{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DIVIDE AND CONQUER", "question": "There are n unsorted arrays: A 1 , A 2 , …, A n . Assume that n is odd. Each of A 1 , A 2 , …, A n  contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A 1 , A 2 , …, A n  isGATE CSE 2019 - [2Marks] (MCQ)", "options": ["O(n)", "O(n log n)", "Ω(n2 log n)"], "correct": 3, "explanation": "Since given arrays are not sorted, so the time complexity to find median is O(n) in an unsorted array. You need to apply this algorithm n time to find all medians and again once to find median of all these medians, so total time complexity is, = O(n)*O(n) + O(n)O(n2) + O(n) ≈ O(n2)", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-divide-and-conquer/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DIVIDE AND CONQUER", "question": "Let A be a priority queue for maintaining a set of elements. Suppose A is implemented using a max-heap data structure. The operation Extract-Max(A) extracts and deletes the maximum element from A. The operation Insert(A, key) inserts a new element key in A. The properties of a max-heap are preserved at the end of each of these operationsWhen A contains n elements, which one of the following statements about the worst case running time of these two operations is TRUE?GATE CSE 2023 - [2Marks] (MCQ)", "options": ["Both Extract-Max(A) and Insert(A, key) run in O(1)", "Extract-Max(A) runs in O(1) whereas Insert(A, key) runs in O(n)", "Extract-Max(A) runs in O(1) whereas Insert(A, key) runs in O(logn)"], "correct": 2, "explanation": "In a max-heap, the Extract-Max operation removes the root (maximum) element and then \"heapifies\" down to restore the max-heap property. This heapify operation takes worst-case O(logn) time, where n is the number of elements.The Insert operation inserts a new element at the last position and then \"bubbles up\" (heapify up) to maintain the max-heap property, which similarly takes O(logn) time worst-case.Thus, both operations have a worst-case running time of O(logn). This matches the option:\"Both Extract-Max(A) and Insert(A, key) run in O(logn).\"", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-divide-and-conquer/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DIVIDE AND CONQUER", "question": "Which one of the following sequences when stored in an array at locations A[1],…,A[10] forms a max-heap?GATE CSE 2023 - [1Marks] (MCQ)", "options": ["23,17,10,6,13,14,1,5,7,12", "23,17,14,6,13,10,1,5,7,15", "23,14,17,1,10,13,16,12,7,5"], "correct": 2, "explanation": "For an array A[1..n] representing a heap, each parent at index i must be ≥ its children at indices 2i and 2i+1 (when they exist). Check this for each internal node.Option (B) satisfies all comparisons: 23 ≥ 17,14; 17 ≥ 7,13; 14 ≥ 10,1; 7 ≥ 5,6; 13 ≥ 12; hence it’s a valid max-heap.The other options violate the property: in (A), parent 10 has child 14 (>10); in (C), parent 6 has child 7 and parent 13 has child 15 (>parents); in (D), parent 1 has children 12 and 7 (>1).", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-divide-and-conquer/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DIVIDE AND CONQUER", "question": "Let P be an array containing n integers. Let t be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of n elements. Which one of the following choices is correct?GATE CSE 2021,SET1 - [1Marks] (MCQ)", "options": ["t > 3⌈n/2⌉ and t ≤ 2n−2", "t>2n−2", "t > ⌈log2(n)⌉ and t ≤ n"], "correct": 1, "explanation": "\"Using divide and conquer min-max algo, WC number of comparisons = 3(n/2)−2.\"It further explains: \"Hence 3(n/2)−2 will lie in the range of n to 3⌈n/2⌉.\"\"Hence option (a) is the correct answer.\"", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-divide-and-conquer/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DYNAMIC PROGRAMMING", "question": "The weight of a sequence a0 , a1 , …, an–1  of real numbers is defined as a0  + a1 / 2 + …+ a n–1 /2n–1 . A subsequence of a sequence is obtained by deleting some elements from the sequence, keeping the order of the remaining elements the same. Let X denote the maximum possible weight of a subsequence of a0 , a1 ,..., an-1 . Then X is equal toGATE CSE 2010 - [2Marks] (MCQ)", "options": ["max(Y, a0 + Y)", "max(Y, a0 + 2Y)", "a0 + Y/2"], "correct": 2, "explanation": "Do not include a0 in the subsequence: then the maximum possible weight will be equal to maximum possible weight of a subsequence of {a1, a2, …..an} which is represented by Y. Include a0: then maximum possible weight will be equal to a0 + (each number picked in Y will get divided by 2) a0 + Y/2. Here you can note that Y will itself pick optimal subsequence to maximize the weight. Final answer will be Max (Case1, Case2) i.e. Max (Y, a 0  + Y/2). Hence (B) is correct.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-dynamic-programming/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DYNAMIC PROGRAMMING", "question": "Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt.  If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed is:GATE CSE 2011 - [2Marks] (MCQ)", "options": ["248000", "44000", "25000"], "correct": 3, "explanation": "Multiply as (M 1  × (M 2  × M 3 )) × M 4 Total number of scalar multiplications is= qrs + psq + pst= 100*20*5+10*100*5+10*5*80= 10000 + 5000 + 4000 = 19000", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-dynamic-programming/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DYNAMIC PROGRAMMING", "question": "An algorithm to find the length of the longest monotonically increasing sequence of numbers in an array A[0: n - 1] is given below. Let L; denote the length of the longest monotonically increasing sequence starting at index i in the array. Initialize L n-1  = 1. For all i such that 0 ≤ i ≤ n – 2$$ begin{aligned} &L_i = & begin{cases} 1 + L_{i+1} & ext{if } A[i] < A[i + 1] 1 & ext{otherwise} end{cases} end{aligned}$$Finally the length of the longest monotonically increasing sequence is Max (L 0 , L 1 ,……., L n-1 ). Which of the following statements is TRUE?GATE CSE 2011 - [1Marks] (MCQ)", "options": ["The algorithm has a linear complexity and uses branch and bound paradigm", "The algorithm has a non-linear polynomial complexity and uses branch and bound paradigm", "The algorithm uses divide and conquer paradigm."], "correct": 1, "explanation": "The algorithm computes the length of the longest increasing sequence starting from each index by building the solution for smaller subproblems (from the end towards the beginning) and reusing previously computed results, which is the essence of dynamic programming. Each computation at index i depends on the result for index i+1, and all results are stored and reused.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-dynamic-programming/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DYNAMIC PROGRAMMING", "question": "The Floyd-Warshall algorithm for all-pair shortest paths computation is based onGATE CSE 2016,SET2 - [1Marks] (MCQ)", "options": ["Greedy paradigm", "Divide-and-Conquer paradigm.", "Neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm"], "correct": 3, "explanation": "The Floyd–Warshall algorithm systematically updates the shortest paths between all pairs of vertices by considering each vertex as an intermediate point, building optimal solutions from previously computed subproblems, which is the essence of dynamic programming.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-dynamic-programming/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DYNAMIC PROGRAMMING", "question": "Assume that multiplying a matrix G 1 of dimension p×q with another matrix G 2 of dimension q × r requires scalar multiplications. Computing the product of  matrices G1 G2 G3 ……Gn can be done by parenthesizing in different ways. Define Gi Gi+1 as an explicitly computed pair for a given parenthesization if they are directlymultiplied. For example, in the matrix multiplication chain G1 G2 G3 G4 G5 G6 using parenthesization (G1 (G2 G3 )) (G4 (G5 G6 )).G2 G3 and G5 G6  are the only explicitly computed pairs. Consider a matrix multiplication chain F1 F2 F3 F4 F5 , where matrices F1 F2 F3 F4 F5  are of dimensions 2 × 25, 25 × 3, 3 × 16, 16 × 1 and 1 × 1000, respectively. In the parenthesization of F1 F2 F3 F4 F5  that minimizes the total number of scalar multiplications, the explicitly computed pairs is/are:GATE CSE 2018 - [2Marks] (MCQ)", "options": ["F1 F2 and F3 F4", "F2 F3 only", "F1 F2 and F4"], "correct": 3, "explanation": "No. of ways of multiplying the chain of matrices  Where m = no. of multiplications (not matrices)6C3 / 3+1$$ begin{aligned} &(A imes (B imes (C imes D))) & quad downarrow & 1750 & quad downarrow &((A imes (B imes C) imes D)) & quad downarrow & 2000 & quad downarrow &((A imes B) imes (C imes D)) & quad downarrow & 3000 end{aligned} quad quad quad quad quad begin{aligned} &(A imes (B imes C) imes D) & quad downarrow & 1500 & quad downarrow &(((A imes B) imes C) imes D) & end{aligned}$$Total number of scalar multiplications are 48 + 75 + 50 + 2000 = 2173 and optimal parenthesis is ((F1(F2(F3 F4))) F5). Asconcluded, F3, F4 are explicitly computed pairs.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-dynamic-programming/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | DYNAMIC PROGRAMMING", "question": "Consider a table T, where the elements T[i][j], 0 <= i, j <= n, represent the cost of the optimal solutions of different subproblems of a problem that is being solved using a dynamic programming algorithm. The recursive formulation to compute the table entries is as follows: T[0][k] = T[k][0] = 1 for k = 0, 1, 2, …, n T[i][j] = 2T[i−1][j]+3T[i][j−1] for 1 ≤ i, j ≤ n Consider the following two algorithms to compute entries of T. Assume that for both the algorithms, for all 0 ≤ i, j ≤ n, T[i][j] has been initialized to 1. Algorithm B₁: For i = 1 to n For j = 1 to n T[i][j] = 2T[i − 1][j] + 3T[i][j − 1] Algorithm B₂: For s = 2 to 2n For i = 1 to n For j = 1 to n If (i + j == s) T[i][j] = 2T[i − 1][j] + 3T[i][j − 1] Algorithm Bₖ, k ∈ {1, 2}, is said to be correct if and only if it calculates the correct values of T[i][j], for all 0 ≤ i, j ≤ n, as per the recursive formulation, at the end of the execution of the algorithm Bₖ. Which one of the following statements is true? [GATE 2026 || SET-2 MCQ || 2-mark]", "options": ["Algorithm B1 is correct, but algorithm B2 is incorrect", "Algorithm B2 is correct, but algorithm B1 is incorrect", "Both algorithms B1 and B2 are incorrect"], "correct": 1, "explanation": "In dynamic programming, an algorithm is correct if it calculates T[i][j] only after its dependencies T[i−1][j] and T[i][j−1] have been computed. Algorithm B₁ (Row-major):When computing T[i][j], T[i−1][j] (above) is already computed in the previous row, and T[i][j−1] (left) is already computed in the current row. Correct statement. Algorithm B₂ (Diagonal / Sum-based): For cell (i, j), both dependencies (i−1, j) and (i, j−1) have sum s−1, where s = i + j. Since s increases sequentially, all required cells are computed earlier. Correct statement.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-dynamic-programming/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | GREEDY METHOD", "question": "G = (V, E ) is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE?I. If e is the lightest edge of some cycle in G, then every MST of G includes eII. If e is the heaviest edge of some cycle in G, then every MST of G excludes eGATE CSE 2016,SET1 - [2Marks] (MCQ)", "options": ["I only", "both I and II", "neither I and II"], "correct": 2, "explanation": "Here in below Graph G in (Cycle 3, 4, 5) 3 is the lightest edge and still it is not included in MST..Statement 2:- True by[ Cycle property of MST] : (in above Graph G 1 - 2- 3  is a cycle and 3 is the heaviest edge) If heaviest edge is in cycle then we will always exclude that because cycle is there means, we can have other choice of low cost edges. (If edge weights are not distinct even the heaviest edge can be part of the MST and here in question distinct edge weight is clearly mentioned)So, option B is answer.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-greedy-method/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | GREEDY METHOD", "question": "Let G be a weighted directed acyclic graph with m edges and n vertices. Given G and a source vertex s in G, which one of the following options gives the worst case time complexity of the fastest algorithm to find the lengths of shortest paths from s to all vertices that are reachable from s in G? [GATE 2026 || SET-2 MCQ || 2-mark]", "options": ["Θ(m + n log(n))", "Θ(nm)", "Θ(n³)"], "correct": 1, "explanation": "Θ(m + n) Since the graph is a Directed Acyclic Graph (DAG), the shortest paths from source s can be found using: 1. Topological sorting of the graph → Θ(m + n) 2. Relaxing all edges once in topological order → Θ(m) Total time complexity = Θ(m + n).No priority queue is needed (unlike Dijkstra’s algorithm), because the graph has no cycles and the topological order guarantees correct relaxation order. Therefore, the worst-case time complexity of the fastest algorithm is: Θ(m + n)", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-greedy-method/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | GREEDY METHOD", "question": "$$ begin{aligned} & ext{Let } G(V,E) ext{ be an undirected, edge-weighted graph with integer weights. The weight of a path is the sum of the weights of the edges in that path. The length of a path is the number of edges in that path.Let } s in V ext{ be a vertex in } G ext{. For every } u in V ext{ and for every } k ge 0 ext{, let } d_k(u) ext{ denote the weight of a shortest path (in terms of weight) from } s ext{ to } u ext{ of length at most } k ext{. If there is no path from } s ext{ to } u ext{ of length at most } k ext{, then } d_k(u) = infty ext{.Consider the statements:} & ext{S1: For every } k ge 0 ext{ and } u in V, d_{k+1}(u) le d_k(u). & ext{S2: For every } (u,v) in E ext{, if } (u,v) ext{ is part of a shortest} & qquad ext{path (in terms of weight) from } s ext{ to } v ext{, then for} & qquad ext{every } k ge 0, d_k(u) le d_k(v). & ext{Which one of the following options is correct?} end{aligned}$$[GATE 2026 || SET-1 MCQ || 2-mark]", "options": ["Only S2 is true", "Both S1 and S2 are true", "Neither S1 nor S2 is true"], "correct": 1, "explanation": "When we increase k to k+1, we allow more paths (paths of length ≤ k are a subset of paths of length ≤ k+1). Taking minimum over a larger set cannot increase the value. So, dₖ₊₁(u) ≤ dₖ(u). Suppose edge (u, v) is part of a shortest path from s to v. That does not guarantee dₖ(u) ≤ dₖ(v) for every k. Counterexample (with negative weight): s — u has weight 100 u — v has weight −200 Shortest path to v is: s → u → v = −100 For k = 2: d₂(u) = 100 d₂(v) = −100 So, d₂(u) ≤ d₂(v) becomes 100 ≤ −100 → FALSE. Hence S2 is not always true", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-greedy-method/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | GREEDY METHOD", "question": "Let G be any undirected graph with positive edge weights, and T be a minimum spanning tree of G. For any two vertices, u and v, let d1(u,v) and d2(u,v) be the shortest distances between u and v in G and T, respectively. Which ONE of the options is CORRECT for all possible G, T, u and v?GATE CSE 2025,SET1 - [1Marks] (MCQ)", "options": ["d1(u, v) = d2(u, v)", "d1(u, v) ≥ d2(u, v)", "d1(u, v) != d2(u, v)"], "correct": 2, "explanation": "MST distance from u to v may not be the shortest path distance from u to v.Shortest path distance from u to v i.e. d1 (u, v) ≤ MST path distance from u to v i.e. d2(u, v)", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-greedy-method/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | GREEDY METHOD", "question": "Let G be an edge-weighted undirected graph with positive edge weights. Suppose a positive constant α is added to the weight of every edge.Which ONE of the following statements is TRUE about the minimum spanning trees (MSTs) and shortest paths (SPs) in G before and after the edge weight update?GATE CSE 2025,SET2 - [2Marks] (MCQ)", "options": ["Every MST remains an MST, and every SP remains an SP.", "MSTs need not remain MSTs, and every SP remains an SP", "MSTs need not remain MSTs, and SPs need not remain SPs"], "correct": 3, "explanation": "Every MST will remain an MST because if we use Kruskal's Algorithm, adding alpha to each edge weight will not change the ordering of the edges, and the tree will be formed as it is. for shortest paths, consider an undirected graph of 4  vertices v1, v2, v3, v4. The edge set of this graph is defined as {[v1,v2], [v2,v3], [v3,v4] and [v1,v4]}. Let edge weight of [v1,v2], [v2,v3], [v3,v4] and [v1,v4] be x1, x2, x3 and x4 respectively with the condition: x1+x2+x3 = x4 - 1. Thus originally the shortest path between v1 and v4 is x1+x2+x3. However after adding positive constant to each edge, the shortest path between v1 and v4 is x4 + alpha.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-greedy-method/"}
{"subject": "Data Structures And Algorithms", "topic": "GATE 2026 Algorithms PYQs | GREEDY METHOD", "question": "Let G be a connected undirected weighted graph. Consider the following two statements. S 1 : There exists a minimum weight edge in G which is present in every minimum spanning tree of G.S 2 : If every edge in G has distinct weight, then G has a unique minimum spanning tree.Which one of the following options is correct?GATE CSE 2021,SET2 - [2Marks] (MCQ)", "options": ["S 1 is true and S 2 is false.", "Both S 1 and S 2 are true.", "Both S 1 and S 2 are false."], "correct": 2, "explanation": "S1 : consider the graph.ansBut the minimum weight edge BC in G is not present. So, the S 1 is a false statement. S 2 : In any undirected graph G, distinct edge weights means Unique MST. So, the S 1 is false and S 2 is true.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-algorithms-pyqs-greedy-method/"}
{"subject": "Mathematics General", "topic": "GATE 2026 Engineering Mathematics PYQs | Linear Algebra", "question": "Consider 4 × 4 matrices with their elements from {𝟎, 𝟏}. What is the number of such matrices with even number of 𝟏s in every row and every column? [ MCQ || GATE 2026 Set-1 || 1 Marks]", "options": ["1025", "1023", "255"], "correct": 1, "explanation": "We need 4×4 matrices with entries {0,1} such that each row and each column has even number of 1s. Think in mod 2 (even = sum = 0). Step 1: First 3 rows and 3 columns can be filled freely. So we can choose a 3×3 block arbitrarily. Number of ways: 29 Step 2: Now fix the last column. For each of the first 3 rows, choose the 4th element so that row sum becomes even. So last column entries are uniquely determined for first 3 rows. Step 3: Fix the last row. For each of first 3 columns, choose entry so column sum becomes even. Again uniquely determined. Step 4: The bottom-right element is automatically fixed (both row and column condition match). So total number of valid matrices: 29=512", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-engineering-mathematics-pyqs-linear-algebra/"}
{"subject": "Mathematics General", "topic": "GATE 2026 Engineering Mathematics PYQs | Linear Algebra", "question": "For 𝑛 > 1, the maximum multiplicity of any eigenvalue of an 𝑛 × 𝑛 matrix with elements from ℝ is [ MCQ || GATE 2026 Set-1 || 1 Marks]", "options": ["n-1", "1", "n+1"], "correct": 1, "explanation": "Multiplicity of an eigenvalue means how many times it appears (algebraic multiplicity). For an n×n matrix, the characteristic polynomial has degree n, so total multiplicities of all eigenvalues add up to n. Maximum possible multiplicity of a single eigenvalue occurs when all eigenvalues are same (e.g., identity matrix or scalar matrix). So maximum multiplicity = n.", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-engineering-mathematics-pyqs-linear-algebra/"}
{"subject": "Mathematics General", "topic": "GATE 2026 Engineering Mathematics PYQs | PROBABILITY & STATISTICS", "question": "An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another ball of the same color is put back in the urn. The probability that there are equal number of red and blue balls after two steps is [MCQ || GATE-2026 Set-1 || 2-marks]", "options": ["1/4", "1/2", "2/3"], "correct": 2, "explanation": "$$ begin{aligned} & ext{After 2 draws we will have total of 4 balls in the} & ext{urn. In our case we want equal number of Red and} & ext{Blue balls i.e. } 2R , & ,2B & ext{So one draw should be Blue and another should be} & ext{Red, the 2 sequence can be } RB ext{ & } BR & qquad o P(RB) = P( ext{`` first is '' } R) & qquad qquad qquad qquad imes P( ext{`` second is '' } B & qquad qquad qquad qquad mid ext{`` first is '' } R) & qquad qquad qquad quad = left( frac{1}{2} ight) left( frac{1}{3} ight) = frac{1}{6} & qquad o P(BR) = ext{`` same case as '' } P(RB) = frac{1}{6} & ext{Total Probability } P( ext{ Equal } R ext{ & } B) = frac{1}{6} + frac{1}{6} = frac{1}{3} end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-engineering-mathematics-pyqs-probability-statistics/"}
{"subject": "Mathematics General", "topic": "GATE 2026 Engineering Mathematics PYQs | PROBABILITY & STATISTICS", "question": "$$ begin{aligned} & ext{The probability density function } f(x) ext{ of a random} & ext{variable } X ext{ which takes real values is} & qquad qquad f(x) = frac{1}{3 sqrt{2 pi}} exp left(- frac{x^2}{18} ight), ; x in (- infty, + infty) & ext{Which one of the following statements is correct} & ext{about the random variable } X ext{ ?} extbf{[MCQ || GATE-2026 Set-2 || 1-marks]} end{aligned}$$", "options": ["X is an exponential random variable", "X is a Poisson random variable", "X is a uniform random variable"], "correct": 2, "explanation": "$$ begin{aligned} & ext{Poisson is Discrete, eliminates Poisson} & ext{immediately.} & ext{Now check Domain:} & quad bullet quad ext{Exponential PDF: } f(x) = lambda e^{(- lambda x)} ext{ for } x ge 0 & qquad implies ext{eliminates Exponential (question says } x in (- infty, + infty) ext{)} & quad bullet quad ext{Uniform: defined on } (a, b) implies ext{finite interval} & qquad implies ext{eliminates Uniform} & quad bullet quad ext{Normal: only distribution that lives on } (- infty, + infty) end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-engineering-mathematics-pyqs-probability-statistics/"}
{"subject": "Operating Systems", "topic": "GATE 2026 OS PYQs | PROCESSES AND THREADS", "question": "Which one of the following CPU scheduling algorithms cannot be preemptive? [GATE 2026 || SET-2 MCQ || 1-mark]", "options": ["Shortest Remaining Time First (SRTF) Scheduling", "Round Robin Scheduling", "Priority Scheduling"], "correct": 2, "explanation": "FCFS cannot be pre-emptive", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-2026-os-pyqs-processes-and-threads/"}
{"subject": "Digital Logic", "topic": "GATE || Digital Logic || PYQ || 2026 || Module 2: Logic Gates", "question": "Which one of the following options is not a property of Boolean Algebra? [GATE || 2026|| SET2 ||MCQ ||1-mark]", "options": ["a + b = b + a", "a + a' = 1", "a · b = b · a"], "correct": 2, "explanation": "$$ begin{aligned} & ext{(a) } a + b = b + a & ext{This is the } extbf{Commutative Law of OR} ext{. So (a) is} & extbf{correct.} & ext{(b) quad Complement law states:} & a + a' = 1 & a cdot a' = 0 & ext{So (b) } mathbf{a cdot a' = 1} ext{ is incorrect.} & ext{(c) quad } a + a' = 1 . & ext{This is the Complement Law (OR form). So } mathbf{(c)} ext{ is} & extbf{correct.} & ext{(d) } a cdot b = b cdot a & ext{This is the Commutative Law of AND. So, option} & ext{(d) is correct.} end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-digital-logic-pyq-2026-module-2-logic-gates/"}
{"subject": "Digital Logic", "topic": "GATE || Digital Logic || PYQ || 2026 || Module 5:Sequential Circuits", "question": "Consider a 2-bit saturating up/down counter that performs the saturating up count when the input P is 0, and the saturating down count when P is 1. The Next State table of the counter is as shown. The counter is built as a synchronous sequential circuit using D flip-flops  [GATE|| 2026 MCQ || Set-1 || 2-mark ]Input (P)Current StateCurrent StateNext StateNext StateQ₁Q₀Q₁⁺Q₀⁺0000100110010110111110000101001100111110", "options": ["$$ begin{aligned} D_1 &= PQ_1 + bar{P}Q_0 + Q_1Q_0 D_0 &= PQ_0 + bar{P}Q_1 + Q_1 overline{Q_0} end{aligned}$$", "$$ begin{aligned} D_1 &= bar{P} bar{Q}_1 + bar{P}Q_0 + Q_1Q_0 D_0 &= bar{P}Q_0 + bar{P}Q_1 + Q_1 bar{Q}_0 end{aligned}$$", "$$ begin{aligned} D_1 &= P{Q_1} + bar{P}Q_0 + Q_1{Q_0} D_0 &= P overline{Q_0} + bar{P}Q_1 + Q_1 overline{Q_0} end{aligned}$$"], "correct": 2, "explanation": "$$ begin{aligned} & ext{For a D flip-flop, the characteristic equation is} & Q_{ ext{next}} = D ext{. Therefore, the required inputs } D_1 ext{ and } D_0 & ext{are exactly equal to the next state values } Q1_{ ext{ _next}} ext{ and} & Q0_{ ext{ _next}} ext{ respectively.} & ext{Let's extract the min-terms from the provided Next} & ext{State table and simplify them using Boolean algebra} & ext{(or K-maps). The variables are } P, Q_1, ext{ and } Q_0. & ext{1. qquad Solving for } D_1 (Q1_{ ext{ _next}}) & ext{Looking at the } Q1_{ ext{ _next}} ext{ column, the output is 1 for the} & ext{following input combinations of } P, Q_1, Q_0 ext{:} & 0, 0, 1 longrightarrow m1 & 0, 1, 0 longrightarrow m2 & 0, 1, 1 longrightarrow m3 & 1, 1, 1 longrightarrow m7 & ext{The boolean expression in sum-of-min-terms form} & ext{is: } D1 = ext{Sum of min-terms }(1, 2, 3, 7) & ext{Now, let's group these min-terms to simplify the} & ext{expression:} & bullet ext{Group 1 }(m1 ext{ and } m3) ext{: } P'Q_1'Q_0 + P'Q_1Q_0 = P'Q_0 & bullet ext{Group 2 }(m2 ext{ and } m3) ext{: } P'Q_1Q_0' + P'Q_1Q_0 = P'Q_1 & bullet ext{Group 3 }(m3 ext{ and } m7) ext{: } P'Q_1Q_0 + PQ_1Q_0 = Q_1Q_0 & ext{Combining these simplified groups gives us the final} & ext{expression for } D1 ext{: } D1 = P'Q_1 + P'Q_0 + Q_1Q_0 & ext{2. qquad Solving for } D_0 (Q0_{ ext{ _next}}) & ext{Looking at the } Q0_{ ext{ _next}} ext{ column, the output is 1 for the} & ext{following input combinations of } P, Q_1, Q_0 ext{:} & bullet 0, 0, 0 longrightarrow m0 & bullet 0, 1, 0 longrightarrow m2 & bullet 0, 1, 1 longrightarrow m3 & bullet 1, 1, 0 longrightarrow m6 & ext{The boolean expression in sum-of-min-terms form} & ext{is: } D0 = ext{Sum of min-terms }(0, 2, 3, 6) & ext{Now, let's group these min-terms to simplify:} & ext{Group 1 }(m0 ext{ and } m2) ext{: } P'Q_1'Q_0' + P'Q_1Q_0' = P'Q_0' & ext{Group 2 }(m2 ext{ and } m3) ext{: } P'Q_1Q_0' + P'Q_1Q_0 = P'Q_1 & ext{Group 3 }(m2 ext{ and } m6) ext{: } P'Q_1Q_0' + PQ_1Q_0' = Q_1Q_0' & ext{Combining these simplified groups gives us the final} & ext{expression for } D_0 ext{: } D_0 = P'Q_0' + P'Q_1 + Q_1Q_0' end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-digital-logic-pyq-2026-module-2sequential-circuits/"}
{"subject": "Digital Logic", "topic": "GATE || Digital Logic || PYQ || 2026 || Module 3: Minimization", "question": "$$ begin{aligned} & ext{Consider the following 4-variable Boolean} & ext{function} & F(A, B, C, D) = Sigma m(0, 1, 2, 3, 8, 9, 10, 11) & ext{Consider A as MSB, D as LSB. Which one of the} & ext{following options represents the minimal sum of} & ext{products form for the above function?} & ext{Note: } + ext{ is OR operation, } cdot ext{ is AND operation, } ' ext{ is} & ext{NOT operation} end{aligned}$$[GATE || 2026|| SET2 ||MCQ ||2-mark]", "options": ["A' + B' + C' + D'", "A'·B' + A·B", "A'"], "correct": 2, "explanation": "K-map", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-digital-logic-pyq-2026-module-3-minimization/"}
{"subject": "Digital Logic", "topic": "GATE || Digital Logic || PYQ || 2026 || Module 4: Combinational Circuit", "question": "Consider a digital display system (DDS) shown in the figure that displays the contents of register X. A 16- bit code word is used to load a word in X, either from S or from R. S is a 1024-word memory segment and R is a 32-word register file. Based on the value of mode bit M, T selects an input word to load in X. P and Q interface with the corresponding bits in the code word to choose the addressed word. Which one of the following represents the functionality of P, Q, and T? [GATE || 2022 MCQ || 2-mark ]DDS", "options": ["P is 10:1 multiplexer;Q is 5: 1 multiplexer; T is 2: 1 multiplexer", "P is 10: 210 decoder; Q is 5: 25 decoder;T is 2: 1 encoder", "P is 1: 10 de-multiplexers; Q is 1: 5 demultiplexers; T is 2: 1 multiplexer"], "correct": 3, "explanation": "$$ begin{aligned} & S = 1024 ext{ words } (2^{10}) longrightarrow ext{needs 10-bit address} longrightarrow & ext{use } 10 longrightarrow 2^{10} ext{ decoder (P)} & R = 32 ext{ words} longrightarrow ext{needs 5-bit address} longrightarrow ext{use } 5 longrightarrow & 2^5 ext{ decoder (Q)} & M ext{ selects between } S ext{ and } R longrightarrow ext{use 2:1 multiplexer} & ext{(T)} & ext{Final:} & P = 10 : 2^{10} ext{ decoder} & Q = 5 : 2^5 ext{ decoder} & T = 2 : 1 ext{ multiplexer} end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-digital-logic-pyq-2026-module-4-combinational-circuit/"}
{"subject": "Digital Logic", "topic": "GATE || Digital Logic || PYQ || 2026 || Module 1: Number System", "question": "Consider the real valued variables X, Y and Z represented using the IEEE -754 single precision floating-point format. The binary representations of X and Y in hexadecimal notation are as follows: X: 35C00000 Y: 34A00000 Let Z = X + Y. Which one of the following is the binary representation of Z, in hexadecimal notation? [GATE ||2026 SET1 || MCQ || 1-mark]", "options": ["35C80000", "35CD0000", "35EC0000"], "correct": 3, "explanation": "$$ begin{aligned} & ext{X = 35C00000} & ext{Binary: 0 01101011 10000000000000000000000} & ext{Exponent = 107 - 127 = -20} & ext{X = } 1.100000 dots imes 2^{(-20)} & ext{Y = 34A00000} & ext{Binary: 0 01101001 01000000000000000000000} & ext{Exponent = 105 - 127 = -22} & ext{Y = } 1.010000 dots imes 2^{(-22)} & ext{Align Y to exponent -20:} & ext{Y = } 0.010100 dots imes 2^{(-20)} & ext{Add mantissas:} & quad 1.100000 & ext{+} 0.010100 & ext{=} 1.110100 & ext{Z = } 1.110100 imes 2^{(-20)} & ext{New exponent = -20 + 127 = 107} & ext{Binary exponent = 01101011} & ext{Final binary:} & ext{0 01101011 11010000000000000000000} & ext{Hex = 35E80000} end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-digital-logic-pyq-2026/"}
{"subject": "Operating Systems", "topic": "GATE || OS || Memory", "question": "Let the page fault service time to 10 ms in a computer with average memory access time being 20 ns. If one page fault is generated for every 106 memory accesses, what is the effective access time for the memory?GATE CSE 2011 - [1Marks] (MCQ)", "options": ["21 ns", "23 ns", "35 ns"], "correct": 2, "explanation": "ansans", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-os-memory/"}
{"subject": "Operating Systems", "topic": "GATE || OS || Memory", "question": "Consider a demand paging memory management system with 32-bit logical address, 20-bit physical address, and page size of 2048 bytes. Assuming that the memory is byte addressable, what is the maximum number of entries in the page table?(MCQ-SET-1-2025) - 1Marks", "options": ["220", "222", "224"], "correct": 1, "explanation": "Let's break down the problem:32-bit logical address: This means the address space is 232 bytes.20-bit physical address: This means the physical memory is 220 bytes.Page size: 2048 bytes, which is 211 bytes (since 2048 = 211).Now, to calculate the maximum number of entries in the page table, we need to determine the number of pages and how many frames are available in physical memory.Number of pages: The total size of the logical address space is 232 bytes. With a page size of 211 bytes, the number of pages is: 232/211 =221 pages.Number of frames: The total physical memory size is 220 bytes. With a page size of 211 bytes, the number of frames is: 220/211 = 29 frames.Each page table entry holds the physical address of a frame. Since the physical address is 20 bits, each page table entry requires 20 bits (or 5 bytes) to store the frame number.Therefore, the maximum number of entries in the page table corresponds to the number of pages, which is 221.Thus, the correct answer is: 221", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-os-memory/"}
{"subject": "Operating Systems", "topic": "GATE || OS PYQ IO", "question": "A file system with 300 Gbyte disk uses a file descriptor with 8 direct block addresses, 1 indirect block address and 1 doubly indirect block address. The size of each disk block is 128 Bytes and the size of each disk block address is 8 Bytes. The maximum possible file size in this file system isGATE CS 2012, [2Marks] (MCQ)", "options": ["3 KBytes", "280 KBytes", " dependent on the size of the disk"], "correct": 2, "explanation": "It is given data as disk block is of size 128B. One direct block addressing will be pointing to 8 disk blocks = 8*128 B = 1 KB Singly Indirect block addressing will be pointing to 1 disk block which has 128/8 disc block addresses = (128/8)*128 B = 2 KB Doubly indirect block addressing will be pointing to 1 disk block which has 128/8 addresses to disk blocks which has 128/8 addresses to disk blocks = 16*16*128 B = 32 KB Maximum file size possible = 1 KB + 2 KB + 32 KB = 35 KB", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-os-pyq-io/"}
{"subject": "Mathematics General", "topic": "GATE | PYQ | Discrete Mathematics |2026", "question": "For two different persons 𝑥 and 𝑦, the predicate 𝑀(𝑥, 𝑦) denotes that x knows y. Consider the following statement. There is a person who does not know anyone else, but that person is known by everyone else. Which one of the following expressions represents the above statement? [MCQ || GATE 2026 Set-2 || 1 Marks ]", "options": ["(∀𝑦)(∃𝑥) ((𝑥 ≠ 𝑦) → (𝑀(𝑥, 𝑦) ∧ ¬𝑀(𝑦, 𝑥)))", "(∃𝑦)(∃𝑥) ((𝑥 ≠ 𝑦) → (𝑀(𝑥, 𝑦) ∧ ¬𝑀(𝑦, 𝑥)))", "(∀𝑦)(∀𝑥) ((𝑥 ≠ 𝑦) → (𝑀(𝑥, 𝑦) ∧ ¬𝑀(𝑦, 𝑥)))"], "correct": 1, "explanation": "$$ begin{aligned} & mathbf{ ext{Statement meaning:}} & ext{There exists a person } y ext{ such that} & bullet quad ext{everyone else knows } y & bullet quad y ext{ knows no one else} & mathbf{ ext{Formally:}} & bullet quad ext{“There is a person” } ightarrow exists y & bullet quad ext{“For every other person } x != y ext{” } ightarrow forall x & bullet quad ext{“}x ext{ knows } y ext{” } ightarrow M(x,y) & bullet quad ext{“}y ext{ does not know } x ext{” } ightarrow eg M(y,x) & mathbf{ ext{So we get:}} & ( exists y)( forall x)((x != y) ightarrow (M(x,y) land eg M(y,x))) end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-pyq-discrete-mathematics-2026/"}
{"subject": "Mathematics General", "topic": "GATE | PYQ | Discrete Mathematics |2026", "question": "Let 𝐺(𝑉, 𝐸) be a simple, undirected graph. A vertex cover of 𝐺 is a subset 𝑉 ′ ⊆ 𝑉 such that for every (𝑢, 𝑣) ∈ 𝐸, 𝑢 ∈ 𝑉 ′or 𝑣 ∈ 𝑉 ′ . Let the size of the smallest vertex cover in 𝐺 be 𝑘. Let 𝑆 be any vertex cover of size 𝑘.For a vertex 𝑣 ∈ 𝑉, which of the following constraints will always ensure that 𝑣 ∈ 𝑆 ? [MCQ || GATE 2026 Set-2 || 2 Marks ]", "options": ["The vertex 𝑣 is on a path of length 𝑘 + 1", "The vertex 𝑣 is on a cycle of length 𝑘 + 1", "The vertex 𝑣 is a part of a clique of size k"], "correct": 1, "explanation": "$$ begin{aligned} & bullet quad G(V,E) ext{ is a simple undirected graph.} & bullet quad ext{The minimum vertex cover size is } k. & bullet quad S ext{ is a vertex cover of size } k ext{ (so } S ext{ is a minimum vertex cover).} & ext{We want a condition that forces a vertex } v ext{ to belong to } extit{every} ext{ minimum vertex cover of size } k. & mathbf{ ext{Option (A) Degree}(v) ge k+1} & ext{If } v otin S ext{, then all its neighbors must be in } S. & ext{But } deg(v) ge k+1 ext{ means at least } k+1 ext{ neighbors are needed in } S ext{, which is impossible since } |S|=k. & ext{So } v ext{ must be included.} & mathbf{ ext{Option (B) On a path of length } k+1} & ext{A path of length } k+1 ext{ needs only about } (k+1)/2 ext{ vertices in a cover. Not forced.} & mathbf{ ext{Option (C) On a cycle of length } k+1} & ext{A cycle needs about } (k+1)/2 ext{ vertices. Not forced.} & mathbf{ ext{Option (D) In a clique of size } k} & ext{A clique of size } k ext{ needs only } k-1 ext{ vertices in a cover. One vertex can be excluded.} end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-pyq-discrete-mathematics-2026/"}
{"subject": "Mathematics General", "topic": "GATE | PYQ | Discrete Mathematics |2026", "question": "Consider a complete graph 𝐾𝑛 with 𝑛 vertices (𝑛 > 4). Note that multiple spanning trees can be constructed over 𝐾𝑛. Each of these spanning trees is represented as a set of edges. The Jaccard coefficient between any two sets is defined as the ratio of the size of the intersection of the two sets to the size of the union of the two sets. Which one of the following options gives the lowest possible value for the Jaccard coefficient between any two spanning trees of 𝐾𝑛? [MCQ || GATE 2025 Set-2 || 2-marks ]", "options": ["1/n", "1/(2n-3)", "1/(n-1)"], "correct": 3, "explanation": "$$ begin{aligned} & bullet quad ext{Each spanning tree of } K_n ext{ has } n-1 ext{ edges.} & bullet quad ext{The Jaccard coefficient is} & qquad qquad qquad J = frac{|T_1 cap T_2|}{|T_1 cup T_2|} & bullet quad ext{To minimize } J ext{, we minimize the intersection.} & ext{In a complete graph } K_n ext{ (with } n>4 ext{), it is possible to construct two edge-disjoint} & ext{spanning trees (they share no common edges).} & ext{So:} & qquad qquad qquad |T_1 cap T_2| = 0 & ext{Hence,} & qquad qquad qquad J = frac{0}{|T_1 cup T_2|} = 0 end{aligned}$$", "source_url": "https://www.geeksforgeeks.org/quizzes/gate-pyq-discrete-mathematics-2026/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "What is the main difference between microcomputers and mainframe computers in terms of usage?", "options": ["Greater power and smaller storage limits", "Identical tasks and identical performance", "Smaller systems and lower computing power"], "correct": 1, "explanation": "Microcomputers are designed for personal use, and mainframes handle large-scale data processing for organizations.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "Which component of the CPU is responsible for directing the operation of the processor?", "options": ["Cache", "Register", "Clock"], "correct": 2, "explanation": "The Control Unit manages and coordinates all activities of the processor by sending control signals.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "How many times will the loop run? C++ #include <iostream> using namespace std; int main() { for (int i = 1; i < 15; i++) { cout << i << endl; } return 0; }", "options": ["16", "Error", "15"], "correct": 1, "explanation": "The loop runs 14 times, because i starts at 1 and continues up to (but not including) 15.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "Predefined words in a programming language that have a special meaning and cannot be used as a variable name or function name are called", "options": ["data types", "predefined words", "literals"], "correct": 2, "explanation": "Keywords are predefined words in a programming language that have a special meaning and cannot be used as a variable name or function name. eg, \"int\", \"float\", \"const\", etc.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "Which property is used to remove the bullet points in an unordered list?", "options": ["bullet: hidden;", "remove-bullet: true;", "list-decoration: none;"], "correct": 1, "explanation": "The list-style-type: none; removes bullets from unordered lists.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "Which type of RAM is known for its high speed and is commonly used in cache memory?", "options": ["Dynamic RAM (DRAM)", "Read Only Memory (ROM)", "Flash Memory"], "correct": 3, "explanation": "SRAM is very fast, so it is used in cache memory for quick data access.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "What is a characteristic feature of Erasable Programmable ROM (EPROM)?", "options": ["It is permanently programmed during manufacturing", "It is volatile and loses data when powered off", "It can only be read, not written"], "correct": 2, "explanation": "EPROM can be erased using ultraviolet (UV) light and then reprogrammed with new data.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}
{"subject": "Computer Science General Test", "topic": "Google Hackathon Fundamentals Quiz", "question": "What is the do-while loop also known as?", "options": ["Entry control", "Per tested", "All of the above"], "correct": 2, "explanation": "A do-while loop is called an exit-controlled loop because the condition is checked after executing the loop body. This guarantees that the loop runs at least once, even if the condition is false initially.", "source_url": "https://www.geeksforgeeks.org/quizzes/google-hackathon-fundamentals-quiz/"}