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1

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' ... is reported one day that climber Chebyshev has lost her way. What is the probability that she took $\text{APPROACH-II?}$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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2

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.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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3

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)?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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4

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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5

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 $1?$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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6

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 $\text{C?}$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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7

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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8

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 ... $50 \%$.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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9

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 $0?$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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10

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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11

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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12

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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13

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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14

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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15

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?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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16

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 $\textsf{foo (A, x, n)}?$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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17

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 $G$?

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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18

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 $b$.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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19

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.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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20

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.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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21

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 $\mathbb{V}(T)=p(1-p)$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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22

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$ $4$ $6$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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23

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.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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24

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 $P(E \cup F)=0.8$. $P\left(E^{c} \cap F^{c}\right)=0.3$. $P(F)=0.6$. $P(E)=0.6$.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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25

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 $(A B)^{-1}=\left(I+B^{-1} A^{-1}\right)$ $(A B)^{-1}=A^{-1} B^{-1}$ $C=C^{T}$ $D=D^{T}$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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26

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.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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27

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 $r$.

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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28

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 $0.$

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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29

CMI-2022-DataScience-A: 9
In order to select a debating team to represent a school, $7$ students from class XII and $13$ students from class XI were shortlisted and were undergoing trials. The coach had to select a team of $5$ students, out of which at least two students should be from each ...

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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30

CMI-2022-DataScience-A: 10
Which of the following plots correspond to a function whose derivative is continuous? (i) and (ii) (ii) and (iii) (iii) and (iv) (ii) and (iv)

Lakshman Patel RJIT asked in Others Jul 23, 2022

by Lakshman Patel RJIT

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