GATE DA 2027 | 25-30 Questions Daily - 27-10-2026

Q1HardMCQProbability and Statistics

• (A) 5/6
• (B) 1/6
• (C) 5/11
• (D) 11/36

Q2HardMCQProbability and Statistics

• (A) 3/4
• (B) 2/3
• (C) 1/2
• (D) 1/3

Q3HardMCQProbability and Statistics

• (A) 2/3
• (B) 3/4
• (C) 1
• (D) 1/2

Q4HardMCQProbability and Statistics

• (A) 2/5
• (B) 1/15
• (C) 0
• (D) 1/12

Q5AIR 1 ChallengeMCQProbability and Statistics

• (A) 1/8
• (B) 1 divided by (4 times e)
• (C) 1/2
• (D) 1/4

Q6MediumMCQLinear Algebra

• (A) A has only real eigenvalues
• (B) A has at least one zero eigenvalue
• (C) The trace of A is nonzero
• (D) The columns of A are linearly independent

Q7MediumMCQCalculus and Optimization

• (A) The first derivative of f at c is zero
• (B) The second derivative of f at c is less than zero
• (C) The value f(c) is the global maximum
• (D) f is concave on its entire domain

Q8MediumMCQLinear Algebra

• (A) A must have rank less than n
• (B) A must be a diagonal matrix as written
• (C) A is positive definite
• (D) A must have determinant zero

Q9MediumMCQCalculus and Optimization

• (A) f is strictly increasing on the closed interval from a to b
• (B) f has a local maximum inside the open interval
• (C) f is concave on the closed interval
• (D) The second derivative of f is greater than zero at every point in the open interval

Q10MediumMCQLinear Algebra

• (A) x-star cannot be a local minimum
• (B) x-star is necessarily a strict local minimum
• (C) x-star is necessarily a global minimum
• (D) The second-order test is inconclusive in general

Q11MediumMCQ

• (A) Train on the same data for more epochs without other changes
• (B) Remove the test set from evaluation
• (C) Increase model complexity further
• (D) Use regularization or reduce model complexity

Q12MediumMCQ

• (A) The classifier always produces a linear decision boundary
• (B) The classifier becomes independent of the training data
• (C) The classifier usually has lower bias and higher variance
• (D) The classifier usually has higher bias and lower variance

Q13MediumMCQ

• (A) It prevents all forms of overfitting
• (B) It prevents features with large numerical ranges from dominating distance calculations solely because of their scale
• (C) It guarantees that all features become equally predictive
• (D) It guarantees that every feature becomes normally distributed

Q14MediumMCQ

• (A) A high accuracy necessarily means the model has high positive-class recall
• (B) Precision must equal recall when classes are imbalanced
• (C) Accuracy cannot be calculated for imbalanced datasets
• (D) Predicting every example as negative can yield 99% accuracy while detecting no positive examples

Q15MediumMCQ

• (A) The algorithm is guaranteed to converge faster
• (B) The algorithm becomes equivalent to closed-form optimization
• (C) The loss may oscillate or diverge instead of converging
• (D) The gradient becomes exactly zero after one update

Q16HardMCQProgramming, Data Structures and Algorithms

def f(n):
    if n <= 1:
        return n
    return f(n // 2) + f(n // 2) + n % 2
print(f(11))

• (A) 11
• (B) 6
• (C) 5
• (D) Infinite recursion

Q17HardMCQProgramming, Data Structures and Algorithms

s = []
for x in [3, 1, 4, 1, 5]:
    while s and s[-1] < x:
        s.pop()
    s.append(x)
print(s)

• (A) [3, 5]
• (B) [3, 1, 4, 5]
• (C) [1, 1, 3, 4, 5]
• (D) [5]

Q18HardMCQProgramming, Data Structures and Algorithms

def bsearch(a, x):
    lo, hi = 0, len(a)
    while lo < hi:
        mid = (lo + hi) // 2
        if a[mid] < x:
            lo = mid + 1
        else:
            hi = mid
    return lo
print(bsearch([1, 2, 2, 2, 4, 7], 2))

• (A) 1
• (B) 3
• (C) 2
• (D) -1

Q19HardMCQProgramming, Data Structures and Algorithms

import heapq
h = [7, 2, 5, 1]
heapq.heapify(h)
ans = []
for _ in range(3):
    ans.append(heapq.heappop(h))
print(ans, h[0])

• (A) [1, 2, 5] 7
• (B) [7, 5, 2] 1
• (C) [1, 2, 7] 5
• (D) [1, 2, 5] 5

Q20HardMCQProgramming, Data Structures and Algorithms

from collections import deque
G = {0: [1, 2], 1: [3], 2: [3], 3: []}
q = deque([0])
seen = {0}
order = []
while q:
    u = q.popleft()
    order.append(u)
    for v in G[u]:
        if v not in seen:
            seen.add(v)
            q.append(v)
print(order)

• (A) [0, 1, 3, 2]
• (B) [0, 2, 1, 3]
• (C) [0, 1, 2, 3, 3]
• (D) [0, 1, 2, 3]

Q21MediumMCQDatabase Management and Warehousing

• (A) The schedule is conflict-serializable, equivalent to the serial order T1, then T2, then T3.
• (B) The schedule is conflict-serializable, equivalent to the serial order T2, then T1, then T3.
• (C) The schedule is not conflict-serializable because its precedence graph contains a cycle.
• (D) The schedule is conflict-serializable, equivalent to the serial order T3, then T1, then T2.

Q22MediumMCQDatabase Management and Warehousing

• (A) The schedule is cascadeless and recoverable.
• (B) The schedule is recoverable but not cascadeless.
• (C) The schedule is not recoverable because T2 reads a value written by T1.
• (D) The schedule is strict because all transactions commit in order.

Q23MediumMCQDatabase Management and Warehousing

• (A) The transaction follows basic 2PL because every lock request occurs before commit.
• (B) The transaction violates 2PL because T1 requests a new lock after releasing a lock.
• (C) The transaction follows strict 2PL because it holds the lock on Y until the end.
• (D) The schedule is conflict-serializable only if Z is never accessed by another transaction.

Q24MediumMCQDatabase Management and Warehousing

• (A) Projection of Enroll on SID, divided by projection of Required on CID
• (B) Projection of Enroll on CID, divided by projection of Required on SID
• (C) Projection of Enroll on both SID and CID, divided by projection of Required on CID
• (D) Projection of Enroll on SID, natural-joined with projection of Required on CID

Q25MediumMCQDatabase Management and Warehousing

• (A) A is a candidate key, but B is also necessarily a candidate key.
• (B) A is a candidate key, and B cannot be a candidate key unless B also determines A.
• (C) C must be a candidate key because B determines C.
• (D) No candidate key can be determined from the given dependencies.

Q26HardMCQ

• (A) The heuristic is consistent, so A* is guaranteed to return an optimal path.
• (B) The heuristic is admissible but inconsistent, so permanently closing nodes can cause a suboptimal answer in general.
• (C) The heuristic is not admissible, because the heuristic value of A (which is 3) exceeds the cost of the edge from A to B (which is 1).
• (D) A* returns the path S, A, G, whose cost is 9.

Q27HardMCQ

• (A) All six leaves are evaluated; the root value is 6.
• (B) Leaves 8, 6, 9, 5 and 4 are evaluated; the root value is 6.
• (C) Leaves 8, 6, 5 and 4 are evaluated; the root value is 6.
• (D) Leaves 8, 6, 9 and 5 are evaluated; the root value is 6.

Q28HardMCQ

• (A) Exactly 0.4, because A and B are independent.
• (B) About 0.604, which is the probability that A equals 1 given that C equals 1.
• (C) About 0.525, found by first computing the probability of D=1 for each value of A (summing over B and C), and then applying Bayes' rule.
• (D) Exactly 0.8, because the probability that D equals 1 given C equals 1 is 0.8.

Q29HardMCQ

• (A) X = {1, 2, 3}, Y = {1, 2, 3}, Z = {1, 2, 3}; no values are removed.
• (B) X = {1, 2, 3}, Y = {1, 2, 3}, Z = {2, 3}.
• (C) X = {1, 2, 3}, Y = {1, 2, 3}, Z = {3}.
• (D) X = {3}, Y = {1}, Z = {2, 3}. Answer_Key ANSWER Q. No. Correct Answer _KEY 11 1 D 36 2 2 B 3 3 C 1 1 4 B 15 1 5 D 4 6 D Linearly independent columns 7 A 𝑓′(𝑐) = 0 8 C Positive definite 9 A Strictly increasing 10 D Second-order test inconclusive 11 D Regularization / reduce complexity 12 C Low bias, high variance 13 B Feature scaling 14 D 99% accuracy, zero positive recall possible 15 C Oscillation / divergence 16 A 11 17 D [5] 18 A 1 19 A [1, 2, 5] 7 20 D [0, 1, 2, 3] 21 C Not conflict-serializable 22 B Recoverable, not cascadeless ANSWER Q. No. Correct Answer _KEY 23 B 2PL violation 24 C Relational division 25 B 𝐴 is a candidate key 26 A Consistent heuristic; optimal A* 27 D Leaves 8, 6, 9, 5; root value 6 28 C Approximately 0.525 29 D 𝑋 = {3}, 𝑌 = {1}, 𝑍 = {2,3}