Pattern Query Paper for GATE DA 2024

(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;
    }
    else
    {
        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
X Y Z
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?

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

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?

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 ______.

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;
        proceed;
    }
    if (j % 3 == 0)
        break;
}
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)
  Pop(S)
  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;
            break;
        }
    }

    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:

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

Q55. Take into account the next relational schema:

SELECT empName
FROM worker E
WHERE NOT EXISTS (
    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.

Conclusion

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

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