GATE DA 2027 | 25-30 Questions Daily - 01-11-2026

Two fair dice are rolled. It is known that the sum of the outcomes is an even number. What is the probability that both dice show even numbers?

A random variable 𝑋 has mean 5 and variance 4. Define 𝑌 = 3𝑋2 − 2𝑋. Given that 𝐸[𝑋2] = 29 E[X3]=171 and 𝐸[𝑋4] = 945, calculate Var(𝑌).

Let 𝑋 follow an exponential distribution with parameter 𝜆 > 0. Given that 𝑃(𝑋 > 3) = 𝑒−6, find 𝑃(𝑋 > 5 ∣ 𝑋 > 2).

Evaluate 2 𝑥 ln(1 + 𝑥) − 𝑥 + 𝑥→0lim𝑥3 2.

Let 𝑓(𝑥, 𝑦) = 𝑥2𝑦 + 𝑥𝑦2. Find the value of the mixed partial derivative ∂/∂𝑥 ∂𝑦 𝑓 at the point (1,2).

Consider 𝑓(𝑥, 𝑦) = 𝑥2 + 𝑦2 − 4𝑥 − 6𝑦 + 13. The minimum value of 𝑓(𝑥, 𝑦) over ℝ2 is:

A stack supports three operations: PUSH, POP, and MULTIPOP(𝑘), where MULTIPOP(𝑘) removes at most 𝑘 elements. Starting with an empty stack, consider any sequence of 𝑛 operations. Each element is pushed at most once. What is the maximum total time complexity of the entire sequence, assuming each individual push or pop takes 𝑂(1) time?

Consider a directed weighted graph with edges 𝐴 → 𝐵 (4), 𝐴 → 𝐶 (1), 𝐶 → 𝐵 (2), 𝐵 → 𝐷 (1), 𝐶 → 𝐷 (5). What is the shortest distance from 𝐴 to 𝐷?

Consider two strings 𝑋 = ABCDGH and 𝑌 = AEDFHR. Find the length of their Longest Common Subsequence (LCS).

A logistic regression model predicts 1 𝑃(𝑌 = 1 ∣ 𝑥) = −(𝑤𝑇𝑥+𝑏). 1 + 𝑒 The classification threshold is 0.5. Which condition defines the decision boundary?

Consider two regression models evaluated on the same dataset distribution. • Model A has very low training error but high test error. • Model B has relatively high training error and similarly high test error. Which interpretation is most appropriate?

Consider a one-dimensional dataset: Point Coordinate Class 𝑃1 A 1 𝑃3 B 2 𝑃5 A 3 𝑃8 B 4 𝑃10 B 5 A 3-nearest-neighbour classifier uses Euclidean distance and majority voting. Predict the class (A or B) of the query point 𝑥 = 4. Answer: ____________________

Consider a relation 𝑅(𝐴, 𝐵, 𝐶, 𝐷) with the functional dependencies 𝐴 → 𝐵, 𝐵 → 𝐶, 𝐶 → 𝐷, 𝐷 → 𝐶. Which of the following is the complete set of candidate keys?

Consider the relation Employee(Eid, Dept, Salary): Eid Dept Salary 1 A 40 2 A 60 3 B 80 4 B 20 5 C 50 6 C 70 Execute the query: Which departments will be returned?

Consider the schedule 𝑆: 𝑤1(𝑋), 𝑟2(𝑋), 𝑤2(𝑌), 𝑟3(𝑌), 𝑐1, 𝑐2, 𝑐3 Which statement is correct?

Consider the following graph: 𝑆 → 𝐴 (2), 𝑆 → 𝐵 (5), 𝐴 → 𝐶 (3), 𝐵 → 𝐶 (1), 𝐶 → 𝐺 (2), 𝐴 → 𝐺 (8). The heuristic values are ℎ(𝑆) = 5, ℎ(𝐴) = 4, ℎ(𝐵) = 2, ℎ(𝐶) = 2, ℎ(𝐺) = 0. Assuming A* graph search with proper reopening of nodes when a better path is found, what is the optimal path cost?

A MAX root has two MIN children, 𝐿 and 𝑅. The terminal values, evaluated from left to right, are 𝐿: (7, 9, 5) and 𝑅: (6, 4, 8). Alpha-beta pruning is performed from left to right. How many terminal nodes are pruned?

Consider the knowledge base 𝑃 ⇒ 𝑄, 𝑄 ⇒ 𝑅, and 𝑃. Which statement is necessarily entailed?

Two discrete random variables 𝑋 and 𝑌 have the joint probability mass function 𝑐 (𝑥 + 𝑦), 𝑥, 𝑦 ∈ {1,2,3} 𝑃(𝑋 = 𝑥, 𝑌 = 𝑦) = { 0, otherwise. Find the conditional probability 𝑃(𝑋 = 1 ∣ 𝑋 + 𝑌 = 4).

Let 𝑓 be twice differentiable near zero, with 𝑓(0) = 1, 𝑓′(0) = 2 and 𝑓″(0) = 6. Define 𝑔(𝑥) = 𝑓(𝑥2). Find 𝑔″(0).

Consider the following code: The array is sorted in non-decreasing order and may contain duplicate elements. If the target 𝑥 occurs multiple times, which statement is guaranteed?

Consider the optimization problem 1 min𝑤 [2 ∥ 𝑋𝑤 − 𝑦 ∥ 2/2 + 𝜆 ∥ 𝑤 ∥ 2/2 ], where 𝑋 has full column rank and 𝜆 > 0. Let the optimal solution be 𝑤𝜆. Which statement is always correct?

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

Consider the Bayesian network 𝐴 → 𝐶 ← 𝐵, 𝐶 → 𝐷. Assume 𝐴 and 𝐵 are marginally independent. Which statement is generally correct?

A positive integer 𝑁, when divided by 5, leaves remainder 2. When divided by 7, it leaves remainder 4. What is the smallest positive value of 𝑁 satisfying both conditions?