GATE DA 2027 | 25-30 Questions Daily - 03-11-2026

Let 𝐴, 𝐵 and 𝐶 be three events such that 𝐴 and 𝐵 are independent. Which statement is necessarily correct?

A continuous random variable 𝑋 has a probability density function that is symmetric about zero. Define 𝑌 = 𝑋2. Which statement must hold?

An estimator 𝜃̂ of a parameter 𝜃 is unbiased and has finite variance. Which statement is necessarily correct?

Let 𝐴 be a 5 × 7 matrix with rank(𝐴) = 4. Consider the linear system 𝐴𝑥 = 𝑏. Which statement is necessarily correct?

Let 𝐴 be a real symmetric matrix satisfying 𝐴2 = 𝐴. Which statement must be true?

Consider the function 𝑓(𝑥) = 𝑥4 − 4𝑥2. Which statement correctly describes its critical points?

In binary logistic regression, the predicted probability is 𝑃(𝑌 = 1 ∣ 𝑥) = 𝜎(𝑤𝑇𝑥 + 𝑏), where 𝜎(𝑧) = 1/1+𝑒 −𝑧. Which statement is correct?

Consider the objective function of Ridge Regression, 𝐽(𝑤) =∥ 𝑋𝑤 − 𝑦 ∥ 2/2 + 𝜆 ∥ 𝑤 ∥ 2/2 , where 𝜆 > 0. Which statement is correct?

A model has very low training error but significantly higher test error. Which change is most likely to improve its generalization performance?

Consider a relation 𝑅(𝐴, 𝐵, 𝐶, 𝐷) with the functional dependencies 𝐴 → 𝐵, 𝐵 → 𝐶 and 𝐶 → 𝐷. Which is the candidate key?

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

Consider the table Employee: Dept Salary A 40 A 60 B 50 B 70 B 90 What does the following query return?

Consider the following Python code: What is the output?

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?

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

A* search uses 𝑓(𝑛) = 𝑔(𝑛) + ℎ(𝑛), where 𝑔(𝑛) is the path cost and ℎ(𝑛) is the heuristic estimate. Which condition on ℎ(𝑛) guarantees that A* tree search finds an optimal solution?

A MAX node has two MIN children, 𝐿 and 𝑅. Their terminal leaf values are 𝐿 = (8,3,6) and 𝑅 = (5,9,4). Assuming optimal play, what is the value returned by the MAX node?

Consider the statements: 1. Every student who studies AI knows logic. 2. Some student studies AI. Which conclusion necessarily follows?

A sequence of random variables {𝑋𝑛} converges in probability to a constant 𝑐. Which statement is necessarily implied?

Let 𝑓: ℝ𝑛 → ℝ be twice continuously differentiable. Suppose that at a point 𝑥∗ we have ∇𝑓(𝑥∗) = 0, and the Hessian matrix ∇2𝑓(𝑥∗) is positive semidefinite but singular. Which conclusion is necessarily valid?

Suppose observations 𝑥1, 𝑥2, … , 𝑥𝑛 are independently sampled from a Bernoulli distribution with unknown parameter 𝑝. A model uses the maximum likelihood estimate 𝑝̂. Now every observation is duplicated exactly once, producing a dataset of size 2𝑛. What happens to the MLE?

Consider the relations Student(Sid, Name), Enroll(Sid, Cid) and Required(Cid). Assume Required contains all courses that every student must complete. Which relational algebra expression retrieves the IDs of students enrolled in every required course?

A connected undirected graph 𝐺 = (𝑉, 𝐸) has distinct positive edge weights. Let 𝑇 be its minimum spanning tree (MST). An edge 𝑒 ∉ 𝑇 is added to 𝑇, creating exactly one cycle. Which statement is necessarily correct?

Consider the Bayesian network with edges 𝐴 → 𝐵, 𝐵 → 𝐶, 𝐴 → 𝐷 and 𝐷 → 𝐶. Which statement is necessarily correct under the local Markov property?