GATE DA 2027 | 25-30 Questions Daily - 31-10-2026

Let 𝐴 and 𝐵 be two independent events with non-zero probabilities. Which statement is necessarily true?

Which of the following statements about a continuous random variable 𝑋 is correct?

Which statement about an unbiased estimator is correct?

Suppose 𝑋1, 𝑋2, … , 𝑋𝑛 are independent and identically distributed random variables with finite mean 𝜇 and finite, non-zero variance 𝜎2. Which statement correctly describes the Central Limit Theorem?

Let 𝐴 be a 4 × 5 matrix such that rank(𝐴) = 3. Which statement must be true?

A real 3 × 3 matrix 𝐴 has eigenvalues 1, 2 and 3. Define 𝐵 = 𝐴2 − 4𝐴 + 3𝐼. What is the rank of 𝐵?

The Maclaurin expansion of 𝑒𝑥 is 23 𝑥𝑥 𝑥 𝑒= 1 + 𝑥 + + + ⋯ 2! 3! Using this expansion, what is the coefficient of 𝑥3 in 𝑒2𝑥 − 𝑒−𝑥?

Evaluate 2 𝑥 𝑥 𝑒− 1 − 𝑥 − 𝑥→0lim𝑥3 2.

Which statement about Ridge Regression is correct?

Suppose a dataset has binary class labels in equal proportions. A feature perfectly separates the two classes into two pure subsets. What is the information gain of this split?

For a hard-margin SVM, the separating hyperplane is 𝑤𝑇𝑥 + 𝑏 = 0. Which change preserves the same geometric decision boundary and the same classification predictions?

Consider the following array of records, where each record is written as (key, original position): [(3, 𝑎), (1, 𝑏), (3, 𝑐), (2, 𝑑), (1, 𝑒)] After applying a stable sorting algorithm in ascending order of key, which sequence is guaranteed?

Consider an undirected graph with edges (𝐴, 𝐵), (𝐴, 𝐶), (𝐵, 𝐷), (𝐶, 𝐷), (𝐷, 𝐸), (𝐶, 𝐹). BFS starts from vertex 𝐴, and neighbours are explored in alphabetical order. What is the BFS traversal order?

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

Consider an entity set Dependent that is existence-dependent on Employee. Each dependent is identified by the combination of the employee’s primary key and the dependent’s partial key. Which statement is correct?

Consider the relation Sales(EmpID, Dept, Amount): EmpID Dept Amount 1 A 100 2 A 200 3 B 150 4 B 250 5 C 300 6 C 100 Consider the query: Which department(s) will be returned?

Consider the relation 𝑅(𝐴, 𝐵, 𝐶) with the functional dependencies 𝐴 → 𝐵 and 𝐵 → 𝐶. Assume 𝐴 is the candidate key. What is the highest normal form satisfied by 𝑅?

A graph has the following edge costs: 𝑆 → 𝐴: 2, 𝑆 → 𝐵: 3, 𝐴 → 𝐶: 2, 𝐵 → 𝐶: 1, 𝐶 → 𝐺: 3. A heuristic function is given by ℎ(𝑆) = 5, ℎ(𝐴) = 4, ℎ(𝐵) = 3, ℎ(𝐶) = 2, ℎ(𝐺) = 0. Which statement is correct?

Consider a game tree in which the root is a MAX node, its two children are MIN nodes, and each MIN node has three terminal children. The leaf values from left to right are 8, 6, 9, 5, 7, 4. What is the minimax value at the root?

Consider the Bayesian network 𝐴 → 𝐶 ← 𝐵, 𝐶 → 𝐷. Assume all variables are binary and the network has no additional edges. Which statement is generally correct?

Consider the Bayesian network 𝐴 → 𝐶 ← 𝐵, 𝐶 → 𝐷, whose joint distribution factorizes as 𝑃(𝐴, 𝐵, 𝐶, 𝐷) = 𝑃(𝐴) 𝑃(𝐵) 𝑃(𝐶 ∣ 𝐴, 𝐵) 𝑃(𝐷 ∣ 𝐶). We want to compute 𝑃(𝐴 ∣ 𝐷 = 𝑑) by eliminating 𝐵 and 𝐶. Which expression is proportional to the unnormalized posterior over 𝐴?

Consider two nested hypothesis classes ℋ1 ⊂ ℋ2. A learning algorithm selects a model by minimizing the empirical training error within the respective hypothesis class. Which statement is necessarily true about their minimum training errors?

A binary search tree is constructed by inserting the following keys in the given order: 50, 30, 70, 20, 40, 60, 80, 35. What is the inorder traversal after deleting the node 30, using its inorder successor to replace it?

Consider the schedule 𝑆: 𝑟1(𝑋), 𝑟2(𝑌), 𝑤1(𝑌), 𝑟3(𝑋), 𝑤2(𝑋), 𝑤3(𝑌) Which statement is correct?

A person travels from 𝐴 to 𝐵 at a constant speed and returns from 𝐵 to 𝐴 at another constant speed. If the average speed for the entire journey is 40 km/h, and the return speed is 20 km/h greater than the onward speed, find the onward speed in km/h. (Average speed is total distance divided by total time, not the arithmetic mean of the two speeds.)