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GATE DA 2026 Set 1

All 65 solved GATE DA 2026 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

65

Paper marks

100

Question formats

3

MCQ · NAT · MSQ

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 22Medium 40Hard 3

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Verbosity : Brevity :: Insolence :___________
    Choose the word that best fills the blank.
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    Question

    The product of the digits of a three-digit number is 70. The sum of the digits of this three-digit number is _____
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    Question

    The four pieces of a puzzle are shown in the figure below.
    Four black puzzle pieces with various cutouts
    Which one of the figures labelled as P, Q, R, and S can be constructed by using each of the four pieces only once without overlaps?
    Four square figures labelled P, Q, R, and S with white central shapes
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    Question

    Consider two distinct positive real numbers m,nm, n, with m>nm > n.
    Let x=nlog⁡10(m)x = n^{\log_{10}(m)} and y=mlog⁡10(n)y = m^{\log_{10}(n)}. The relation between xx and yy is _______.
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    Question

    ‘If his latest movie had been a commercial success, the actor would have made enough money to sponsor his next movie.’
    Based only on the above sentence, which one of the following statements is true?
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    Question

    ‘My friend and I parted ＿＿ the door ＿＿ the cabin that I had rented ＿＿ the night.’
    Choose the option with the correct sequence of words to fill the blanks.
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    Question

    Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.
    Ignoring permutations, the number of ways to pick these five integers is _____
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    Question

    Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that:
    (i) the first game was the only game where two students of the same class played against each other,
    (ii) the students of Class 5 won more games than the students of Class 4, and
    (iii) the boys won two games and the girls won one game.
    The student who did not lose any game is __________.
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    Question

    P,Q,R,S,X,P, Q, R, S, X, and YY are distinct single-digit whole numbers taking values from 0 to 9.
    PQPQ is a two-digit number with QQ being in the units place and PP in the tens place. Similarly, RSRS is a two-digit number.
    It is known that PQPQ and RSRS are consecutive numbers and (PQ)2+(RS)2=XYP(PQ)^2 + (RS)^2 = XYP, with XYPXYP being a three-digit number.
    The value of YY is __________
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    Question

    In the given figure, PP, QQ, and RR are three points on a circle of radius 10 cm with OO as its center, PQ‾=RQ‾\overline{PQ} = \overline{RQ}, and ∠PQR=45∘\angle PQR = 45^\circ. The figure is representative.
    The area of the shaded region PQROPQRO is ______________ cm2^2.

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Data Science and Artificial Intelligence (DA)

55
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    Question

    For a classification problem, Principal Component Analysis (PCA) has been used to reduce the dimensionality of a feature space from 100 to 10.
    Which of the following options is true about the angle θ\theta between the first and the tenth principal components?
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    Question

    Consider that you are training a classifier for a 10-class classification problem. Each input is represented as a 512-dimensional vector. There are 1000 samples, out of which first 100 will be used for testing. Let Leave-One-Out-Cross-Validation (LOOCV) be used for selection of the classifier model before testing.
    Which of the following options is the correct number of validation splits that will be generated?
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    Question

    Which of the following algorithms is NOT an example of uninformed search?
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    Question

    Which of the following statements is NOT true?
    (The names of the predicates are intuitive.)
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    Question

    Consider that the quick sort algorithm is used to sort an array of nn distinct randomly ordered elements. In every call, the pivot is chosen as the first element of the current subarray.
    Let T(n)T(n) denote the expected time to sort the array. Assume that the time to partition is linear in the size of the current subarray.
    Which of the following recurrence relations correctly represents T(n)T(n) in this scenario?
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    Question

    Consider the given Python program.
    def append_to_lst(val, lst=[]):
    lst.append(val)
    return lst
print(append_to_lst(1))
print(append_to_lst(2))
print(append_to_lst(3, []))
    Which of the following is the correct output of this program?
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    Question

    Let R(A,B,C,D,E)\text{Let } R(A,B,C,D,E) be a relational schema with functional dependency set F={A→BC,CD→E,E→A}F=\{A \rightarrow BC, CD \rightarrow E, E \rightarrow A\}.
    Which of the following statements is correct?
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    Question

    Consider that the visualization of a 3-dimensional data cube is showing Sales Quantity for each combination of the attributes Product Type, Month and Country.
    From this, if we want to further visualize the Sales Quantity for each combination of Product Type, Month and State, which of the following OLAP operations should be performed?
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    Question

    Let MM be a randomly chosen non-empty subset of S={1,2,3,…,2026}S = \{1, 2, 3, \dots, 2026\}.
    Which of the following is the probability that the product of all the elements of MM is even?
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    Question

    Suppose that a computer program provides a non-negative and integer-valued random solution to the equation n1+n2+n3+n4=20n_1 + n_2 + n_3 + n_4 = 20.
    Which of the following is the probability that all of n1,n2,n3,n4n_1, n_2, n_3, n_4 in the provided solution are positive?
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    Question

    Let M=(cos⁡θ−sin⁡θsin⁡θcos⁡θ)M = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix} be a 2×22 \times 2 matrix, where θ=2π5\theta = \frac{2\pi}{5}, and I2=(1001)I_2 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}.
    Which of the following options is equal to M2026M^{2026} ?
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    Question

    Consider a set S1={x=(x1,x2,x3)T∈R3∣xTx≤16}S_1 = \{x = (x_1, x_2, x_3)^T \in \mathbb{R}^3 \mid x^T x \leq 16\}. Let S2S_2 be another set which is a subspace of R3\mathbb{R}^3 with dimension two.
    Which of the following gives the area of S1∩S2S_1 \cap S_2?
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    Question

    In the following table, the Task column lists a few tasks related to machine learning. The Algorithm column lists a few algorithms.
    Each entry “t” from the Task column is to be matched with an appropriate entry “a” from the Algorithm column such that the task “t” can be solved using the algorithm “a”. Denote such a match as t:a
    TaskAlgorithm
    T1 – ClusteringA1 – Markov Chain Monte Carlo
    T2 – ClassificationA2 – K-Medoid
    T3 – SamplingA3 – Linear Discriminant Analysis
    T4 – Feature ExtractionA4 – Naive Bayes
    Which of the following options is/are the correct matching(s)?
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    Question

    Sentence XX is said to entail Sentence YY if whenever XX is TRUE, YY also must hold TRUE.
    Which of the following statements is/are correct if XX entails YY?
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    Question

    You are given the following Pre-order and In-order traversals of a Binary Tree T with nodes E, F, G, P, Q, R, S.
    Pre-order: P Q S E R F G
    In-order: S Q E P F R G
    Which of the following statements is/are true about the Binary Tree T?
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    Question

    Consider two relations r and s defined on the relational schemas R(A,B) and S(E,C), respectively. A is the primary key of R and E is a foreign key of S referencing A in R.
    Which of the following operations will NEVER violate the foreign key constraint?
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    Question

    Let f(x)=x3−3x2+2f(x) = x^3 - 3x^2 + 2 be a function defined on (−1,3](-1, 3].
    Which of the following statements is/are correct?
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    Question

    Suppose a random variable ZZ follows Normal(μ=0,σ2=1)Normal(\mu = 0, \sigma^2 = 1) distribution with probability density function g(z)g(z) and cumulative distribution function G(z)G(z).
    Another random variable YY follows t1t_1 distribution with probability density function h(y)h(y) and cumulative distribution function H(y)H(y). Let cc be the positive real number for which g(c)=h(c)g(c) = h(c).
    Which of the following statements is/are correct?
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    Question

    Consider that for a supervised learning task, the objective function being minimized is fw(x)=wxf_w(x) = wx, where x∈Rx \in \mathbb{R} is the input and w∈Rw \in \mathbb{R} is the parameter. Stochastic Gradient Descent with learning rate of 0.10 is used for parameter updates.
    Suppose that at the end of iteration ii, the value of ww becomes 10.00.
    Let x=10.00x = 10.00 be the input for iteration (i+1)(i + 1).
    The value of ww at the end of iteration (i+1)(i + 1) is __________ . (Rounded off to two decimal places)
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    Question

    Consider the game tree for a two-player turn-taking minimax game as shown in the figure. The value of a terminal node represents the utility of the game state if the game ends there. The numbers written next to the edges denote the strategies.
    There are two players MAX and MIN. At any particular state of the game, MAX prefers to move to a state of maximum value. On the other hand, MIN prefers to move to a state of minimum value.
    Suppose MAX starts the game at the root and has three strategies: 1, 2 and 3.
    Next, MIN plays and also has three strategies: 1, 2 and 3. The game ends there.
    Both players always take optimal strategies throughout the game.
    At the root, the best strategy for MAX is ___________ . (Answer in integer)
    Game tree with MAX at root and MIN at next level
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    Question

    Let A be a sorted array containing 1000 distinct integers. You perform a recursive binary search on A to find an element y. Suppose each comparison checks whether the middle element computed during the current recursive step is equal to, less than, or greater than y.
    The maximum number of comparisons that may have to be performed if y is not an element of A is _______ . (Answer in integer)
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    Question

    In a relational database, a B+ Tree Index is to be constructed for a relation on a key field. In a B+ Tree, a Node Pointer points to a sub-tree and a Data Record Pointer points to a block of database records.
    Let, Node size = 4096 bytes, Node Pointer size = 10 bytes, Search Key Field size = 11 bytes and Data Record Pointer size = 12 bytes.
    The maximum number of Node Pointers that can be present in a non-leaf node of the B+ Tree is ________ . (Answer in integer)
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    Question

    The number of bijections f(⋅)f(\cdot) from the set S={1,2,3,4}S = \{1, 2, 3, 4\} to itself such that f(f(n))=nf(f(n)) = n, for all n∈Sn \in S, is __________ . (Answer in integer)
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    Question

    Let XX be an exponentially distributed random variable with mean λ(>0)\lambda (> 0). If P(X>5)=0.35P(X > 5) = 0.35, then the conditional probability P(X>10∣X>5)P(X > 10 \mid X > 5) is ___________ . (Rounded off to two decimal places)
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    Question

    The value of ∑i=0∞∑j=1∞2−i3−j\sum_{i=0}^{\infty} \sum_{j=1}^{\infty} 2^{-i} 3^{-j} is ______________ . (Answer in integer)
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    Question

    Let four points in three-dimensional space be:
    P1: [2,3,−1][2, 3, -1], P2: [3,1,1][3, 1, 1], P3: [5,−2,3][5, -2, 3] and P4: [3,3,3][3, 3, 3].
    Hierarchical Agglomerative Clustering is used to cluster the above points. If Manhattan Distance is used as the distance metric during clustering, which of the following options indicates the two points that will be merged first?
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    Question

    Which of the following statements is true for Ridge Regression?
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    Question

    Assume that a Creative (CC) person will Succeed (SS) if the person is also Disciplined (DD), but will not succeed otherwise. Now, consider the following statements:
    (i) C∧S⇔DC \wedge S \Leftrightarrow D
    (ii) C⇒(S⇔D)C \Rightarrow (S \Leftrightarrow D)
    (iii) C⇔((D⇒S)∨¬S)C \Leftrightarrow ((D \Rightarrow S) \vee \neg S)
    Which of the following options is correct?
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    Question

    A recursive function in Python is given.
    def mystery(n):
    if n <= 0:
        return 1
    else:
        return mystery(n-1) + mystery(n-2)
    Now, consider the following function call:
    mystery(4)
    Assume that a typical runtime stack is used to manage function calls. Each function call is pushed onto the stack and removed only after it finishes execution.
    Which of the following options denotes the total number of function calls (i.e., the total number of stack activations), including the initial call, to compute mystery(4)?
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    Question

    Consider a directed graph G=(V,E)G = (V, E), where VV is the finite set of vertices and EE is the set of directed edges between the vertices. GG may contain cycles but there is no self-loop. Further, GG may not be strongly connected.
    Let GRG^R be the graph obtained by reversing the directions of all the edges in GG without changing the set of vertices.
    Assume that Breadth First Search (BFS) or Depth First Search (DFS) from any given vertex vv of a graph visits only the reachable vertices from vv in that graph.
    Which of the following statements must always be true, regardless of the structure of GG?
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    Question

    Consider a B+ Tree where the maximum number of key values in each leaf node is 2 and the maximum number of pointers in each non-leaf node is 3. Let the content of the B+ Tree be as shown in the figure.
    B+ Tree with root [5, 8

    Which of the following options denotes the key value(s) stored in the root node after inserting a key value 3 in the given B+ Tree?
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    Question

    Consider the given relations XX, YY and ZZ. The relation XX has three columns PP, QQ and RR. The relation YY has three columns PP, QQ and SS. The relation ZZ has two columns PP and TT.
    Relation X
    PQR
    P1Q1R1
    P2Q2R2
    P3Q3R2
    Relation Y
    PQS
    P1Q12
    P1Q25
    P2Q16
    P3Q31
    Relation Z
    PT
    P1T1
    P3T2
    P4T3
    P4NULL
    Consider the relational algebra expressionΠPRS[(σ(Q=Q3∨R=R2)[X⋈Y])⋈(σ(S>1)[Y⋈Z])]\Pi_{PRS} [ (\sigma_{(Q=Q3 \lor R=R2)} [X \bowtie Y]) \bowtie (\sigma_{(S>1)} [Y \bowtie Z]) ]where ⋈\bowtie denotes natural join operation.
    Which of the following options is the correct output for the given expression?
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    Question

    Consider the concept hierarchies as shown in the figure.
    Which of the following options denotes the total number of possible data cuboids from these concept hierarchies?
    Concept hierarchies for Time (Year-Month-Day), Location (Country-State-City), and Item (Item Category-Item Type-Item)
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    Question

    Let XX and YY be two independent random variables. XX follows Bernoulli(p=0.3)Bernoulli(p = 0.3) distribution and YY follows Normal(μ=0,σ2=100)Normal(\mu = 0, \sigma^2 = 100) distribution.
    Which of the following options is the variance of (2X−1)Y(2X - 1)Y?
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    Question

    LetL=lim⁡n→∞∑k=0ne−nnkk!L = \lim_{n \to \infty} \sum_{k=0}^{n} \frac{e^{-n} n^k}{k!}Which of the following is the value of LL?
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    Question

    Let γ1,γ2,γ3\gamma_1, \gamma_2, \gamma_3 be the eigenvalues of the matrix [1000cos⁡tsin⁡t0−sin⁡tcos⁡t]\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{bmatrix}, where t∈[−π,π]t \in [-\pi, \pi] is in radians.
    Which one of the following options lists all the possible values of tt satisfying γ1+γ2+γ3=1+2\gamma_1 + \gamma_2 + \gamma_3 = 1 + \sqrt{2}?
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    Question

    Consider that 20 stories of Author X and 10 stories of Author Y were kept together without mentioning the names of the authors. A classifier was then asked to predict the author (X or Y) of each of these stories. Let, out of X’s stories, 6 were classified as that of Y. On the other hand, out of Y’s stories, 2 were classified as that of X.
    Considering X and Y as two classes, which of the following statements is/are true?
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    Question

    Let P(x)P(x) be a predicate.
    Which of the following statements is/are NOT valid in first-order logic?
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    Question

    Consider the problem of sorting the given array in ascending order:P=[1,2,3,5,4]P = [1, 2, 3, 5, 4]Consider two sorting algorithms Bubble Sort (BS) and Insertion Sort (IS).
    Let N1\text{N1} be the total number of comparisons done by BS on the elements of P and N2\text{N2} be the total number of comparisons done by IS on the elements of P.
    Which of the following options is/are correct?
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    Question

    Consider the given Python program.
    def outer():
    x = []
    def inner(val):
        x.append(val)
        return x
    return inner
f1 = outer()
f2 = outer()
print(f1(10)) # Line P
print(f1(20)) # Line Q
print(f2(30)) # Line R
print(f1(40)) # Line S
    Which of the following options is/are correct?
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    Question

    Consider a table Employee(EmpID, TeamID), where the column EmpID (ID of an employee) is the primary key. The column TeamID denotes the team ID of the team of which the employee is a member. TeamID is a NOT NULL column.
    We want to display the size of the team (denoted as TeamSize) in which each employee is a member by using SQL. As an example, the desired output for the given Employee table is also shown in tabular form.
    Which of the following is/are correct?
    Employee
    EmpIDTeamID
    18
    28
    38
    47
    57
    69
    Output
    EmpIDTeamSize
    13
    23
    33
    42
    52
    61
    Your answer

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    Question

    Let M=(In−1n11T)M = (I_n - \frac{1}{n} \mathbf{1}\mathbf{1}^T) be a matrix, where 1=(1,1,1,…,1)T∈Rn\mathbf{1} = (1,1,1, \dots, 1)^T \in \mathbb{R}^n and InI_n is the identity matrix of order nn.
    Which of the following options is/are correct?
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    Question

    Let X1,X2,…,XnX_1, X_2, \dots, X_n be nn independent random variables. Each of the random variables follows Normal(μ=0,σ2=1)Normal(\mu=0, \sigma^2=1) distribution. Define Xˉ=1n∑i=1nXi\bar{X} = \frac{1}{n} \sum_{i=1}^n X_i.
    Which of the following statements is/are correct?
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    Question

    Let XX be a discrete valued random variable with cumulative distribution function F(x)F(x).
    Which of the following statements is/are correct?
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    Question

    Consider that Linear Ridge Regression is being used to learn a prediction function ypred=wTxy_{\text{pred}} = w^T x, where w,x∈R2w, x \in \mathbb{R}^2 and Mean Absolute Error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer.
    At an intermediate step of the training process, assume that the parameter w=[−3.00,4.00]Tw = [-3.00, 4.00]^T. In the next step, for the input x=[1.00,2.00]Tx = [1.00, 2.00]^T, the predicted value of yy is noted. Let the relation between x=[x1,x2]Tx = [x_1, x_2]^T and the true value of yy be ytrue=x1+x2y_{\text{true}} = x_1 + x_2.
    The value of the overall regularized loss function for this instance is _______ . (Rounded off to two decimal places)
    Your answer

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    Question

    Consider a fully-connected feed-forward multi-layer perceptron. It has 30 neurons in the input layer, followed by two hidden layers and an output layer. The first hidden layer has 4 neurons and the second hidden layer has 3 neurons. The output layer has only one neuron. Assume that no bias parameters are used.
    The number of learnable parameters in the multi-layer perceptron is __________ . (Answer in integer)
    Your answer

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    Question

    A clinic specializes in testing for a disease D. The result of the test can be either positive or negative.
    A study revealed that if a person suffers from the disease D, the test result in that clinic comes out positive 80% of the time, and negative 20% of the time. If a person is not suffering from the disease D, the test comes out positive 10% of the time and negative 90% of the time. It is also known that among the general population, the disease D occurs in 30% of the individuals.
    If a person tests positive for D in that clinic, the probability that he/she actually suffers from the disease D is __________ . (Rounded off to two decimal places)
    Your answer

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    Question

    Consider the given Python program.
    def fun(L, i=0):
    if i >= len(L)-1:
        return 0
    if L[i] > L[i+1]:
        L[i+1], L[i] = L[i], L[i+1]
        return 1+fun(L, i+1)
    else:
        return fun(L, i+1)
data = [5, 3, 4, 1, 2]
count = 0
for _ in range(len(data)):
    count += fun(data)
print(count)
    The output of the program is __________ . (Answer in integer)
    Your answer

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    Question

    Let there be two relations XX and YY as shown. XX has three columns PP, QQ and RR. YY has two columns PP and SS.
    Relation XX
    PPQQRR
    P1Q1R1
    P2Q2R2
    P3Q3R2
    Relation YY
    PPSS
    P110
    P115
    P220
    P31
    Consider that the following tuple relational calculus expression is evaluated.{t∣t∈X∧∃z∈X(t[P]=z[P])∧∃m∈Y(m[P]=t[P]∧m[S]>1)}\{t \mid t \in X \wedge \exists z \in X (t[P] = z[P]) \wedge \exists m \in Y (m[P] = t[P] \wedge m[S] > 1)\}The number of tuples that will be returned is __________ . (Answer in integer)
    Your answer

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    Question

    Let Account be a relation as shown.
    Account
    AccNoBalance
    A15000
    A25000
    A310000
    A415000
    A518000
    Consider the given SQL query.
    SELECT AccNo FROM Account AS A
WHERE (SELECT COUNT(*) FROM Account AS B 
WHERE A.Balance < B.Balance) >= (SELECT COUNT(*) 
FROM Account AS C WHERE A.Balance > C.Balance)
    The number of rows returned by the SQL query is __________ . (Answer in integer)
    Your answer

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    Question

    Consider an ER model with the entities E1(A11,A12,A13)E1(A_{11}, A_{12}, A_{13}) and E2(A21,A22,A23)E2(A_{21}, A_{22}, A_{23}), where, A11,A12,A13A_{11}, A_{12}, A_{13} are the attributes of E1E1, and A21,A22,A23A_{21}, A_{22}, A_{23} are the attributes of E2E2. Let A22A_{22} be a multi-valued attribute. A11A_{11} and A21A_{21} are the primary keys of E1E1 and E2E2, respectively.
    Let R12R12 be a many-to-many relationship between E1E1 and E2E2. Participation of both E1E1 and E2E2 in R12R12 is total.
    The minimum number of relations required to convert the ER model into relational model (assuming there is no other functional dependency) where each relation is in third normal form (3NF) is __________ . (Answer in integer)
    Your answer

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    Question

    For a given data set {x1,x2,…,xn}\{x_1, x_2, \dots, x_n\}, where n=100n = 100, it is known that12000∑i=1n∑j=1n(xi−xj)2=99\frac{1}{2000} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = 99Let us denote xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_iThe value of 199∑i=1n(xi−xˉ)2\frac{1}{99} \sum_{i=1}^{n} (x_i - \bar{x})^2 is __________ . (Answer in integer)
    Your answer

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    Question

    Let XX be a random variable that follows Uniform(−1,1)Uniform(-1,1) distribution. The conditional distribution of the random variable YY given X=xX = x is the Uniform(x2−0.1,x2+0.1)Uniform(x^2 - 0.1, x^2 + 0.1) distribution.
    The value of correlation(X,Y)correlation(X, Y) is __________ . (Answer in integer)
    Your answer

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    Question

    Let A5×5A_{5 \times 5} be a matrix such that each of its elements follows Bernoulli(p=0.50)Bernoulli(p = 0.50) distribution independently.
    The probability that the row-sum of the second row and the column-sum of the third column are both equal to 3 is ________ . (Rounded off to two decimal places)
    Your answer

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    Question

    Let A=(In−1n11T)A = \left(I_n - \frac{1}{n} \mathbf{1}\mathbf{1}^T\right) be a matrix, where 1=(1,1,1,...,1)T∈Rn\mathbf{1} = (1,1,1, ...,1)^T \in \mathbb{R}^n and InI_n is the identity matrix of order nn.
    The value of max⁡SxTAx\max_{S} x^T A x , where S={x∈Rn∣xTx=1}S = \{x \in \mathbb{R}^n \mid x^T x = 1\}, is ________ .
    (Answer in integer)
    Your answer

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