Recent questions tagged cmi2022-datascience

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From where to practice questions for Data Science and AI paper of GATE 2024?
Which resources to follow to practice questions for DS and AI paper of GATE 2024? Which resources to follow? where to find them Questions for Mathematics and questions for AI? A bit of help on that would be much appreciated

Which resources to follow to practice questions for DS and AI paper of GATE 2024?Which resources to follow?where to find themQuestions for Mathematics and questions for A...

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rajveer43 asked Dec 10, 2023

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I am planning to take the GATE 2024 exam in Data Science and AI. Will I be eligible for admission to the Master in Computer Engineering? More specifically for admission in Government institutions like IITs, NITs, IIITs, and IISC.

I am planning to take the GATE 2024 exam in Data Science and AI. Will I be eligible for admission to the Master in Computer Engineering? More specifically for admission i...

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Babil asked Sep 8, 2023

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CMI-2022-DataScience-B: 1
There are three different approaches that climbers can take to reach the summit of Mount Chernoff, namely, $\text{APPROACH-I, APPROACH-II,}$ and $\text{APPROACH-III.}$ Each attempt at the summit uses exactly one of these approaches. From climbers' ... reported one day that climber Chebyshev has lost her way. What is the probability that she took $\text{APPROACH-II?}$

There are three different approaches that climbers can take to reach the summit of Mount Chernoff, namely, $\text{APPROACH-I, APPROACH-II,}$ and $\text{APPROACH-III.}$ Ea...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 2
Dasholytics Inc runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At any point in time one of these three machines has the job of serving ... total service outage caused by all the three servers, as a percentage of the total duration over which the information was collected.

Dasholytics Inc runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At an...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 3
Dasholytics Ine runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At any point in time one of these three machines has the job of serving the data, ... over which this information was collected. What is the expected number of hours of service outage in an year ( $365$ days)?

Dasholytics Ine runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At an...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 4
Dasholytics Inc runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At any point in time one of these three machines has the job of serving the data, ... was a service outage at this point in time, and that Server $1$ was the server responsible for serving data at that time?

Dasholytics Inc runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At an...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 5
Dasholytics Inc runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At any point in time one of these three machines has the job of serving the data ... the three servers, was sent out to the Dasholyltics team. What is the probability that this outage was caused by Server $1?$

Dasholytics Inc runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At an...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 6
In a question paper, there are $5$ questions in part $\text{A}, 4$ in part $\text{B},$ and $3$ in part $\text{C}$. In how many ways can a candidate make up her choice, if she has to select $3$ from part $\text{A}, 2$ from part $\text{B}$, and $2$ from part $\text{C?}$

In a question paper, there are $5$ questions in part $\text{A}, 4$ in part $\text{B},$ and $3$ in part $\text{C}$. In how many ways can a candidate make up her choice, if...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 7
The probability density function of a normal distribution with mean $\mu$ and variance $\sigma^{2}$ is of the form $ f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-0.5\left(\frac{x-\mu}{\sigma}\right)^{2}}, \quad-\infty<x<\infty . $ Let ... the average number of sales in a week will be more than $8?$ What is the total number of sales over the $36$ weeks which were sampled?

The probability density function of a normal distribution with mean $\mu$ and variance $\sigma^{2}$ is of the form $$ f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-0.5\left(\fra...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 8
The probability density function of a normal distribution with mean $\mu$ and variance $\sigma^{2}$ is of the form $ f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-0.5\left(\frac{x-\mu}{\sigma}\right)^{2}}, \quad-\infty<x<\infty . $ Let $X$ be ... $50 \%$.

The probability density function of a normal distribution with mean $\mu$ and variance $\sigma^{2}$ is of the form $$ f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-0.5\left(\fra...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 9
Two particles move in opposite directions around a circular track. The first moves at a constant speed of $\text{10 m/s.}$ The speed of the second increases at a constant rate of $\text{2 m/s}$ every second. The particles are at the same ... this information: What is the circumference of the track? At what time did the particles meet for the first time after time $0?$

Two particles move in opposite directions around a circular track. The first moves at a constant speed of $\text{10 m/s.}$ The speed of the second increases at a constant...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 10
Words are formed using the characters $0$ and $1.$ The length of a word is the number of characters in it. We say there is a path from word $x$ to word $y$ if starting from the word $x$ ... equivalence class. How many three letter words are there in this language which have no shorter descriptions and which are all in different equivalance classes?

Words are formed using the characters $0$ and $1.$ The length of a word is the number of characters in it. We say there is a path from word $x$ to word $y$ if starting fr...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 11
You are given an $8 \times 8$ chessboard and a large supply of $\text{T}$-shaped tiles and square-shaped tiles of the kind shown below. Note that the squares in these two shaped tiles are of the same size as the black/white squares on the chessboard. ... shaped tiles? Why? Is it possible to cover the chessboard with $15 \; \text{T}$ shaped tiles and one square tile? Why?

You are given an $8 \times 8$ chessboard and a large supply of $\text{T}$-shaped tiles and square-shaped tiles of the kind shown below. Note that the squares in these two...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 12
To guard against login attempts by bots, Alphabet Bank of India uses a captcha challenge on their net banking login page. The captcha text is a sequence of five letters from the English alphabet. An early version of the captcha text ... the probability that the captcha text generated in this way has the first two letters in increasing alphabetical order, and why?

To guard against login attempts by bots, Alphabet Bank of India uses a captcha challenge on their net banking login page. The captcha text is a sequence of five letters f...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 13
Among $40$ bicycle gears, $28$ are broken or rusted but not both, $6$ are non-defective (i.e., neither rusted nor broken), and the number of broken gears equals the number of rusted ones. How many gears are rusted?

Among $40$ bicycle gears, $28$ are broken or rusted but not both, $6$ are non-defective (i.e., neither rusted nor broken), and the number of broken gears equals the numbe...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 14
Consider the following code, in which $\text{A}$ and $\text{B}$ are arrays indexed from $0$ and $\textsf{lenA}$ and $\textsf{lenB}$ are the numbers of elements in $\text{A}$ and $\text{B}$, respectively. function foo (A, B, lenA, lenB) { acc = 0; for i = 0 to (lenA ... $\text{B}=[9, 5, 5, 3, 3, 1]$. What are the two values printed by $\textsf{foo (A, B, 5,6)},$ in order?

Consider the following code, in which $\text{A}$ and $\text{B}$ are arrays indexed from $0$ and $\textsf{lenA}$ and $\textsf{lenB}$ are the numbers of elements in $\text{...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 15
Consider the following code, in which $\text{A}$ and $\text{B}$ are arrays indexed from $0$ and $\textsf{lenA}$ and $\textsf{lenB}$ are the numbers of elements in $\text{A}$ and $\text{B}$, respectively. function foo (A, B, lenA, lenB) { sum = lenA + lenB; i = 0 ; j = 0 ; ... $\text{B} = [1, 3, 5, 7, 9, 11, 13]$. What does $\textsf{foo(A, B, 7, 7)}$ return?

Consider the following code, in which $\text{A}$ and $\text{B}$ are arrays indexed from $0$ and $\textsf{lenA}$ and $\textsf{lenB}$ are the numbers of elements in $\text{...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 16
Consider the following code, in which $\textsf{A}$ is an integer array of length $\textsf{n}$ indexed from $\textsf{0},$ and $\textsf{x}$ is an integer. function foo (A, x, n) { found = False ; while (found != True) { i = randInt (0, n) ; if ... the expected number of times that the call $\textsf{randInt (0, n)}$ is made from within this call to $\textsf{foo (A, x, n)}?$

Consider the following code, in which $\textsf{A}$ is an integer array of length $\textsf{n}$ indexed from $\textsf{0},$ and $\textsf{x}$ is an integer. function foo (A, ...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 17
A graph consists of a finite set of vertices, and edges between some (unordered) pairs of these vertices. The graphs in this question have no loops (an edge between a vertex and itself) or multiple edges (more than one edge between the same pair of vertices). ... vertex $v_{1}$ is a global vertex in graph $G$? What is the expected number of global vertices in graph $G$?

A graph consists of a finite set of vertices, and edges between some (unordered) pairs of these vertices. The graphs in this question have no loops (an edge between a ver...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 18
The sum of two positive integers $a$ and $b$ is $48$ and their least common multiple is $189.$ Find $a$ and $b$.

The sum of two positive integers $a$ and $b$ is $48$ and their least common multiple is $189.$ Find $a$ and $b$.

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 19
Recall that for an $n \times n$ matrix $A$, $\text{det}(A)=\operatorname{det}(A^{T})$. Here $A^{T}$ is the transpose of matrix $A$. An $n \times n$ matrix $A$ is said to be skew-symmetric if $a_{i, j}=-a_{j, i}$ ... determinant of an $n \times n$-skew symmetric matrix is $0.$ Give an example of a $2 \times 2$ skew-symmetric matrix whose determinant is non-zero.

Recall that for an $n \times n$ matrix $A$, $\text{det}(A)=\operatorname{det}(A^{T})$. Here $A^{T}$ is the transpose of matrix $A$. An $n \times n$ matrix $A$ is said to ...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-B: 20
An object $X$ is viewed from a camera placed at point $C_{1}$. The camera is then moved to the point $C_{2}$ and $X$ is again viewed from this new position. Suppose $H$ is the plane containing the points $C_{1}$ and $C_{2}$ ... depth $z$ i.e. distance of the object from the camera plane in terms of $f$, the distance $b$ between the cameras, and the disparity.

An object $X$ is viewed from a camera placed at point $C_{1}$. The camera is then moved to the point $C_{2}$ and $X$ is again viewed from this new position. Suppose $H$ i...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-A: 1
Let $X$ be a $\operatorname{Binomial}(n, p)$ random variable with the probability mass function $ \mathbb{P}(X=k)=\left(\begin{array}{l} n \\ k \end{array}\right) p^{k}(1-p)^{n-k}, \quad k=0,1,2, \ldots, n . $ Let $T$ ... $\mathbb{E}\left(T^{2}\right)=n p(1-p)^{n-1}$ $\mathbb{E}(T)=p$ and $\mathbb{V}(T)=p(1-p)$

Let $X$ be a $\operatorname{Binomial}(n, p)$ random variable with the probability mass function$$ \mathbb{P}(X=k)=\left(\begin{array}{l} n \\ k \end{array}\right) p^{k}(1...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-A: 2
Consider the following code, in which $\textsf{A}$ is an array indexed from $\textsf{0}$ and $\textsf{n}$ is the number of elements in $\textsf{A}$. function foo (A, n) { L = 0; R = n - 1; while (L <= R) { i = ceil ((L + R) / 2); if (A [i] , i) { L = i + 1 ; } ... $\textsf{foo (A, 10)}$ return? $ - 5$ $ - 1$ $4$ $6$

Consider the following code, in which $\textsf{A}$ is an array indexed from $\textsf{0}$ and $\textsf{n}$ is the number of elements in $\textsf{A}$.function foo (A, n) { ...

185 views

admin asked Jul 23, 2022

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CMI-2022-DataScience-A: 3
Which of the following statements is/are true? For any real number $r$ with $|r|>1, \displaystyle{}\lim _{n \rightarrow \infty} \sum_{i=1}^{n} 17 r^{n}=\frac{17}{1-r}$. Let $i$ be the positive square root of $-1$ and let $x$ be any real number ... is a probability density function.

Which of the following statements is/are true?For any real number $r$ with $|r|>1, \displaystyle{}\lim _{n \rightarrow \infty} \sum_{i=1}^{n} 17 r^{n}=\frac{17}{1-r}$.Let...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-A: 4
Let $E$ and $F$ be events such that $P\left(E \cap F^{c}\right)=0.2, P\left(F \cap E^{c}\right)=0.3, P\left((E \cap F)^{c}\right)=0.7$, where, for an event $E$, the notation $E^{c}$ denotes the complement of the event. Then we can conclude that $P(E \cup F)=0.8$. $P\left(E^{c} \cap F^{c}\right)=0.3$. $P(F)=0.6$. $P(E)=0.6$.

Let $E$ and $F$ be events such that $P\left(E \cap F^{c}\right)=0.2, P\left(F \cap E^{c}\right)=0.3, P\left((E \cap F)^{c}\right)=0.7$, where, for an event $E$, the notat...

161 views

admin asked Jul 23, 2022

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27

CMI-2022-DataScience-A: 5
Let $A, B$ be $n \times n$ invertible matrices of real numbers. Let $C=I+A A^{T}, D=I+B A A^{T} B^{T}$. We can conclude that $(A B)^{-1}=\left(I+B^{-1} A^{-1}\right)$ $(A B)^{-1}=A^{-1} B^{-1}$ $C=C^{T}$ $D=D^{T}$

Let $A, B$ be $n \times n$ invertible matrices of real numbers. Let $C=I+A A^{T}, D=I+B A A^{T} B^{T}$. We can conclude that$(A B)^{-1}=\left(I+B^{-1} A^{-1}\right)$$(A B...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-A: 6
A matrix $C$ is said to be symmetric if $C^{T}=C$. Which of the following is/are true? Let $A, B$ be $n \times n$ matrices. If $A$ is symmetric and invertible, then $A^{-1}$ is also symmetric and invertible. If $A$ and $B$ ... $A$ and $B$ are invertible, then $C=A B$ is also invertible. If $A$ and $B$ are symmetric, then $D=A+B$ is also symmetric.

A matrix $C$ is said to be symmetric if $C^{T}=C$. Which of the following is/are true? Let $A, B$ be $n \times n$ matrices.If $A$ is symmetric and invertible, then $A^{-1...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-A: 7
Which of the following statements is/are true? Let $A$ be a $n \times m$ matrix with $n<m$. Then there is a nonzero solution $y$ with $A y=0$ only if $A$ has full row rank. Let $A$ be a $n \times m$ matrix with $n>m$. There is a nonzero solution $y$ with ... , where $B$ has size $n \times r$ and $C$ has size $r \times n$. The rank of $A$ is less than or equal to $r$.

Which of the following statements is/are true?Let $A$ be a $n \times m$ matrix with $n<m$. Then there is a nonzero solution $y$ with $A y=0$ only if $A$ has full row rank...

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admin asked Jul 23, 2022

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CMI-2022-DataScience-A: 8
Let $n \geq 5$ be a natural number, let $X=\left\{x_{1}, x_{2}, \dots, x_{n}\right\}$, and let $Y=\left\{y_{1}, y_{2}\right\}$. Let $F$ be the set of functions from $X$ to $Y$ and $G$ be the set of bijective functions from $X$ to $Y$. ... number of functions in $F$ equals $2^{n}$. The number of functions in $G$ equals $n^{2}-2$. The number of functions in $G$ equals $0.$

Let $n \geq 5$ be a natural number, let $X=\left\{x_{1}, x_{2}, \dots, x_{n}\right\}$, and let $Y=\left\{y_{1}, y_{2}\right\}$. Let $F$ be the set of functions from $X$ t...

187 views

admin asked Jul 23, 2022

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