GATE DA 2027 | 25-30 Questions Daily - 09-11-2026

A fair die is rolled twice. Given that the sum of the two outcomes is at least 9, what is the probability that at least one outcome is 6?

A continuous random variable 𝑋 has the probability density function 𝑐 𝑥, 0 ≤ 𝑥 ≤ 2 𝑓(𝑥) = { 𝑋 0, otherwise. Find the value of 𝐸[𝑋]. (The answer may be an integer or a finite decimal.) Answer: ____________________

A statistical test has significance level 𝛼 = 0.05. Which statement correctly describes the meaning of this significance level?

Let 𝑋 and 𝑌 be random variables such that Var(𝑋) = 4, Var(𝑌) = 9 and Var(𝑋 + 𝑌) = 19. Find Cov(𝑋, 𝑌). (The answer may be an integer or a finite decimal.) Answer: ____________________

Let 𝐴 be a 5 × 7 matrix with rank(𝐴) = 4. Let 𝑁(𝐴) denote its null space. Which statement is necessarily true?

A 3 × 3 matrix 𝐴 has eigenvalues 2, −1 and 3. Find det(𝐴2 − 2𝐴 + 𝐼). (Give your answer as an integer or a finite decimal.) Answer: ____________________

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

Let 𝐴 and 𝐵 be real symmetric positive definite matrices of the same order. Which of the following statements are necessarily true?

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

A binary classification problem has two classes 𝐶1 and 𝐶2 with equal prior probabilities. For an observation with features 𝑥1 and 𝑥2, assume conditional independence, with 𝑃(𝑥1 ∣ 𝐶1) = 0.8, 𝑃(𝑥2 ∣ 𝐶1) = 0.5, 𝑃(𝑥1 ∣ 𝐶2) = 0.4, 𝑃(𝑥2 ∣ 𝐶2) = 0.25. Using Naive Bayes, calculate the posterior probability 𝑃(𝐶1 ∣ 𝑥1, 𝑥2). (Give your answer up to 3 decimal places.) Answer: ____________________

A learning algorithm is modified by increasing the model complexity while keeping the training dataset fixed. Which outcome is generally expected?

Consider a linearly separable binary classification dataset trained using a hard-margin SVM. Which statements are necessarily true?

What is the output of the following code?

What is printed by the following code? Answer: ____________________

Consider the following code: What is the time complexity in terms of 𝑛?

What is the output?

Let 𝑅(𝐴, 𝐵, 𝐶, 𝐷) have the functional dependencies 𝐹 = {𝐴 → 𝐵, 𝐵 → 𝐶, 𝐶 → 𝐷}. Which statement is correct?

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

Consider two transactions 𝑇1: 𝑅(𝑋), 𝑊(𝑋) and 𝑇2: 𝑅(𝑋), 𝑊(𝑋). A schedule is conflict- serializable if its precedence graph is acyclic. Which statement is correct?

Which statements about a data warehouse are correct?

Consider a game tree in which the root is a MAX node with two MIN children, 𝐴 and 𝐵. Node 𝐴 has terminal values 8, 3, 6, and node 𝐵 has terminal values 4, 9, 7. Assuming optimal play, what value does the root MAX node obtain?

In A* search, the evaluation function is 𝑓(𝑛) = 𝑔(𝑛) + ℎ(𝑛), where 𝑔(𝑛) is the cost from the start node and ℎ(𝑛) estimates the remaining cost. Which condition guarantees that A* tree search finds an optimal solution, assuming non-negative edge costs?

Consider the formula (𝑃 → 𝑄) ∧ (𝑄 → 𝑅). Which statements are logically entailed by this formula?

Consider the Bayesian network 𝐴 → 𝐵 ← 𝐶. Assume 𝐴 and 𝐶 are marginally independent. 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, what is the one-way distance between A and B?