GATE DA 2027 | 25-30 Questions Daily - 02-11-2026

A disease affects 2% of a population. A diagnostic test has sensitivity 90% and specificity 95%. If a randomly selected person tests positive, what is the probability that the person actually has the disease?

Let 𝑋 ∼ Poisson(𝜆), where 𝜆 > 0. Given that 𝑃(𝑋 = 0) = 𝑃(𝑋 = 1), find the value of 𝜆. Answer: ____________________

Let 𝑋1, 𝑋2, … , 𝑋𝑛 be independent observations from an exponential distribution with probability density function 𝑓(𝑥; 𝜆) = 𝜆𝑒−𝜆𝑥 for 𝑥 ≥ 0. What is the maximum likelihood estimator (MLE) of 𝜆?

Two discrete random variables 𝑋 and 𝑌 have the joint probability mass function 𝑃(𝑋 = 𝑥, 𝑌 = 𝑦) = 𝑐 𝑥𝑦 for 𝑥, 𝑦 ∈ {1,2}, and zero otherwise. Find 𝑃(𝑋 = 1 ∣ 𝑌 = 2). Answer: ____________________

Let 𝐴 be a 3 × 3 matrix with eigenvalues 2, 3 and 5. Find det(𝐴2 − 5𝐴 + 6𝐼).

Consider the function 𝑓(𝑥) = 𝑥4 − 4𝑥3 + 4𝑥2. Which statement is correct?

Consider the following Python code: What is the output? (The three print statements produce three lines, in order.)

A binary search tree is constructed by inserting the following keys in order: 40, 20, 60, 10, 30, 50, 70, 25. Find the number of nodes in the left subtree of the root. Answer: ____________________

Consider a directed acyclic graph with vertices {𝐴, 𝐵, 𝐶, 𝐷, 𝐸} and edges 𝐴 → 𝐶, 𝐵 → 𝐶, 𝐶 → 𝐷, 𝐶 → 𝐸. How many distinct topological orderings are possible?

A dataset contains 40 samples: 25 belong to Class A and 15 belong to Class B. Calculate the Gini impurity of the dataset.

Consider the linear regression model 𝑦 = 𝑋𝑤 + 𝜖, where 𝑋 has full column rank. Given 𝑋𝑇𝑋 = ( 4/0 / 0/2 ) , 𝑋𝑇𝑦 = ( 8/6 ), find the second component of the least-squares estimate 𝑤̂. Answer: ____________________

A binary classifier produces the following results: True Positive = 40, False Positive = 10, False Negative = 20, True Negative = 30. What is the F1-score?

Consider the relation Employee(Eid, Dept, Salary). What does the following query return?

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

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

Consider the weighted graph 𝑆 → 𝐴 (1), 𝑆 → 𝐵 (4), 𝐴 → 𝐶 (5), 𝐴 → 𝐷 (2), 𝐷 → 𝐶 (1), 𝐶 → 𝐺 (3), 𝐷 → 𝐺 (7). Uniform Cost Search starts from 𝑆 and stops when the goal 𝐺 is removed from the priority queue. What is the optimal path cost?

Three variables 𝑋, 𝑌, 𝑍 each have the domain {1,2,3}. The constraints are 𝑋 ≠ 𝑌, 𝑌 ≠ 𝑍 and 𝑋 < 𝑍. How many valid assignments exist?

Consider the clauses (𝑃 ∨ 𝑄), (¬𝑃 ∨ 𝑅) and (¬𝑄 ∨ 𝑅). Which statement is logically entailed by these clauses?

A can complete a certain task in 12 days, while B can complete the same task in 18 days. They work together for 4 days, after which A leaves. How many additional days will B require to complete the remaining work?

Let 𝑋 and 𝑌 be independent random variables with 𝑋 ∼ 𝑈(0,1) and 𝑌 ∼ 𝑈(0,1). Given that 𝑋 + 𝑌 < 1, find 𝐸[𝑋 ∣ 𝑋 + 𝑌 < 1].

Let 𝐴 be a real symmetric positive definite matrix. Define 𝑓(𝑥) = 1/2 𝑥𝑇 𝐴𝑥 − 𝑏𝑇𝑥, where 𝑥, 𝑏 ∈ ℝ𝑛. Suppose 𝑥∗ is the global minimizer of 𝑓. Find the value (expression) of ∇𝑓(𝑥∗). Answer: ____________________

Consider the recurrence 𝑇(𝑛) = 𝑇(𝑛 − 1) + 𝑇(𝑛 − 2) + 1 with 𝑇(0) = 0 and 𝑇(1) = 1. Find the value of 𝑇(5). Answer: ____________________

Consider the feature mapping 2 𝑥 1 𝜙(𝑥) = (√2 𝑥1𝑥2). 2 𝑥 2 The corresponding kernel is 𝐾(𝑥, 𝑧) = 𝜙(𝑥)𝑇𝜙(𝑧). Which expression is equal to this kernel?

Consider the relations Student(Sid, Name), Enroll(Sid, Cid) and Course(Cid, Cname). We need to find the names of students who are enrolled in every course. Which relational algebra expression correctly represents this query?

Consider the Bayesian network 𝐴 → 𝐵, 𝐴 → 𝐶, 𝐵 → 𝐷, 𝐶 → 𝐷. Which statement is correct?