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Recent questions tagged cmi2018-datascience

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1

CMI-2018-DataScience-A: 1
If $P$ is an invertible matrix and $A=PBP^{-1},$ then which of the following statements are necessarily true? $B=P^{-1}AP$ $|A|=|B|$ $A$ is invertible if and only if $B$ is invertible $B^T=A^T$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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3 answers

2

CMI-2018-DataScience-A: 2
Let ... $|A|=|B|$ $|C|=|D|$ $|B|=-|C|$ $|A|=-|D|$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

391 views

2 votes

2 answers

3

CMI-2018-DataScience-A: 3
Let $x=\begin{bmatrix} 3& 1 & 2 \end{bmatrix}$. Which of the following statements are true? $x^Tx$ is a $3\times 3$ matrix $xx^T$ is a $3\times 3$ matrix $xx^T$ is a $1\times 1$ matrix $xx^T=x^Tx$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

280 views

1 vote

1 answer

4

CMI-2018-DataScience-A: 4
A $n\times n$ matrix $A$ is said to be $symmetric$ if $A^T=A$. Suppose $A$ is an arbitrary $2\times 2$ matrix. Then which of the following matrices are symmetric (here $0$ denotes the $2\times 2$ matrix consisting of zeros): $A^TA$ $\begin{bmatrix} 0&A^T \\ A & 0 \end{bmatrix}$ $AA^T$ $\begin{bmatrix} A & 0 \\ 0 & A^T \end{bmatrix}$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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5

CMI-2018-DataScience-A: 5
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ ... .02 $\int^{18} _{-\infty} \frac{1}{\sqrt{2\pi .2^2}}\exp\{-\frac{1}{2}(\frac{x-24}{2})^2\}dx$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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6

CMI-2018-DataScience-A: 6
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ ... more than 0.4 less than 0.5

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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7

CMI-2018-DataScience-A: 7
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$ ... than $26$ months approximately equals $16\%$ is more than $15\%$ is less than $14\%$ is between $10\%$ and $15\%$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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8

CMI-2018-DataScience-A: 8
$\text{Description for the following question:}$ Given below is the time table for a transcontinental train cutting across several time zones. All times given below are local time in respective cities. It is given that the average speed between any two cities is ... the following pairs of cities are in the same time zone? Zut and Yag Xum and Wip Vaq and Uap Tix and Sab

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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9

CMI-2018-DataScience-A: 9
$\text{Description for the following question:}$ Given below is the time table for a transcontinental train cutting across several time zones. All times given below are local time in respective cities. It is given that the average speed between any two cities is the ... Write down the total time taken in minutes by the train to go from Zut to Raz.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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10

CMI-2018-DataScience-A: 10
$\text{Description for the following question:}$ Given below is the time table for a transcontinental train cutting across several time zones. All times given below are local time in respective cities. It is given that the average speed between any two cities is the same for ... $12:00$ noon at Zut.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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11

CMI-2018-DataScience-A: 11
$\text{Description for the following question:}$ Given below is the time table for a transcontinental train cutting across several time zones. All times given below are local time in respective cities. It is given that the average speed between any two cities is the same for ... $12:00$ noon at Raz.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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2 answers

12

CMI-2018-DataScience-A: 12
In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only $20\%$ candidates think they know the answer to one difficult question and only half of them know it ... same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew the answer?

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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13

CMI-2018-DataScience-A: 13
There are $n$ songs segregated into $3$ play lists. Assume that each play list has at least one song.The number of ways of choosing three songs consisting of one song from each play list is: $>\frac{n^3}{27}$ for all $n$ $\leq \frac{n^3}{27}$ for all $n$ $\left( \begin{array}{c} n \\ 3 \end{array} \right)$ for all $n$ $n^3$ for all $n$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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14

CMI-2018-DataScience-A: 14
Consider the following functions defined from the interval $(0,1)$ to real numbers. Which of these functions attain their maximum value in the interval $(0,1)?$ $f(x)=\frac{1}{x(1-x)}$ $g(x)=-(x-0.75)^2$ $u(x)=\sin(\frac{\pi x}{2})$ $v(x)=x^2+2x$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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15

CMI-2018-DataScience-A: 15
A farmer owns $50$ papaya trees. Each tree produces $600$ papayas in a year. For each additional tree planted in the orchard, the output of each tree (including the pre-existing ones) drops by $5$ papayas. How many trees should be added to the existing orchard in order to maximize the total production of papayas?

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

285 views

1 vote

1 answer

16

CMI-2018-DataScience-A: 16
Let $a,b$ be numbers between $1$ and $2$ and let $c,d$ be numbers between $3$ and $4$. Let $u=a^{-1},v=b^{-1},w=c^{-1}$ and $x=d^{-1}$. Say which of the following inequalities are true: $(a+b+c+d)(u+v+w+x)>16$ $(a^4+b^4+c^4+d^4)\leq 4abcd$ $(a^2+b^2)wx\leq (c^2+d^2)uv$ $d(a^3+b^3+c^3)<3abc$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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17

CMI-2018-DataScience-A: 17
In the code fragment below, $\text{start}$ and $\text{end}$ are integer values and $\text{square(x)}$ is a function that returns $\text{Ture}$ if $\text{x}$ is a perfect square and $\text{False}$ otherwise. i := 0; j := 0; k :=0; for m in [start,start+1,...,end] ... $\text{j = k-i if (end - start)}$ is even $\text{i = k-j if (end - start)}$ is odd

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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18

CMI-2018-DataScience-A: 18
Given the following definition of the function $foo$, what does $foo(1037,2)$ return? Note that $a//b$ denotes the quotient (integer part) of $a\div b$, for integers $a$ and $b$. For instance $7//3$ is $2$. function foo(n,d) { x:=0; while(n>=1) { x:=x+1; n:=n//d; } return(x); }

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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19

CMI-2018-DataScience-A: 19
A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet three inhabitants: Ramesh, Bharath and Menaka. Ramesh claims, Bharat is a knave. Bharat says, Menaka and I are both ... correct? Bharat is a knave Ramesh is a knight Exactly two of the three are knaves Exactly two of the three are knights

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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2 votes

1 answer

20

CMI-2018-DataScience-A: 20
There are $7$ switches on a switchboard, some of which are $on$ and some of which are $off$. In one move, you pick any $2$ switches and toggle each of them-if the switch you pick is currently $off$, you turn it $on$, if it is $on$, you turn it $off$. Your aim is ... $\text{(off,on,on,on,off,on,off)}$ $\text{(off,on,off,off,on,off,on)}$ $\text{(off,on,off,off,off,on,off)}$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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21

CMI-2018-DataScience-B: 1
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Let $N=\{1,2,3,...\}$ be the set of natural integers and let $f:N\times N \mapsto N$ be defined by $f(m,n)=(2m-1)*2^n.$Is $f$ injective? Is $f$ surjective? Give reasons.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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2 answers

22

CMI-2018-DataScience-B: 2
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Suppose $A,B$ and $C$ are $m\times m$ matrices. What does the following algorithm compute? (Here $A(i,j)$ ... .) for i=1 to m for j=1 to m for k=1 to m C(i,j)=A(i,k)*B(k,j)+C(i,j) end end end

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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23

CMI-2018-DataScience-B: 3
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Find $A^{10}$ where $A$ is the matrix $\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$. Justify your answer.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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24

CMI-2018-DataScience-B: 4
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. In computing, a floating point operation (flop) is any one of the following operations ... . How does this number change if both the matrices are upper triangular?

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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25

CMI-2018-DataScience-B: 5
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. A function $f$ from the set $A$ to itself is said to have a fixed point if $f(i)=i$ ... $A$ is the set $\{a,b,c,d\}$. Find the number of bijective functions from the set $A$ to itself having no fixed point.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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26

CMI-2018-DataScience-B: 6
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. A $4$-digit number is represented as $abcd$ ... $a\neq0.$ Suppose the number $dcba$, obtained by reversing the digits of $abcd$, is $9$ times $abcd$. Find the number $abcd$.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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1 answer

27

CMI-2018-DataScience-B: 7
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. A computer password requires you to use exactly $1$ uppercase letter, $3$ ... $33$ special characters that can be used). In how many ways can you create such a password$?$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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28

CMI-2018-DataScience-B: 8
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. $\text{Description for the following question:}$ Suppose $X$ is the ... credit default in a year. You can assume that whether a given debtor will default or not is independent of the behavior of other debtors.

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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29

CMI-2018-DataScience-B: 9
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. $\text{Description for the following question:}$ Suppose $X$ is the number ... expected number of success is $\mathbb{E}(X)=np$. For the situation in the previous problem, what is the expected number defaults?

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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30

CMI-2018-DataScience-B: 10
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. $\text{Description for the following question:}$ Suppose $X$ is the number of ... credit than the bank loses the entire loan amount. What is the expected revenue of the bank from a loan of $Rs. 100,000?$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

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