GATE 2025 DA – Previous Year Questions with Solutions
All 65 questions of GATE 2025 DA with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Courage : Bravery :: Yearning : Select the most appropriate option to complete the analogy.
- Question 2 – We tennis in the lawn when it suddenly started to rain. Select the most appropriate option to complete the above sentence.
- Question 3 – A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with U 4 is: 0 1 0 2 --- --- --- --- 4 7 3 3 5 5 4 4 6 7…
- Question 4 – In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options…
- Question 5 – A rectangle has a length L and a width W, where L > W. If the width, W, is increased by 10%, which one of the following statements is correct for all…
- Question 6 – Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk. Column-I Column-II --- --- P. This house is in a mess. 1.…
- Question 7 – Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical…
- Question 8 – A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r cm as shown in the figure. The side of the dodecagon is d cm. All…
- Question 9 – If a real variable x satisfies 3x2 = 27 9x, then the value of 2x2(2x)2 is:
- Question 10 – The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹ 1000(X - 0.2),…
- Question 11 – Suppose X and Y are random variables. The conditional expectation of X given Y is denoted by E[X Y]. Then E[E[X Y]] equals
- Question 12 – The number of additions and multiplications involved in performing Gaussian elimination on any n n upper triangular matrix is of the order
- Question 13 – The sum of the elements in each row of A Rn n is 1. If B = A3 - 2A2 + A, which one of the following statements is correct (for x Rn)?
- Question 14 – Let f(x) = ex - e-x2, x R. Let f(k)(a) denote the kth derivative of f evaluated at a. What is the value of f(10)(0)? (Note: ! denotes factorial)
- Question 15 – Let p and q be any two propositions. Consider the following propositional statements. S 1: p q, S 2: p q, S 3: p q, S 4: p q, where denotes…
- Question 16 – If a relational decomposition is not dependency-preserving, which one of the following relational operators will be executed more frequently in order…
- Question 17 – Consider the following three relations: Car (model, year, serial, color) Make (maker, model) Own (owner, serial) A tuple in Car represents a specific…
- Question 18 – Consider a hash table of size 10 with indices \0, 1, , 9\, with the hash function h(x) = 3x 10, where linear probing is used to handle collisions. The…
- Question 19 – Let X be a continuous random variable whose cumulative distribution function (CDF) F X(x), for some t, is given as follows: F X(x) = cases 0 & x t \\…
- Question 20 – Let X = aZ + b, where Z is a standard normal random variable, and a, b are two unknown constants. It is given that E[X] = 1, E[(X - E[X])Z] = -2, E[(X…
- Question 21 – It is given that P(X 2) = 0.25 for an exponentially distributed random variable X with E[X] = 1, where E[X] denotes the expectation of X. What is the…
- Question 22 – Consider designing a linear classifier y = sign(f(x; w, b)), f(x; w, b) = w x + b on a dataset D = \(x 1, y 1), (x 2, y 2), , (x N, y N)\, x i Rd, y i…
- Question 23 – Consider the following Python declarations of two lists. Which one of the following statements results in A= [1, 2, 3, 4, 5, 6]?
- Question 24 – Consider two functions f: R R and g: R (1, ). Both functions are differentiable at a point c. Which of the following functions is/are ALWAYS…
- Question 25 – Which of the following statements is/are correct?
- Question 26 – Which of the following statements is/are correct in a Bayesian network?
- Question 27 – For which of the following inputs does binary search take time O( n) in the worst case?
- Question 28 – Let A = I n + xx, where I n is the n n identity matrix and x Rn, x x = 1. Which of the following options is/are correct?
- Question 29 – Suppose that insertion sort is applied to the array [1, 3, 5, 7, 9, 11, x, 15, 13] and it takes exactly two swaps to sort the array. Select all…
- Question 30 – Let C 1 and C 2 be two sets of objects. Let D(x, y) be a measure of dissimilarity between two objects x and y. Consider the following definitions of…
- Question 31 – There are three boxes containing white balls and black balls. Box-1 contains 2 black and 1 white balls. Box-2 contains 1 black and 2 white balls.…
- Question 32 – t +t2 + t - t = (*Round off to one decimal place*)
- Question 33 – On a relation named Loan of a bank: loan number branch name amount --- --- --- L11 Banjara Hills 90000 L14 Kondapur 50000 L15 SR Nagar 40000 L22 SR…
- Question 34 – Given data \(-1, 1), (2, -5), (3, 5)\ of the form (x, y), we fit a model y = wx using linear least-squares regression. The optimal value of w is…
- Question 35 – The naive Bayes classifier is used to solve a two-class classification problem with class-labels y 1, y 2. Suppose the prior probabilities are P(y 1)…
- Question 36 – Let Y = Z2, Z = X - , where X is a normal random variable with mean and variance 2. The variance of Y is
- Question 37 – Let A Rn n be such that A3 = A. Which one of the following statements is ALWAYS correct?
- Question 38 – Let \x 1, x 2, , x n\ be a set of linearly independent vectors in Rn. Let the (i, j)-th element of matrix A Rn n be given by A ij = x i x j, 1 i, j n.…
- Question 39 – Consider the cumulative distribution function (CDF) of a random variable X: F X(x) = cases 0 & x -1 \\ 14(x + 1)2 & -1 x 1 \\ 1 & x 1 cases The value…
- Question 40 – A random variable X is said to be distributed as Bernoulli(), denoted by X Bernoulli(), if P(X = 1) = , P(X = 0) = 1 - for 0 < < 1. Let Y = i=1300 X…
- Question 41 – For x R, the floor function is denoted by f(x) = x and defined as follows x = k, k x < k + 1, where k is an integer. Let Y = X , where X is an…
- Question 42 – Consider the neural network shown in the figure with inputs: u, v weights: a, b, c, d, e, f output: y R denotes the ReLU function, R(x) = (0, x).…
- Question 43 – Consider game trees Tree-1 and Tree-2 as shown. The first level is a MAX agent and the second level is a MIN agent. The value in the square node is…
- Question 44 – The state graph shows the action cost along the edges and the heuristic function h associated with each state. [Figure: A directed state graph. S goes…
- Question 45 – A random experiment consists of throwing 100 fair dice, each die having six faces numbered 1 to 6. An event A represents the set of all outcomes where…
- Question 46 – Consider a fact table in an OLAP application: Facts(D1, D2, val), where D1 and D2 are its dimension attributes and val is a dependent attribute.…
- Question 47 – Consider the following Python code snippet. When the above program is executed, at the end, which of the following sets contains "this"?
- Question 48 – Which of the following statements is/are correct about the rectified linear unit (ReLU) activation function defined as ReLU(x) = (x, 0), where x R?
- Question 49 – Consider the function f(x) = x33 + 72x2 + 10x + 1332, x [-8, 0]. Which of the following statements is/are correct?
- Question 50 – Let x 1, x 2, x 3, x 4, x 5 be a system of orthonormal vectors in R10. Consider the matrix A = x 1x 1 + + x 5x 5. Which of the following statements…
- Question 51 – Let f: R R be a twice-differentiable function and suppose its second derivative satisfies f''(x) > 0 for all x R. Which of the following statements…
- Question 52 – An n n matrix A with real entries satisfies the property: \ Ax\ 2 = \ x\ 2, for all x Rn, where \ \ denotes the Euclidean norm. Which of the following…
- Question 53 – Consider designing a linear binary classifier f(x) = sign(w x + b), x R2 on the following training data: Class-1: pmatrix 2 \\ 0 pmatrix, pmatrix 0 \\…
- Question 54 – Consider a coin-toss experiment where the probability of head showing up is p. In the ith coin toss, let X i = 1 if head appears, and X i = 0 if tail…
- Question 55 – Consider a two-class problem in Rd with class labels red and green. Let red and green be the means of the two classes. Given test sample x Rd, a…
- Question 56 – Consider the following two relations, named Customer and Person, in a database: Person (aadhaar CHAR(12) PRIMARY KEY, name VARCHAR(32)); Customer…
- Question 57 – Consider a database relation R with attributes ABCDEFG, and having the following functional dependencies: A BCEF E DG BC A Which of the following…
- Question 58 – Let G be a simple, unweighted, and undirected graph. A subset of the vertices and edges of G are shown below. [Figure: Eight vertices in two rows. Top…
- Question 59 – Let f: R R be such that f(x) - f(y) (x - y)2 for all x, y R. Then f(1) - f(0) = (*Answer in integer*)
- Question 60 – Let D = \x(1), , x(n)\ be a dataset of n observations where each x(i) R100. It is given that i=1n x(i) = 0. The covariance matrix computed from D has…
- Question 61 – A bag contains 5 white balls and 10 black balls. In a random experiment, n balls are drawn from the bag one at a time with replacement. Let S n denote…
- Question 62 – Consider the following tables, Loan and Borrower, of a bank. Loan: loan num branch name amount --- --- --- L11 Banjara Hills 90000 L14 Kondapur 50000…
- Question 63 – Consider the following Python code snippet. The value printed by the code snippet is (*Answer in integer*)
- Question 64 – Consider the following pseudocode. The value of sum output by a program executing the above pseudocode is (*Answer in integer*)
- Question 65 – Consider a directed graph G = (V, E), where V = \0, 1, 2, , 100\ and E = \(i, j) : 0 < j - i 2, for all i, j V\. Suppose the adjacency list of each…