GATE Data Science & AI

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

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

The four pieces of a puzzle are shown in the figure below. 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...

Consider two distinct positive real numbers m, n, with m > n. Let x = nlog10(m) and y = mlog10(n). The relation between x and y is _________.

'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...

'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.

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...

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 g...

P, Q, R, S, X, and Y are distinct single-digit whole numbers taking values from 0 to 9. PQ is a two-digit number with Q being in the units place and P in the tens place. Similarly,...

In the given figure, P, Q, and R are three points on a circle of radius 10 cm with O as its center, PQ = RQ, and ∠PQR = 45°. The figure is representative. The area of the shaded re...

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 tru...

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...

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

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

Consider that the quick sort algorithm is used to sort an array of n distinct randomly ordered elements. In every call, the pivot is chosen as the first element of the current suba...

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 t...

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

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...

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

Suppose that a computer program provides a non-negative and integer-valued random solution to the equation n₁ + n₂ + n₃ + n₄ = 20. Which of the following is the probability that al...

Let $M = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}$ be a $2 \times 2$ matrix, where $\theta = \frac{2\pi}{5}$, and $I_2 = \begin{pmatrix...

Consider a set $S_1 = \{x = (x_1, x_2, x_3)^T \in \mathbb{R}^3 \mid x^T x \le 16\}$. Let $S_2$ be another set which is a subspace of $\mathbb{R}^3$ with dimension two. Which of the...

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 mat...

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

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 follo...

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...

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

Suppose a random variable Z follows Normal($\mu$ = 0, $\sigma^2$ = 1) distribution with probability density function $g(z)$ and cumulative distribution function $G(z)$. Another ran...

Consider that for a supervised learning task, the objective function being minimized is $f_w(x) = wx$, where $x \in \mathbb{R}$ is the input and $w \in \mathbb{R}$ is the parameter...

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 ther...

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 elemen...

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...

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

Let X be an exponentially distributed random variable with mean λ(> 0). If P(X > 5) = 0.35, then the conditional probability P(X > 10|X > 5) is __________. (Rounded off to two deci...

The value of $\Sigma_{i=0}^{\infty} \Sigma_{j=1}^{\infty} 2^{-i} 3^{-j}$ is __________. (Answer in integer)

Let four points in three-dimensional space be: P1: [2, 3, -1], P2: [3, 1, 1], P3: [5, -2, 3] and P4: [3, 3, 3]. Hierarchical Agglomerative Clustering is used to cluster the above p...

Which of the following statements is true for Ridge Regression?

Assume that a Creative (C) person will Succeed (S) if the person is also Disciplined (D), but will not succeed otherwise. Now, consider the following statements: (i) C ∧ S ⇔ D (ii)...

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 t...

Consider a directed graph $G = (V, E)$, where $V$ is the finite set of vertices and $E$ is the set of directed edges between the vertices. $G$ may contain cycles but there is no se...

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...

Consider the given relations X, Y and Z. The relation X has three columns P, Q and R. The relation Y has three columns P, Q and S. The relation Z has two columns P and T. Consider...

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?

Let X and Y be two independent random variables. X follows Bernoulli(p = 0.3) distribution and Y follows Normal(μ = 0, σ² = 100) distribution. Which of the following options is the...

Let L = lim_{n→∞} Σ_{k=0}^{n} (e^{-n} n^k / k!) Which of the following is the value of L?

Let $\gamma_1, \gamma_2, \gamma_3$ be the eigenvalues of the matrix $\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{bmatrix}$, where $t \in [-\pi, \p...

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...

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

Consider the problem of sorting the given array in ascending order: P = [1, 2, 3, 5, 4] Consider two sorting algorithms Bubble Sort (BS) and Insertion Sort (IS). Let N1 be the tota...

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 p...

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...

Let M = (I_n - (1/n)11^T) be a matrix, where 1 = (1,1,1, ...,1)^T ∈ R^n and I_n is the identity matrix of order n. Which of the following options is/are correct?

Let X_1,X_2,...,X_n be n independent random variables. Each of the random variables follows Normal(μ = 0, σ² = 1) distribution. Define X̄ = (1/n)Σ_{i=1}^n X_i . Which of the follow...

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

Consider that Linear Ridge Regression is being used to learn a prediction function y_pred = w^T x, where w, x ∈ R^2 and Mean Absolute Error (MAE) is used to measure the prediction...

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...

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 r...

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...

Let there be two relations X and Y as shown. X has three columns P, Q and R. Y has two columns P and S. Consider that the following tuple relational calculus expression is evaluate...

Let Account be a relation as shown. Consider the given SQL query. SELECT AccNo FROM Account AS A WHERE (SELECT COUNT(*) FROM Account AS B WHERE A.Balance = (SELECT COUNT(*) FROM Ac...

Consider an ER model with the entities E1 (A11, A12, A13) and E2 (A21, A22, A23), where, A11, A12, A13 are the attributes of E1, and A21, A22, A23 are the attributes of E2. Let A22...

For a given data set {x1, x2, ..., xn}, where n = 100, it is known that $\frac{1}{2000} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = 99$ Let us denote $\bar{x} = \frac{1}{n} \sum_...

Let X be a random variable that follows Uniform(-1,1) distribution. The conditional distribution of the random variable Y given X = x is the Uniform($x^2 - 0.1, x^2 + 0.1$) distrib...

Let A$_{5 \times 5}$ be a matrix such that each of its elements follows Bernoulli(p = 0.50) distribution independently. The probability that the row-sum of the second row and the c...

Let A = $(I_n - \frac{1}{n} \mathbf{1} \mathbf{1}^T)$ be a matrix, where $\mathbf{1} = (1,1,1, ...,1)^T \in \mathbb{R}^n$ and $I_n$ is the identity matrix of order n. The value of...

Let $\quad f: \mathbb{R} \rightarrow \mathbb{R} \quad$ be such that $|f(x)-f(y)| \leq(x-y)^2$ for all $x, y \in \mathbb{R}$. Then $\quad f(1)-f(0)=$ ____________

Consider the function $$ f(\mathrm{x})=\frac{x^3}{3}+\frac{7}{2} x^2+10 x+\frac{133}{2}, x \in[-8,0] . $$ Which of the following statements is/are correct?

Which of the following statements is/are correct in a Bayesian network?

Consider a hash table of size 10 with indices $\{0,1, \ldots, 9\}$, with the hash function $$ h(x)=3 x(\bmod 10) $$ where linear probing is used to handle collisions. The hash tabl...

Let $D=\left\{x^{(1)}, \ldots ., x^{(n)}\right\}$ be a dataset of $n$ observations where each $x^i \in \mathbb{R}^{100}$. It is given that $\sum_{i=1}^n x^{(\mathrm{i})}=0$ The cov...

Let $f(x)=\frac{e^x-e^{-x}}{2}, x \in R$. Let $f^{(k)}(a)$ denote the $k^{\text {th }}$ derivative of $f$ evaluated at $a$. What is the value of $f^{(10)}(0)$ ?(Note: ! denotes fac...

$$\mathop {\lim }\limits_{t \to + \infty } \sqrt{t^2+t}-t= $$ (Round off to one decimal place)

Consider two functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow(1, \infty)$. Both functions are differentiable at a point c . Which of the following fu...

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a twice-differentiable function and suppose its second derivative satisfies $f^{\prime \prime}(x)>0$ for all $x \in \mathbb{R}$. Which...

Consider a directed graph $G=(V, E)$, where $V=\{0,1,2, \ldots, 100\}$ and $E=\{(i$, $j): 0

Let $A \in \mathbb{R}^{n \times n}$ be such that $A^3=A$. Which one of the following statements is ALWAYS correct?

Which of the following statements is/are correct?

The sum of the elements in each row of $A \in \mathbb{R}^{n \times n}$ is 1 . If $B=A^3-2 A^2+A$, which one of the following statements is correct (for $x \in \mathbb{R}^n$ )?

Let $A=I_n+x x^T$, where $I_n$ is the $n \times n$ identity matrix and $x \in \mathbb{R}^n, x^T x=1$. Which of the following option is/are correct?

For which of the following inputs does binary search take time $O(\log n)$ in the worst case?