the practice questions on this page from real GATE papers
No. They are original questions written by Myndaq in the official style. Use the official PDFs for real past questions.
