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Recent questions tagged cmi2018-datascience
2
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1
answer
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 $B^T=A^T$
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cmi2018-datascience
matrix
linear-algebra
0
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3
answers
2
CMI-2018-DataScience-A: 2
Let ... $|A|=|B|$ $|C|=|D|$ $|B|=-|C|$ $|A|=-|D|$
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cmi2018-datascience
matrix
linear-algebra
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 $xx^T=x^Tx$
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cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
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): $A^TA$ $\begin{bmatrix} 0&A^T \\ A & 0 \end{bmatrix}$ $AA^T$ $\begin{bmatrix} A & 0 \\ 0 & A^T \end{bmatrix}$
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cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
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 $\int^{18} _{-\infty} \frac{1}{\sqrt{2\pi .2^2}}\exp\{-\frac{1}{2}(\frac{x-24}{2})^2\}dx$
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Jan 29, 2021
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411
views
cmi2018-datascience
random-variable
probability
0
votes
0
answers
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
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Jan 29, 2021
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216
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cmi2018-datascience
random-variable
probability
0
votes
0
answers
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 $15\%$
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Jan 29, 2021
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172
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cmi2018-datascience
random-variable
probability
0
votes
0
answers
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
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Jan 29, 2021
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264
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cmi2018-datascience
0
votes
0
answers
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.
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Jan 29, 2021
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114
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cmi2018-datascience
0
votes
0
answers
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.
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Jan 29, 2021
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97
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cmi2018-datascience
0
votes
0
answers
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.
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Jan 29, 2021
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soujanyareddy13
98
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cmi2018-datascience
0
votes
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?
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Jan 29, 2021
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532
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cmi2018-datascience
conditional-probability
probability
0
votes
1
answer
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 $n$
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Jan 29, 2021
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543
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cmi2018-datascience
0
votes
1
answer
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 $(0,1)?$ $f(x)=\frac{1}{x(1-x)}$ $g(x)=-(x-0.75)^2$ $u(x)=\sin(\frac{\pi x}{2})$ $v(x)=x^2+2x$
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Jan 29, 2021
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331
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cmi2018-datascience
functions
discrete-mathematics
0
votes
1
answer
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?
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Jan 29, 2021
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285
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cmi2018-datascience
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: $(a+b+c+d)(u+v+w+x)>16$ $(a^4+b^4+c^4+d^4)\leq 4abcd$ $(a^2+b^2)wx\leq (c^2+d^2)uv$ $d(a^3+b^3+c^3)<3abc$
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Jan 29, 2021
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217
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cmi2018-datascience
0
votes
0
answers
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
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Jan 29, 2021
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163
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cmi2018-datascience
0
votes
1
answer
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); }
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Jan 29, 2021
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218
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cmi2018-datascience
0
votes
1
answer
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
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Jan 29, 2021
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soujanyareddy13
685
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cmi2018-datascience
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 ... $\text{(off,on,on,on,off,on,off)}$ $\text{(off,on,off,off,on,off,on)}$ $\text{(off,on,off,off,off,on,off)}$
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Jan 29, 2021
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165
views
cmi2018-datascience
0
votes
1
answer
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.
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Jan 29, 2021
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soujanyareddy13
128
views
cmi2018-datascience
discrete-mathematics
0
votes
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
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Jan 29, 2021
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223
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cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
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.
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Jan 29, 2021
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114
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cmi2018-datascience
0
votes
1
answer
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?
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Jan 29, 2021
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218
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
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.
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Jan 29, 2021
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176
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cmi2018-datascience
set-theory
discrete-mathematics
0
votes
1
answer
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 $abcd$.
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Jan 29, 2021
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98
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cmi2018-datascience
0
votes
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$?$
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Jan 29, 2021
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119
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cmi2018-datascience
0
votes
1
answer
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.
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Jan 29, 2021
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169
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cmi2018-datascience
probability
0
votes
1
answer
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?
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Jan 29, 2021
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140
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cmi2018-datascience
probability
0
votes
1
answer
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 $Rs. 100,000?$
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Jan 29, 2021
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cmi2018-datascience
probability
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