GATE Data Science and Artificial Intelligence
1. The number of additions and multiplications involved in performing Gaussian elimination on any $n \times n$ upper triang 2. For which of the following inputs does binary search take time $O(\log n)$ in the worst case? 3. Suppose that insertion sort is applied to the array $[1,3,5,7,9,11, x, 15,13]$ and it takes exactly two swaps to sort th 4. Let $G$ be a simple, unweighted, and undirected graph. A subset of the vertices and edges of $G$ are shown below.
It is 5. Which of the following statements is/are correct in a Bayesian network? 6. The state graph shows the action cost along the edges and the heuristic function $h$ associated with each state.
Suppose 7. Consider a hash table of size 10 with indices $\{0,1, \ldots, 9\}$, with the hash function
$$ h(x)=3 x(\bmod 10) $$
wher 8. If a relational decomposition is not dependency-preserving, which one of the following relational operators will be exec 9. Consider the following three relations:
Car (model, year, serial, color)
Make (maker, model)
Own (owner, serial)
A tuple 10. $$ \text { On a relation named Loan of a bank: } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-c 11. Consider a fact table in an OLAP application: Facts (D1, D2, val), where D1 and D2 are its dimension attributes and val 12. Consider the following two relations, named Customer and Person, in a
database:
Person (
aadhaar CHAR(12) PRIMARY KEY, n 13. Consider a database relation $R$ with attributes ABCDEFG , and having the following functional dependencies:
$$ \mathrm{ 14. Consider the following tables, Loan and Borrower, of a bank.
Loan
loan_num
branch_name
amount
L11
Ban 15. Suppose $X$ and $Y$ are random variables. The conditional expectation of $X$ given $Y$ is denoted by $E[X \mid Y]$. Then 16. The sum of the elements in each row of $A \in \mathbb{R}^{n \times n}$ is 1 . If $B=A^3-2 A^2+A$, which one of the follo 17. Let $f(x)=\frac{e^x-e^{-x}}{2}, x \in R$. Let $f^{(k)}(a)$ denote the $k^{\text {th }}$ derivative of $f$ evaluated at $ 18. Let $p$ and $q$ be any two propositions. Consider the following propositional statements.
$$ \begin{aligned} & S_1: p \r 19. Let X be a continuous random variable whose cumulative distribution function (CDF) $F_X(x)$, for some $t$, is given as f 20. Let $X=a Z+b$, where Z is a standard normal random variable, and $a, b$ are two unknown constants. It is given that
$$ \ 21. It is given that $P(X \geq 2)=0.25$ for an exponentially distributed random variable $X$ with $E[X]=\frac{1}{\lambda}$, 22. Consider two functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow(1, \infty)$. Both functions 23. Which of the following statements is/are correct? 24. Let $A=I_n+x x^T$, where $I_n$ is the $n \times n$ identity matrix and $x \in \mathbb{R}^n, x^T x=1$. Which of the follo 25. There are three boxes containing white balls and black balls.
Box-1 contains 2 black and 1 white balls.
Box-2 contains 1 26. $$\mathop {\lim }\limits_{t \to + \infty } \sqrt{t^2+t}-t= $$
(Round
off to one decimal place) 27. Let $Y=Z^2, Z=\frac{X-\mu}{\sigma}$, where $X$ is a normal random variable with mean $\mu$ and variance $\sigma^2$. The 28. Let $A \in \mathbb{R}^{n \times n}$ be such that $A^3=A$. Which one of the following statements is ALWAYS correct? 29. Consider the cumulative distribution function (CDF) of a random variable X :
$$ F_X(x)=\left\{\begin{array}{cc} 0 & x \l 30. A random variable X is said to be distributed as $\operatorname{Bernoulli}(\theta)$, denoted by $X \sim \operatorname{Be 31. For $x \in \mathbb{R}$, the floor function is denoted by $f(x)=\lfloor x\rfloor$ and defined as follows $\lfloor x\rfloo 32. A random experiment consists of throwing 100 fair dice, each die having six faces numbered 1 to 6 . An event $A$ represe 33. 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 f 34. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a twice-differentiable function and suppose its second derivative
satisfie 35. An $n \times n$ matrix $A$ with real entries satisfies the property: $\|A x\|^2=\|x\|^2$ for all $x \in R^n$ where $\|\c 36. Consider a coin-toss experiment where the probability of head showing up is $p$. In the $i^{\text {th }}$ coin toss, let 37. 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{ 38. A bag contains 5 white balls and 10 black balls. In a random experiment, $n$ balls are drawn from the bag one at a time 39. Consider a directed graph $G=(V, E)$, where $V=\{0,1,2, \ldots, 100\}$ and $E=\{(i$, $j): 0 40. Consider designing a linear classifier
$$ y=\operatorname{sign}(f(x ; w ; b)), f(x ; w, b)=w^{\mathrm{T}} x+b $$
on a da 41. Let $C_1$ and $C_2$ be two sets of objects. Let $D(x, y)$ be a measure of dissimilarity between two objects $x$ and $y$. 42. Given data $\{(-1,1),(2,-5),(3,5)\}$ of the form $(x, y)$, we fit a model $y=w x$ using linear least-squares regression. 43. (Round off to three decimal places)
The naive Bayes classifier is used to solve a two-class classification problem with 44. Let $\left\{x_1, x_2, \ldots ., x_n\right\}$ be a set of linearly independent vectors in $\mathbb{R}^n$. Let the $(\math 45. Consider the neural network shown in the figure with inputs: $u, v$ weights: $a, b, c, d, e, f$ output: $y$ R denotes th 46. Consider game trees Tree-1 and Tree-2 as shown. The first level is a MAX agent and the second level is a MIN agent. The 47. Which of the following statements is/are correct about the rectified linear unit (ReLU) activation function defined as $ 48. Let $x_1, x_2, x_3, x_4, x_5$ be a system of orthonormal vectors in $\mathbb{R}^{10}$. Consider the matrix $A=x_1 x_1^T+ 49. Consider designing a linear binary classifier $f(x)=\operatorname{sign} g\left(w^T x+b\right), x \in \mathbb{R}^2$ on th 50. Consider a two-class problem in $R^d$ with class labels red and green. Let $\mu_{\text {red }}$ and $\mu_{\text {green } 51. Let $D=\left\{x^{(1)}, \ldots ., x^{(n)}\right\}$ be a dataset of $n$ observations where each $x^i \in \mathbb{R}^{100}$ 52. Consider the following Python declarations of two lists.
$$ \begin{aligned} & A=[1,2,3] \\ & B=[4,5,6] \end{aligned} $$
53. Consider the following Python code snippet.
$\mathrm{A}=\{$ "this","that" $\}$
$B=\{$ "that","other" $\}$
$\mathrm{C}=\{ 54. Consider the following Python code snippet.
$\operatorname{def} f(a, b)$ :
if ( $a==0$ ):
return b
$$ \begin{aligned} &\ 55. Consider the following pseudocode.
Create empty stack S
set $x=0$, flag $=0$, sum $=0$
Push $x$ onto $S$
while ( $S$ is
General Aptitude
1.
Courage : Bravery :: Yearning :
___________ Select the most appropriate option to complete the analogy. 2. We ___________ tennis in the lawn when it suddenly started to rain. Select the most appropriate option to complete the a 3. A $4 \times 4$ digital image has pixel intensities $(U)$ as shown in the figure. The number of pixels with $U \leq 4$ is 4. In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1,2 , and 3 , respectively. Wh 5. A rectangle has a length L and a width W . where $\mathrm{L}>\mathrm{W}$. If the width, W , is increased by $10 \%$, whi 6. Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.
Column - I
Column-II
7. Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppo 8. A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius $r \mathrm{~cm}$ as shown in the figur 9. If a real variable $x$ satisfies $3^{x^2}=27 \times 9^x$, then the value of $\frac{2^{x^2}}{\left(2^x\right)^2}$ is : 10. The number of patients per shift ( $X$ ) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amoun
1
GATE AI 2025
MCQ (Single Correct Answer)
+2
-0
If a real variable $x$ satisfies $3^{x^2}=27 \times 9^x$, then the value of $\frac{2^{x^2}}{\left(2^x\right)^2}$ is :
A
$2^{-1}$
B
$2^0$
C
$2^3$
D
$2^{15}$
2
GATE AI 2025
MCQ (Single Correct Answer)
+2
-0
The number of patients per shift ( $X$ ) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is Rs $1000(X-0.2)$, what is the average amount (in she has earned per shift in the past 100 shifts?
Note : The figure shown is representative.
A
6,100
B
6,300
C
6,000
D
6,500
Paper Analysis
Total Questions
Algorithms 4
Artificial Intelligence 2
Data Structures 1
Database Management System and Warehousing 7
Discrete Mathematics 25
Machine Learning 12
Python Programming 4
General Aptitude 10
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