GATE Data Science & Artificial Intelligence Mock Test - 4 - GATE Architecture and Planning MCQ

Which of the following statements accurately characterizes the graph?

Determine the number that completes the sequence.

222 : 350 :: 10 : ?

The table below presents data regarding the production of various types of two-wheelers by a company from 2010 to 2015. In which year did the average production of two-wheelers reach its peak?

A traveler can choose between taking a taxi or a train. The likelihood of selecting a taxi is 0.6. If the traveler decides to take the train, they will then have further options between a local train and an express train, with the probability of opting for a local train being 0.7. What are the probabilities of choosing a taxi, a local train, and an express train, respectively?

In what way does the time complexity of Dijkstra's algorithm vary when implemented with a Fibonacci heap as opposed to a conventional data structure?

If the matrix A(a_ij)_mxn is defined such that a_ij = i j for all values of i and j, what is the total sum of all the elements in matrix A = ________.

Imagine we have integers ranging from 1 to 1000 organized in a binary search tree, and we aim to locate the number 363. Which of the following sequences could not represent the order of nodes evaluated during this search?

Which of the following statements is/are accurate?

S1: In a binary search tree, if a node has two children, then its successor will not have a left child, and its predecessor will not have a right child.

S2: Consider a binary search tree T with distinct keys. If node 'x' in T has an empty right subtree and possesses a successor 'y', then 'y' is the nearest ancestor of 'x' whose left child is also an ancestor of 'x' (remember that every node is considered an ancestor of itself).

If the letters of the word “ADDRESS” are arranged randomly in a sequence, what is the likelihood that the two vowels are positioned next to each other?

Given a functional dependency X → Y, a table qualifies as being in BCNF if -

Consider an array of n integers pointed to by p. Our objective is to create a new array, pointed to by q, that contains each element of the original array duplicated. For instance, if the array pointed to by p holds the values 3, 1, 2, 2, 6, the resultant array pointed to by q should consist of 3, 3, 1, 1, 2, 2, 2, 2, 6, 6. What needs to be filled in the blank to finalize the implementation of the following function?

void duplicate (int *p, int n, int *q)

{ int i; for (i = 0; i < n; i) { q = 2; p; }

Marketing predicts that a new device for analyzing soil samples will be categorized as very successful, moderately successful, or unsuccessful, with probabilities of 0.3, 0.6, and 0.1, respectively. The anticipated annual revenue for a very successful, moderately successful, or unsuccessful product is 10,000,00, 85,000,00, and 21,00,000, respectively. What is the expected yearly revenue for this product?

Given a set A = {1,2,3,5,6}, what is the total number of ordered sequences that can be formed by selecting 4 elements without any repetition?

Consider a 3x3 matrix A with eigenvalues 2, 3, and 4, and let I denote the identity matrix of order 3. If the equation A^-1 = (A² - 9A) / (2k 13I/k) holds for some integer k ≠ 0, what is the value of k?

Which of the following assertions are accurate concerning topological ordering?

I. It represents a linear arrangement of vertices such that for every directed edge uv, vertex 'u' precedes 'v' in the arrangement.

II. Topological sorting of a graph cannot be accomplished if the graph is not a Directed Acyclic Graph (DAG).

Create an E-R model based on the following premise and determine the degree of the relationship: "An Employee can be involved in multiple departments and various projects."

In the context of Support Vector Machines (SVM), consider a training dataset { (x_i, y_i) } for i = 1, ..., n, where the labels y_i belong to {-1, 1}.

The primal form of the SVM objective function is:

min_w,b λ w λ 1/2 subject to y_i(w^Tx_i b) ≥ 1

Which of the following statements is accurate regarding the dual formulation of the SVM optimization problem?

Examine the dual formulation in support vector machines (SVM), where the objective is to maximize:

Which of the following statements is/are CORRECT?

S1. A heap containing "n" elements has a height of Llogn.

S2. Within any subtree of a max heap, the root node contains the highest value present in that subtree.

In a Bayesian Neural Network (BNN), suppose the prior over the weights is p (θ) = N (θ | 0, I)  and the likelihood is Gaussian p ( y I x, θ) = N (y I f (x ; θ), σ 2). Using Variational Inference, we approximate the posterior with a variational distribution q (θ | ϕ ). Which of the following is true about the Evidence Lower Bound (ELBO) used in Variational Inference?

Consider a dataset X = {x 1, x 2, …, x n} containing n observations, where each x i is a d-dimensional vector. The covariance matrix Σ of the dataset is determined using the formula: Σ = 1/n ∑ (x i - μ)(x i - μ) T, with μ representing the mean of the dataset. Which of the following statements about the covariance matrix is incorrect?

Consider two similar square matrices, A and B, both of order two. Given that the eigenvalues of A are 1 and -2, what is the trace of B²?

Given the relation R(ABC) with functional dependencies defined as AB→C, AC→B, and BC→A, what is the normal form that this relation adheres to?

Identify which of the following is an example of a supervised learning problem:

1. Classifying similar documents from a collection that lacks labels.
2. Forecasting credit approval using past data.
3. Estimating rainfall based on historical information.
4. Determining whether a customer will return or retain a specific item purchased from an e-commerce site, based on past customer purchase data and details about that item.
5. Recognizing an individual's fingerprint for biometric attendance using fingerprint data from various individuals, including that specific person.

We have 7 tasks labeled J1, J2, J3, J4, J5, J6, and J7. Each task requires one unit of time to complete, and only one task can be executed at any given moment. What is the highest possible profit?

Consider a connected undirected graph G that consists of 200 vertices and 400 edges. The weight of its minimum cost spanning tree is 600. If the weight of each edge is raised by 5, what will be the new weight of the minimum spanning tree?

How many distinct binary search trees can be formed using the elements {12, 34, 22, 43, 13, 45, 55, 94, 99, 23} if 45 is chosen as the root node?