# Checkout the Sample Question Paper for GATE DA 2024

Nitika Sharma 21 Oct, 2023 • 11 min read

## Introduction

GATE 2024 aspirants, here’s some great news for you! The Indian Institute of Science (IISc) has just released sample papers for the upcoming GATE exam. These sample papers are helpful resources to enhance your preparation. In this blog post, we’ve compiled an extensive list of questions for GATE DA exam 2024.

## First 25 Questions Carry One Mark Each

Q1. Let 𝑏 be the branching factor of a search tree. If the optimal goal is reached after 𝑑 actions from the initial state, in the worst case, how many times will the initial 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, how many models are there for the sentence 𝐴 ∨ ¬𝐵 ∨ 𝐶?

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

Q3. Which of the following first order logic sentence matches closest with the sentence “All students are not 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)]

Q4. The mean of the observations of the first 50 observations of a process is 12. If the 51st
observation is 18, then, the mean of the first 51 observations of the process is:

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

Q6. Which among the following may help to reduce overfitting demonstrated by a
model:
i) Change the loss function.
ii) Reduce model complexity.
iii) Increase the training data.
iv) Increase the number of optimization routine steps.

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

Q7. A fair coin is flipped twice and it is known that at least one tail is observed. The probability 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 boxes, we place at random each particle in one of the boxes. The probability that in n preselected boxes, one and only one particle will be found is:

Q9. For two events A and B, 𝐵 ⊂ 𝐴 Which of the following statement is correct?

(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 support in [-2, 2] U [99.5, 100.5]. The mean of X is _

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

Q11. You are reviewing four papers submitted to a conference on machine learning for medical expert systems. All the four papers validate their superiority on a standard benchmarking cancer dataset, which has only 5% of positive cancer cases. Which of the experimental setting is acceptable to you?

1. We evaluated the performance of our model through a 5-fold cross validation process and report an accuracy of 93%.
2. The area under the ROC curve on a single left out test set of our model is around 0.8, which is the highest among all the different approaches.
3. We computed the average area under the ROC curve through 5-fold cross validation and found it to be around 0.75 – the highest among all the approaches.
4. The accuracy on a single left out test set of our model is 95%, which is the highest among all the different approaches.

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

Q12. Increasing the regularizing coefficient value for a ridge regressor will:

i) Increase or maintain model bias.
ii) Decrease model bias.
iii) Increase or maintain model variance.
iv) Decrease model variance.

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

Q13. A decision tree classifier learned from a fixed training set achieves 100% accuracy. Which of the following models trained using the same training set will also achieve 100% accuracy?

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

(A) i
(B) i and ii
(C) all of the above
(D) none of the above

Q14. Consider two relations R(x, y) and S(x,z). Relation R has 100 records, and relation S has 200 records. What will be the number of attributes and records of the following query?
SELECT * from R CROSS JOIN S;

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

Q15. Consider two relations R(x, y) and S(y), and perform the following operation R(x,y) DIVIDE S(Y)
If X is the relation returns by the above operation, which of the following option(s) is/are always TRUE?

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

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

(A) Every relation with two attributes is also in BCNF.
(B) Every relation in BCNF is also in 3NF.
(C) No relation can be in both BCNF and 3NF.
(D) None of Above

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

(A) Minima at x=-0.5
(B) Maxima at x=-0.5
(C) Saddle point at at x=-0.5
(D) None of the above.

Q20. The Pearson’s correlation coefficient between x and y rounded to the first decimal point for the given data in below table is:

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

Q21. The worst-case running times of Insertion sort, Merge sort and Quick sort 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. Consider the following program.

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

The running time of the above function is:

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

Q23. Which of the following correctly describes the recurrence relation for the standard binary search algorithm on a sorted array of n numbers where c is a constant.

(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. Consider the following C program

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

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

Q25. Two eigenvalues of 3 x 3 matrix X are (1 + i) and 2. The determinant of the matrix X is ___________.

## Question 26 to 55 Carry Two Marks Each

Q26. Given the following relation instances
X Y Z
1 4 2
1 5 3
1 4 3
1 5 2
3 2 1
Which of the following conditions 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. Consider the search space depicted in the Figure below. S is the initial state. G1 and G2 are two states that satisfy the goal test. The cost of traversing from one state to another is depicted by the numerical value close to the edge connecting the two states. The estimated cost to the goal is reported inside the states. Use alphabetical order of nodes to break ties. Which goal state is reached if you perform A* (graph) search? What is the largest value that the heuristic function can take for node A while still being admissible?

Q28. Given a discrete 𝐾-class dataset containing 𝑁 points, where sample points are described using 𝐷 features with each feature capable of taking 𝑉 values, how many parameters need to be estimated for Naïve Bayes Classifier?

Q30. For perfectly spherical 2D data centered at the origin, which of the following the pairs of vectors are possible pairs of principal components?
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, otherwise}
The variance of X is:

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

Q34. The function 𝑓(𝑥) = 1 + 2𝑥 + 3x^2+…….+2026x^2025. Which of the following statement is true?

(A) f(x) has global minimum
(B) f(x) has global maximum
(C) f(x) does not have global minimum
(D) None of the above

Q35. Given a smooth sufficiently differentiable function, the following statements are given:
(P) A concave function can have a global minimum
(Q) All convex functions have a global minimum

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

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

Q38. Given a matrix A (m x n). The following statements are made regarding the matrix A.
P. The column space is orthogonal to the row space
Q. The column space is orthogonal to the left null space
R. The row space is orthogonal to the null space
T. The null space is orthogonal to the left null space.
Which of the statement(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 records is indexed with B+ tree. If the size of a memory block is 2K bytes, the size of a key is 4 bytes, the size of a pointer is 4 bytes, what is the minimum possible height of the B+ tree index. Height is always greater than equal to 1.

Hints: No records are store in the nodes, only keys are stored. The sizes of the pointers are same, irrespective of they point to a node of a record.

Q41. Consider a schema R(A, B, C, D, E, F) and functional dependencies A -> B, C -D, and E->F. What is the number of superkeys?

Q43. Consider a Multi-Layer Perceptron (MLP) model with one hidden layer and one output layer. The hidden layer has 10 neurons, and the output layer has 3 neurons. The input to the MLP is a 5-dimensional vector. Each neuron is connected to every neuron in the previous layer, and a bias term is included for each neuron. The activation function used is the sigmoid function. Calculate the total number of trainable parameters in this MLP model.

Q44. A company manufactures a product at the rate of P units per day. The cost per unit in Rs is 𝐶 = 50 + 0.1𝑃 + 9000/𝑃. The selling price per unit is Rs. 300. The production level minimizing the cost per unit and the total profit, respectively, are:

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

Q45. A class contains 60% students who are incapable of changing their opinions about anything, and 40% of students are changing their minds at random, with probability 0.3, between subsequent votes on the same issue. Then, the probability of a student randomly chosen voted twice in the same way is ______.

Q47. Let {O1, O2, O3, O4} represent the outcome of a random experiment, with P({O1})=P({O2})=P({O3})=P({O4}). Consider the following events: P={O1,O2}, Q={O2,O3}, R={O3,O4},S={O1,O2,O3}. Then, which of the following statements is true?

(A) P and Q are independent
(B) P and Q are not independent
(C) R and S are independent
(D) Q and S are not independent

Q48. Consider the matrix X whose eigenvalues are 1, -1 and 3. Then Trace of X^3 – 3X^2 is ______________.

Q49. What is the output of the following program?

int i = 1, j = 1;
for (; i <= 10; i++) {
if (i % 3 != 0) {
j += 2;
continue;
}
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 support the Enqueue and Dequeue operations. Consider the following pseudo code for implementing the Pop and Push operation on S.

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

Which of the following options for the functions A, B, C, and D would correspond to correctly 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. Consider the following program.

int fun(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 following 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. Consider the following undirected graph on 5 nodes:

Assume you are performing breadth first search on this graph using a queue data structure. How many unique breadth first orderings are possible on this graph?

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

Q55. Consider the following relational schema:

SELECT empName
FROM employee E
WHERE NOT EXISTS (
SELECT custId
FROM customer C
WHERE C.salesRepId = E.empId
AND C.rating <> 'GOOD'
);

A) Names of all the employees with at least one of their customers having a ‘GOOD’ rating.
(B) Names of all the employees with at most one of their customers having a ‘GOOD’ rating.
(C) Names of all the employees with none of their customers having a ‘GOOD’ rating.
(D) Names of all the employees with all their customers having a ‘GOOD’ rating.

## Conclusion

The release of the GATE DA sample paper by the Indian Institute of Science (IISc) is a significant resource for aspiring data science and artificial intelligence learners. It provides a valuable glimpse into the kind of questions that may be encountered in the actual examination.