GATE DA 2027 | 25-30 Questions Daily - 07-11-2026

A disease affects 10% of a population. A test has sensitivity 90% and specificity 80%. A randomly selected person tests positive. Find the probability that the person actually has the disease. (Answer as a fraction or a percentage.) Answer: ____________________

Let 𝑋 ∼ 𝑁(50, 102). Find 𝑃(40 < 𝑋 < 60), given that 𝑃(−1 < 𝑍 < 1) = 0.6827.

A discrete random variable 𝑋 has the following probability mass function: 𝑋 0 1 2 𝑃(𝑋) 0.2 0.5 0.3 Calculate Var(𝑋). Answer: ____________________

Two random variables 𝑋 and 𝑌 have Var(𝑋) = 4, Var(𝑌) = 9 and Cov(𝑋, 𝑌) = 3. Find their correlation coefficient.

Consider the matrix 1 2 3 𝐴 = (2 4 6). 1 1 1 Find rank(𝐴). Answer: ____________________

A 3 × 3 matrix 𝐴 has eigenvalues 2, 3 and 4. Find the determinant of 𝐴2.

Consider the vectors 𝑣1 = (1,0,1), 𝑣2 = (0,1,1) and 𝑣3 = (1,1,2). Which statement is correct?

Consider the dataset 𝑋 = [1,2,3] and 𝑦 = [2,4,6]. A linear regression model without an intercept, 𝑦̂ = 𝑤𝑥, is fitted. Using the least squares method, find the optimal value of 𝑤. Answer: ____________________

In binary logistic regression, the predicted probability is 𝑃(𝑦 = 1 ∣ 𝑥) = 1+𝑒 1/−𝑤 𝑇𝑥. If 𝑤𝑇𝑥 = 0, what is the predicted probability?

A dataset contains 8 samples: 4 belong to class A and 4 belong to class B. A split creates two child nodes. Child 1 has 3 samples of A and 1 sample of B. Child 2 has 1 sample of A and 3 samples of B. Using entropy with the base-2 logarithm, where 𝐻(𝑆) = − ∑ 𝑝𝑖 𝑖log2𝑝𝑖, calculate the information gain. (Give your answer up to three decimal places.) Answer: ____________________

What is the output of the following Python code? Answer: ____________________

Consider the following code: What is the time complexity?

Which of the following sorting algorithms has worst-case time complexity 𝛩(𝑛log𝑛)?

Consider the table Employee(Eid, Dept, Salary). Which query returns the departments having more than 5 employees?

Consider a relation 𝑅(𝐴, 𝐵, 𝐶, 𝐷) with the functional dependencies 𝐹 = {𝐴 → 𝐵, 𝐵 → 𝐶, 𝐶 → 𝐷}. Find the candidate key of the relation. Answer: ____________________

A transaction transfers ₹500 from account A to account B. The system crashes immediately after deducting ₹500 from A but before adding it to B. Which ACID property ensures that the incomplete transaction does not leave the database in this inconsistent state?

Consider a graph with the following edge costs: 𝑆 → 𝐴 = 2, 𝑆 → 𝐵 = 5, 𝐴 → 𝐵 = 1, 𝐴 → 𝐺 = 7, 𝐵 → 𝐺 = 2. Uniform Cost Search starts from 𝑆 and searches for the goal 𝐺. What is the minimum path cost?

A* search uses 𝑓(𝑛) = 𝑔(𝑛) + ℎ(𝑛). Which condition on the heuristic ℎ(𝑛) guarantees that it never overestimates the actual minimum remaining cost?

Given 𝑃 → 𝑄, 𝑄 → 𝑅 and 𝑃 = True, find the truth value of 𝑅. (Write 1 for True and 0 for False.) Answer: ____________________

Five people P, Q, R, S and T are sitting in a row facing north. The following conditions hold: 1. P sits immediately to the left of Q. 2. R is not sitting at either end. 3. S sits to the right of Q. 4. T sits to the left of R. Who is sitting in the middle position?

Let 𝐴 be a real symmetric 3 × 3 matrix satisfying 𝐴2 = 𝐼. If tr(𝐴) = 3, find det(𝐴). Answer: ____________________

Two models are trained on the same dataset. • Model 𝑀1 has very low training error but high test error. • Model 𝑀2 has slightly higher training error but lower test error. Which conclusion is most appropriate?

A binary tree has 10 leaf nodes and 9 nodes with exactly two children 5 nodes with exactly one child. Find the total number of nodes in the tree. Answer: __________ . Find the total number of nodes in the tree. Answer: ____________________

Consider the schedule 𝑆: 𝑟1(𝑋), 𝑟2(𝑋), 𝑤1(𝑋), 𝑟2(𝑌), 𝑤2(𝑌), 𝑤1(𝑌) Construct its precedence graph and find the number of directed edges in that graph. Answer: ____________________

Consider the Bayesian network 𝐴 → 𝐵 → 𝐶. Which conditional independence statement is necessarily true?