GATE DA 2027 | 25-30 Questions Daily - 05-11-2026

Let 𝑋 and 𝑌 be independent random variables with finite expectations. Define 𝑍 = 𝐸[𝑋 ∣ 𝑋 + 𝑌]. Which statement is necessarily correct?

Let 𝑋 be a non-negative continuous random variable with finite expectation. Suppose that 𝑃(𝑋 > 𝑠 + 𝑡 ∣ 𝑋 > 𝑠) = 𝑃(𝑋 > 𝑡) for all 𝑠, 𝑡 ≥ 0 for which the conditional probability is defined. Which distribution must 𝑋 follow?

Let 𝑋 and 𝑌 be independent standard normal random variables. Define 𝑈 = 𝑋 + 𝑌 and 𝑉 = 𝑋 − 𝑌. Which statement is correct?

Let 𝐴 be a square matrix satisfying (𝐴 − 𝐼)(𝐴 − 2𝐼) = 0. Which statement must hold?

Let 𝑃 be a real square matrix satisfying 𝑃2 = 𝑃 and 𝑃𝑇 = 𝑃. Which statement is necessarily true?

Consider a regression problem with squared-error loss. The expected prediction error at a fixed input can be decomposed into bias, variance and irreducible noise. Which statement is correct?

A function 𝐾(𝑥, 𝑧) is proposed as a kernel for a Support Vector Machine. Which property is required for it to be a valid positive semidefinite kernel?

Consider an empirical risk minimization problem with an 𝐿2 regularization term. Which statement is most accurate?

Consider the following Python code: Which statement is correct?

A dynamic array doubles its capacity whenever it becomes full. Starting with capacity 1, an element is appended 𝑛 times. What is the amortized time complexity per append operation?

Let 𝐺 be a connected undirected graph with 𝑛 vertices and 𝑛 edges. Which statement is necessarily true?

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

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

A B+ tree has the following properties: • A maximum of 5 children per internal node. • A maximum of 4 keys per leaf node. • A minimum of 2 children for every non-root internal node. • A minimum of 2 keys for every non-root leaf node. Assume the root is not a leaf and all leaves are at the same depth. What is the maximum possible number of data entries in a B+ tree of height 3? (Height is defined as the number of edges from the root to a leaf.) Answer: ____________________

A* search uses 𝑓(𝑛) = 𝑔(𝑛) + ℎ(𝑛), where 𝑔(𝑛) is the path cost so far and ℎ(𝑛) is the estimated remaining cost. Suppose ℎ is admissible but inconsistent. Which statement is correct?

Consider a game tree in which the root is a MAX node. Its two children are MIN nodes, evaluated from left to right. The left MIN node has leaf values 8, 6, 9, and the right MIN node has leaf values 5, 7, 4. Alpha-beta pruning is applied. How many leaf nodes are evaluated in total? Answer: ____________________

Consider the statements: 1. Every student who studies AI knows at least one programming language. 2. Some students who know Python do not study AI. Let 𝑆(𝑥) mean $x$ is a student'', $A(x)$ mean𝑥 studies AI’‘, 𝑃(𝑥) mean $x$ knows represents the first statement?

The price of a product is increased by 20%. Due to a subsequent decrease in sales, the revenue remains unchanged. By what percentage has the number of units sold decreased?

Let {𝑋𝑛} be a sequence of random variables such that 𝑋𝑛 converges to 0 in probability, and sup𝑛𝐸[𝑋 2/𝑛 ] < ∞. Which conclusion is necessarily valid?

Let 𝐴 and 𝐵 be real symmetric positive definite matrices of the same order. Which statement is necessarily true?

Two classifiers ℎ1 and ℎ2 have identical empirical training error on a finite training dataset. Their hypothesis classes have different complexities, with the class containing ℎ1 having lower capacity than the class containing ℎ2. Which conclusion is theoretically most justified?

Consider the activity selection problem: each activity has a start time and a finish time, and the objective is to select the maximum number of mutually compatible activities. Which greedy strategy is guaranteed to produce an optimal solution?

Let a relation 𝑅(𝐴, 𝐵, 𝐶) have the functional dependencies 𝐹 = {𝐴 → 𝐵, 𝐵 → 𝐶}. It is decomposed into 𝑅1(𝐴, 𝐵) and 𝑅2(𝐴, 𝐶). Which statement is correct?

Consider the Bayesian network 𝐴 → 𝐶 ← 𝐵, 𝐶 → 𝐷. Assume all variables are binary and the network is faithful to its graph. Which statement is necessarily correct?

A positive real number 𝑥 satisfies 𝑥 + 1/𝑥 = 3. Find the exact value of 𝑥5 + 1/𝑥 5. (An exact integer value is required, not a decimal approximation.) Answer: ____________________