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Friday, October 20, 2023

Pattern Query Paper for GATE DA 2024


GATE 2024 aspirants, right here’s some nice information for you! The Indian Institute of Science (IISc) has simply launched pattern papers for the upcoming GATE examination. These samples are treasured assets to boost your preparation. On this weblog publish, we’ve compiled an in depth checklist of questions from the GATE DA pattern papers to empower your readiness.


First 25 Questions Carry One Mark Every

Q1. Let 𝑏 be the branching issue of a search tree. If the optimum purpose is reached after 𝑑 actions from the preliminary state, within the worst case, what number of instances will the preliminary state be expanded for iterative deepening depth first search (IDDFS) and iterative Deepening A* search (IDA*)?

(A) IDDFS – 𝑑, IDA* -𝑑
(B) IDDFS – 𝑑, IDA* -(𝑏)^d*
(C) IDDFS – 𝑏^d, IDA* -𝑑
(D) IDDFS – 𝑏^d, IDA* -𝑏^d

Q2. Given 3 literals 𝐴, 𝐵, and 𝐶, what number of fashions are there for the sentence 𝐴 ∨ ¬𝐵 ∨ 𝐶?

(A) 4 fashions
(B) 5 fashions
(C) 6 fashions
(D) 7 fashions

Q3. Which of the next first order logic sentence matches closest with the sentence “All college students will not be equal”?

(A) ∀𝑥 ∃𝑦[𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑥) ∧ 𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑦)] ⇒ ¬𝐸𝑞𝑢𝑎𝑙(𝑥, 𝑦)
(B) ∀𝑥 ∀𝑦[𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑥) ∧ 𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑦)] ⇒ ¬𝐸𝑞𝑢𝑎𝑙(𝑥, 𝑦)
(C) ∀𝑥 ∃𝑦[𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑥) ∧ 𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑦) ∧ ¬𝐸𝑞𝑢𝑎𝑙(𝑥, 𝑦)]
(D) ∀𝑥 ∀𝑦[𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑥) ∧ 𝑠𝑡𝑢𝑑𝑒𝑛𝑡(𝑦) ∧ ¬𝐸𝑞𝑢𝑎𝑙(𝑥, 𝑦)]

This fall. The imply of the observations of the primary 50 observations of a course of is 12. If the 51st
statement is eighteen, then, the imply of the primary 51 observations of the method is:

(A) 12
(B) 12.12
(C) 12.36
(D) 18

Q5. Sample Question Pape GATE

Q6. Which among the many following might assist to scale back overfitting demonstrated by a
i) Change the loss perform.
ii) Scale back mannequin complexity.
iii) Improve the coaching information.
iv) Improve the variety of optimization routine steps.

(A) ii and that i
(B) ii and iii
(C) i, ii, and iii
(D) i, ii, iii, and iv

Q7. A good coin is flipped twice and it’s recognized that not less than one tail is noticed. The chance of getting two tails is:

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

Q8. Given n indistinguishable particles and m (> n) distinguishable bins, we place at random every particle in one of many bins. The chance that in n preselected bins, one and just one particle will likely be discovered is:

indistinguishable particles

Q9. For 2 occasions A and B, 𝐵 ⊂ 𝐴 Which of the next assertion is appropriate?

(A) 𝑃(𝐵 | 𝐴) ≥ 𝑃(𝐵)
(B) 𝑃(𝐵 | 𝐴) ≤ 𝑃(𝐵)
(C) 𝑃(𝐴 | 𝐵) < 1
(D) 𝑃(𝐴 | 𝐵) = 0

Q10. X is a uniform distribution random variable with assist in [-2, 2] U [99.5, 100.5]. The imply of X is _

(A) 49.25
(B) 20.14
(C) 31.21
(D) 50.11

Q11. You’re reviewing 4 papers submitted to a convention on machine studying for medical knowledgeable techniques. All of the 4 papers validate their superiority on a regular benchmarking most cancers dataset, which has solely 5% of optimistic most cancers circumstances. Which of the experimental setting is suitable to you?

  1. We evaluated the efficiency of our mannequin by a 5-fold cross validation course of and report an accuracy of 93%.
  2. The world beneath the ROC curve on a single omitted take a look at set of our mannequin is round 0.8, which is the best amongst all of the completely different approaches.
  3. We computed the typical space beneath the ROC curve by 5-fold cross validation and located it to be round 0.75 – the best amongst all of the approaches.
  4. The accuracy on a single omitted take a look at set of our mannequin is 95%, which is the best amongst all of the completely different approaches.

(A) paper 1
(B) paper 1 and 4
(C) paper 2 and 4
(D) paper 3

Q12. Growing the regularizing coefficient worth for a ridge regressor will:

i) Improve or keep mannequin bias.
ii) Lower mannequin bias.
iii) Improve or keep mannequin variance.
iv) Lower mannequin variance.

(A) i and iii
(B) i and iv
(C) ii and iii
(D) ii and iv

Q13. A call tree classifier realized from a hard and fast coaching set achieves 100% accuracy. Which of the next fashions skilled utilizing the identical coaching set may even obtain 100% accuracy?

i) Logistic regressor.
ii) A polynomial of diploma one kernel SVM.
iii) A linear discriminant perform.
iv) Naïve Bayes classifier.

(A) i
(B) i and ii
(C) the entire above
(D) not one of the above

Q14. Take into account two relations R(x, y) and S(x,z). Relation R has 100 information, and relation S has 200 information. What would be the variety of attributes and information of the next question?

(A) 3 attributes, 20000 information
(B) 4 attributes, 20000 information
(C) 3 attributes, 200 information
(D) 4 attributes, 200 information

Q15. Take into account two relations R(x, y) and S(y), and carry out the next operation R(x,y) DIVIDE S(Y)
If X is the relation returns by the above operation, which of the next possibility(s) is/are at all times TRUE?

(A) |𝑋| ≤ |𝑅|
(B) |𝑋| ≤ |𝑆|
(C) |𝑋| ≤ |𝑅| AND |𝑋| ≤ |𝑆|
(D) All the Above

Q16. Which of the next statements is/are TRUE?

(A) Each relation with two attributes can also be in BCNF.
(B) Each relation in BCNF can also be in 3NF.
(C) No relation could be in each BCNF and 3NF.
(D) None of Above

Q17. Sample Question Pape GATE DSAI
Sample paper GATE DSAI

Q19. The perform f(x)= 1+x+x2 has a:

(A) Minima at x=-0.5
(B) Maxima at x=-0.5
(C) Saddle level at at x=-0.5
(D) Not one of the above.

Q20. The Pearson’s correlation coefficient between x and y rounded to the primary decimal level for the given information in beneath desk is:

(A) -0.5
(B) 0.5
(C) 0.3
(D) -0.3

Q21. The worst-case working instances of Insertion kind, Merge kind and Fast kind respectively are:

(A) Θ(nlogn), Θ(n^2), Θ(n^2)
(B) Θ(n^2), Θ(nlogn), Θ(nlogn)
(C) Θ(n^2), Θ(nlogn), Θ(n^2)
(D) Θ(n^2), Θ(n^2), Θ(nlogn)

Q22. Take into account the next program.

int func(int n)
    if (n <= 1)
        return n;
        return 3 * func(n - 3) - 3 * func(n - 2);

The working time of the above perform is:

(A) Θ(n)
(B) Θ(n^2)
(C) Θ(3^n)
(D) Θ(2^n)

Q23. Which of the next appropriately describes the recurrence relation for the usual binary search algorithm on a sorted array of n numbers the place c is a continuing.

(A) T(n) = 2*T(n/2) + c
(B) T(n) = T(n/2)
(C) T(n) = T(n-1) + c
(D) T(n) = T(n/2) + c

Q24. Take into account the next C program

int func(int A[], int n, int m)
    int s = A[0];
    for (int i = 1; i <= n - 1; i++)
        whole = m * s + A[i];
    return m;

Let Z be an array of 10 components with Z[i] = 2 for all i such that 0<=i<=9; The worth returned by func(Z,10,2) is _______

Q25. Two eigenvalues of three x 3 matrix X are (1 + i) and a couple of. The determinant of the matrix X is ___________.

Query 26 to 55 Carry Two Marks Every

Q26. Given the next relation cases
1 4 2
1 5 3
1 4 3
1 5 2
3 2 1
Which of the next circumstances is/are TRUE?

(A) XY -> Z and Z -> Y
(B) YZ -> X and X ->> Y
(C) Y -> X and Y ->> X
(D) XZ -> Y and Y -> X

Q27. Take into account the search area depicted within the Determine beneath. S is the preliminary state. G1 and G2 are two states that fulfill the purpose take a look at. The price of traversing from one state to a different is depicted by the numerical worth near the sting connecting the 2 states. The estimated price to the purpose is reported contained in the states. Use alphabetical order of nodes to interrupt ties. Which purpose state is reached when you carry out A* (graph) search? What’s the largest worth that the heuristic perform can take for node Some time nonetheless being admissible?

Q27. Sample Question Pape

Q28. Given a discrete 𝐾-class dataset containing 𝑁 factors, the place pattern factors are described utilizing 𝐷 options with every characteristic able to taking 𝑉 values, what number of parameters must be estimated for Naïve Bayes Classifier?


Q30. For completely spherical 2D information centered on the origin, which of the next the pairs of vectors are doable pairs of principal parts?
i) (1, 0) and (0, 1)
ii) (0, -1) and (-1, 0)
iii) (1, 1) and (1, -1)

(-1, 1) and (-1, -1)

(A) i
(B) i and iii
(C) i, ii, and iii
(D) i, ii, iii and iv

Q31. Gate DSAI sample paper
Q32. Gate DSAI sample paper

Q33. X is a uniformly distributed random variable from 0 to 1
𝑓(𝑥) = {1, 0 ≤ 𝑥 ≤ 1; 0, in any other case}
The variance of X is:

(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/12

Q34. The perform 𝑓(𝑥) = 1 + 2𝑥 + 3x^2+…….+2026x^2025. Which of the next assertion is true?

(A) f(x) has international minimal
(B) f(x) has international most
(C) f(x) doesn’t have international minimal
(D) Not one of the above

Q35. Given a easy sufficiently differentiable perform, the next statements are given:
(P) A concave perform can have a worldwide minimal
(Q) All convex capabilities have a worldwide minimal

(A) P and Q are true
(B) P is true and Q is fake
(C) P is fake and Q is true
(D) P and Q are false


(A) X and Y are mutually uncorrelated.
(B) X and Y are mutually unbiased.
(C) The imply of X is 1.
(D) The imply of Y is 0.5


Q38. Given a matrix A (m x n). The next statements are made relating to the matrix A.
P. The column area is orthogonal to the row area
Q. The column area is orthogonal to the left null area
R. The row area is orthogonal to the null area
T. The null area is orthogonal to the left null area.
Which of the assertion(s) is/are true?

(A) P and Q
(B) P and R
(C) Q and R
(D) P and T


(A) 0
(B) 1
(C) 2
(D) 3

Q40. A file with 100,000 information is listed with B+ tree. If the scale of a reminiscence block is 2K bytes, the scale of a key’s 4 bytes, the scale of a pointer is 4 bytes, what’s the minimal doable top of the B+ tree index. Peak is at all times higher than equal to 1.

Hints: No information are retailer within the nodes, solely keys are saved. The sizes of the pointers are identical, no matter they level to a node of a document.

Q41. Take into account a schema R(A, B, C, D, E, F) and purposeful dependencies A -> B, C -D, and E->F. What’s the variety of superkeys?

Q42. Gate sample paper

Q43. Take into account a Multi-Layer Perceptron (MLP) mannequin with one hidden layer and one output layer. The hidden layer has 10 neurons, and the output layer has 3 neurons. The enter to the MLP is a 5-dimensional vector. Every neuron is related to each neuron within the earlier layer, and a bias time period is included for every neuron. The activation perform used is the sigmoid perform. Calculate the whole variety of trainable parameters on this MLP mannequin.

Q44. An organization manufactures a product on the fee of P models per day. The associated fee per unit in Rs is 𝐶 = 50 + 0.1𝑃 + 9000/𝑃. The promoting value per unit is Rs. 300. The manufacturing stage minimizing the fee per unit and the whole revenue, respectively, are:

(A) 300, 1250
(B) 150, 2500
(C) 300, 2500
(D) 150, 1250

Q45. A category incorporates 60% college students who’re incapable of adjusting their opinions about something, and 40% of scholars are altering their minds at random, with chance 0.3, between subsequent votes on the identical challenge. Then, the chance of a scholar randomly chosen voted twice in the identical method is ______.

Q46. Gate DSAI sample paper

Q47. Let {O1, O2, O3, O4} characterize the end result of a random experiment, with P({O1})=P({O2})=P({O3})=P({O4}). Take into account the next occasions: P={O1,O2}, Q={O2,O3}, R={O3,O4},S={O1,O2,O3}. Then, which of the next statements is true?

(A) P and Q are unbiased
(B) P and Q will not be unbiased
(C) R and S are unbiased
(D) Q and S will not be unbiased

Q48. Take into account the matrix X whose eigenvalues are 1, -1 and three. Then Hint of X^3 – 3X^2 is ______________.

Q49. What’s the output of the next program?

int i = 1, j = 1;
for (; i <= 10; i++) {
    if (i % 3 != 0) {
        j += 2;
    if (j % 3 == 0)
printf("%d", i + j);

(A) 3
(B) 5
(C) 12
(D) 15

Q50. Assume that S is a stack and Q1 and Q2 are two Queues which assist the Enqueue and Dequeue operations. Take into account the next pseudo code for implementing the Pop and Push operation on S.

Push(S, x)
  A(Q2, x)
  whereas (Q1 not empty)
    B(Q2, C(Q1))
  Swap(Q1, Q2)
  return (D(Q1))

Which of the next choices for the capabilities A, B, C, and D would correspond to appropriately implementing the Push and Pop operations on the stack S?

(A) A,B – Enqueue C,D – Dequeue
(B) A,C – Enqueue B, D – Dequeue
(C) A,C – Dequeue B,D- Enqueue
(D) A,D – Enqueue B,C – Dequeue

Q51. Take into account the next program.

int enjoyable(float a[], float b[], int d) {
    float n1 = 0;
    float n2 = 0;
    int flag = 1;

    for (int i = 0; i < d; i++) {
        n1 = n1 + (a[i] * a[i]);
        n2 = n2 + (b[i] * b[i]);

    for (int i = 0; i < d; i++) {
        a[i] = a[i] / sqrt(n1);
        b[i] = b[i] / sqrt(n2);

    for (int i = 0; i < d; i++) {
        if (a[i] != b[i]) {
            flag = 0;

    return flag;

For which of the next inputs does the above algorithm produce 1 as an output?
(P) a = {1,2,3,4}; b = {3,4,5,6}, d = 4
(Q) a = {1,2,3,4}; b = {2,4,6,8}, d = 4
(R) a = {1,2,3,4} b = {10,20,30,40}, d = 4
(S) a = {1,2,3,4}, b = {1.1,2.1,3.1,4.1}, d = 4

(A) P, Q, R, S
(B) Q, R, S
(C) Q, R
(D) R, S

Q52. Take into account the next undirected graph on 5 nodes:

Q52. Gate DSAI sample paper

Assume you might be performing breadth first search on this graph utilizing a queue information construction. What number of distinctive breadth first orderings are doable on this graph?

(A) 9
(B) 24
(C) 48
(D) 120

Q53. Gate DSAI sample paper
Q54. Gate DSAI sample paper

Q55. Take into account the next relational schema:

SELECT empName
FROM worker E
    SELECT custId
    FROM buyer C
    WHERE C.salesRepId = E.empId
    AND C.score <> 'GOOD'

A) Names of all the staff with not less than one among their clients having a ‘GOOD’ score.
(B) Names of all the staff with at most one among their clients having a ‘GOOD’ score.
(C) Names of all the staff with none of their clients having a ‘GOOD’ score.
(D) Names of all the staff with all their clients having a ‘GOOD’ score.


The discharge of the GATE DA pattern paper by the Indian Institute of Science (IISc) is a major useful resource for aspiring information science and synthetic intelligence professionals. It offers a priceless glimpse into the type of questions that could be encountered within the precise examination. These pattern papers function important instruments to evaluate their data, observe problem-solving expertise, and refine their test-taking methods.

Be happy so as to add your solutions to the pattern paper questions within the feedback part beneath.

We want you the perfect of luck for GATE DSAI 2024! 👍 


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