GATE DA 2027 | 25-30 Questions Daily - 06-11-2026

A factory has three machines 𝑀1, 𝑀2 and 𝑀3, producing respectively 20%, 30% and 50% of the total production. Their defective-item probabilities are 1%, 2% and 3%, respectively. An item selected at random is found to be defective. Find the probability that it was produced by machine 𝑀2. Give your answer as a percentage, correct to two decimal places. Answer: ____________________

The joint probability density function of continuous random variables 𝑋 and 𝑌 is 2, 0 < 𝑥 < 𝑦 < 1 𝑓(𝑥, 𝑦) = { 𝑋,𝑌 0, otherwise. Find 𝐸[𝑋 ∣ 𝑌 = 𝑦]. Your answer should be an expression in terms of 𝑦.

A population has mean 𝜇 = 10 and variance 𝜎2 = 25. A random sample of size 100 is drawn independently from this population. Using the Central Limit Theorem, approximately what ‾ < 10.5) is 𝑃(9.5 < 𝑋?

Let 𝑉 = 𝑃2(ℝ) be the vector space of all real polynomials of degree at most 2. Consider the set 𝑆 = {1 + 𝑥, 𝑥 + 𝑥2, 1 + 𝑥2}. Which statement is correct?

A matrix 𝐴 of size 5 × 7 has rank 4. Find the dimension of the solution space of the homogeneous system 𝐴𝑥 = 0. Also, can the system 𝐴𝑥 = 𝑏, where 𝑏 ∈ ℝ5, have a solution for every possible 𝑏? Answer in the format: Nullity = ____, Yes/No.

Let 𝐴 be a real 3 × 3 matrix satisfying (𝐴 − 𝐼)(𝐴 − 2𝐼) = 0. Which statement is necessarily true?

Consider the ridge regression objective 𝐽(𝑤) =∥ 𝑋𝑤 − 𝑦 ∥ 2/2 + 𝜆 ∥ 𝑤 ∥ 2/2 , where 𝜆 > 0. Which statement is necessarily correct?

A binary classifier produces the following results: True Positive = 40, False Positive = 10, False Negative = 20, True Negative = 30. Calculate the F1-score, where 𝐹1 = 2𝑃𝑅/𝑃+𝑅 with 𝑃 the precision and 𝑅 the recall. Give your answer up to three decimal places. Answer: ____________________

Consider the K-means clustering algorithm with squared Euclidean distance. Which statement is correct?

Consider the following Python function: What is the value returned by mystery(5)? Answer: ____________________

Consider the recurrence 𝑇(𝑛) = 2𝑇(𝑛/2) + 𝑛 with 𝑇(1) = 𝛩(1). What is the asymptotic log𝑛 complexity of 𝑇(𝑛)?

Consider a connected, unweighted, undirected graph 𝐺 = (𝑉, 𝐸). Which statement is necessarily correct?

Consider two relations 𝑅(𝐴, 𝐵) = {(1,2), (2,3), (3,4)} and 𝑆(𝐴, 𝐵) = {(2,3), (3,5), (4,6)}. What is the result of 𝑅 − 𝑆?

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

Consider the schedule 𝑆: 𝑟1(𝑋), 𝑟2(𝑋), 𝑤1(𝑋), 𝑟2(𝑌), 𝑤2(𝑌), 𝑤1(𝑌) Which statement is correct?

Consider a search problem where all edge costs are non-negative. Which statement is correct?

A game tree has a MAX root with two MIN children. The left MIN node has leaf values 7, 4, 9, and the right MIN node has leaf values 6, 8, 5. Assuming optimal play by both players, find the minimax value of the root. Answer: ____________________

Consider the propositional formula (𝑃 → 𝑄) ∧ (𝑄 → 𝑅). Which statement is logically entailed by this formula?

A researcher tests 𝐻0: 𝜇 = 50 against 𝐻1: 𝜇 > 50. The population standard deviation is known to be 5. A sample of size 25 gives the sample mean 𝑋‾ = 52. At significance level 𝛼 = 0.05, the critical value for the right-tailed standard normal test is 1.645. Which conclusion is correct?

Let 𝐴 be a real 𝑛 × 𝑛 matrix satisfying 𝐴2 = 𝐴. Which of the following statements is necessarily true?

A dataset is centered and has the covariance matrix 4 0 0 𝛴 = (0 4 0). 0 0 1 PCA is performed, retaining only one principal component. Which statement is correct?

Insert the following keys into an initially empty Binary Search Tree in the given order: 50, 30, 70, 20, 40, 60, 80, 35. Now delete the key 30 using the inorder successor replacement strategy. What is the value at the root of the subtree that was originally rooted at 30, after the deletion? Answer: ____________________

A data warehouse stores sales information with the dimensions Time, Product and Location. A manager wants to analyze the total sales by product and location, regardless of individual dates, and then compare sales across different years. Which operation sequence best represents this analysis?

Consider the Bayesian network 𝐴 → 𝐶 ← 𝐵, 𝐶 → 𝐷. Assume the network is faithful to its graph. Which statement is correct?

A person travels from city A to city B at a speed of 40 km/h and returns from B to A at a speed of 60 km/h. If the total journey takes 5 hours, find the one-way distance between A and B, in kilometres. (Do not use the average-speed formula directly; model the total time carefully.) Answer: ____________________