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0
votes
61
CMI-2019-DataScience-B: 2
$\text{Description of the following question:}$ Suppose $X$ is the number of successes out of $n$ trials, where the trails are independent of each other. The probability of success at every trial is $p$. The probability that there will be exactly $k$ successes ... of the event that the gambler will lose all one million times that she/he will try. Note: $1$ million =$10^6$.
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Others
May 8, 2021
86
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cmi2019-datascience
0
votes
62
CMI-2019-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. For positive numbers $a,b,c,$ show that $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\geq 3$
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Others
May 8, 2021
71
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cmi2019-datascience
0
votes
63
CMI-2019-DataScience-A: 17
If $Z$ is a continuous random variable which follows a Gaussian distribution with mean=$0$ and standard deviation=1, then $\mathbb{P}(Z \leq a)= \int^a_{-\infty}\frac{\exp \{ -z^2 / 2 \}} {\sqrt{2 \pi} }dz=\Phi (a)$ ... $\mu=53.33\;\text{and}\;\sigma=13.33$; $\mu=50\;\text{and}\;\sigma=15$;
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Others
May 8, 2021
135
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cmi2019-datascience
0
votes
64
CMI-2019-DataScience-A: 13
Abha and Vibha both have white and yellow handkerchieves. To distinguish them, their mother has marked Abha's handkerchieves with the letter $A$ and Vibha's handkerchieves with letter $V$. There are $8$ white handkerchieves of which $3$ belong to Abha, and $11$ yellow ... marked $V$. What is the probability that the handkerchief was yellow? $5/12$ $7/19$ $7/12$ $11/19$
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Others
May 8, 2021
113
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cmi2019-datascience
0
votes
65
CMI-2019-DataScience-A: 12
Three boxes are presented to you. At most one of them contains some gold. Each box has printed on it a clue about its contents. The clues are: $\textbf{(Box 1)}\; The\; gold\; is\; not\; here.$ $\textbf{(Box 2)} \; The\; gold\; is\; not\; here.$ ... Only one clue is true; the other two are false. Which box has the gold? Box 1 Box 2 Box 3 None of them has the gold
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Others
May 8, 2021
74
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cmi2019-datascience
0
votes
66
CMI-2019-DataScience-A: 10
$\text{Description for the following question:}$ The following table gives the budget allocation (in Rupees Crores) to $5$ ... percentage of total allocation, the maximum quarterly expenditure ( in any quarter) was shown by $D2$ $D5$ $D1$ $D3$
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Others
May 8, 2021
91
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cmi2019-datascience
0
votes
67
CMI-2019-DataScience-A: 9
In the code fragment below, $\text{start}$ and $\text{end}$ are integer values and $\text{prime(x)}$ is a function that returns $\text{True}$ if $\text{x}$ is a prime number and $\text{False}$ otherwise. i = 0; j = 0; k = 0; for m=start to end { if prime(m)==True ... $\text{k = k + 1}$ Statement 1: $\text{k = k - 1}$ and Statement 2: $\text{k = k - 1}$
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Others
May 8, 2021
108
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cmi2019-datascience
0
votes
68
CMI-2019-DataScience-A: 8
Consider the following Venn diagram. The universal set $U$ is the set of all natural numbers from $1$ to $1000.$ The sets $A,B,C$ contain integers in $U$ that are multiples of $6,7,8$ respectively. The number of elements in the shaded region is: $12$ $15$ $16$ $17$
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Others
May 8, 2021
188
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cmi2019-datascience
0
votes
69
CMI-2019-DataScience-A: 7
We need to choose a team of $11$ from a pool of $15$ players and also select a captain. The number of different ways this can be done is: $\begin{pmatrix}15\\11 \end{pmatrix}$ $11\cdot \begin{pmatrix}15\\11 \end{pmatrix}$ ... $(15\cdot 14\cdot 13 \cdot 12 \cdot 11\cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5)\cdot 11$
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Others
May 8, 2021
86
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cmi2019-datascience
0
votes
70
CMI-2019-DataScience-A: 2
If $P(A\cup B)=0.7$ and $P(A\cup B^c)=0.9$ then find $P(A).$
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Others
May 8, 2021
95
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cmi2019-datascience
0
votes
71
CMI-2019-DataScience-A: 1
Let $X=\{ x_1,x_2,\dots,x_n\}$ and $Y=\{y_1,y_2\}$. The number of surjective functions from $X$ to $Y$ equals $2^n$ $2^n-1$ $2^n-2$ $2^{n/2}$
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Others
May 8, 2021
94
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cmi2019-datascience
2
votes
72
CMI-2020-DataScience-B: 4
In the figure shown below, the circle has diameter $5$. Moreover, $AB$ is parallel to $DE.$ If $DE=3$ and $AB=6,$ what is the area of triangle $ABC?$
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Quantitative Aptitude
May 8, 2021
175
views
cmi2020-datascience
geometry
triangle
1
vote
73
CMI-2020-DataScience-B: 5
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2,\dots ,n\}$ to itself. We denote it using the notation $\begin{pmatrix}1 & 2 & & n \\ {\sigma(1)} & {\sigma(2)} &\dots & {\sigma(n)} \end{pmatrix},$ ...
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in
Others
May 8, 2021
153
views
cmi2020-datascience
combinatory
0
votes
74
CMI-2020-DataScience-B: 6
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2, ,n\}$ to itself. We denote it using the notation $\begin{pmatrix}1 & 2 & & n \\ {\sigma(1)} & {\sigma(2)} & & {\sigma(n)} \end{pmatrix},$ e.g. ... $|A_{\sigma} |$ and $|A_\tau|?$ Can you relate these with the signs of permutations $\sigma$ and $\tau ?$
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Others
May 8, 2021
110
views
cmi2020-datascience
combinatory
0
votes
75
CMI-2020-DataScience-B: 7
The case fatality rate ($CFR$) of a disease is the ratio of the number of deaths from the disease to the total number of people diagnosed with the disease ( patients ), and is usually expressed as a percentage. It has been reported that the ... an elderly Pandamic-$20$ patient in Gondwanaland survives the disease if they were put on a ventilator as part of the treatment?
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Others
May 8, 2021
116
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cmi2020-datascience
0
votes
76
CMI-2020-DataScience-B: 8
Owing to a defect in a certain machine which makes $N95$ masks, there is a $0.1\%$ probability that a mask it makes is $\text{not}$ effective in preventing airbone viruses from being inhaled. What is the probability that the first $1000$ masks that ... among the first one crore $(10^7)$ masks that the machine produces, there is at least one mask which is not effective?
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Others
May 8, 2021
153
views
cmi2020-datascience
0
votes
77
CMI-2020-DataScience-B: 9
The International Chess Federation is organizing an online chess tournament in which $20$ of the world's top players will take part. Each player will play exactly one game against each other player. The tournament is spread over three weeks; it starts ... there are at least two players who would have completed the same number of games in the tournament till that point.
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Others
May 8, 2021
97
views
cmi2020-datascience
0
votes
78
CMI-2020-DataScience-B: 10
Your class has a textbook and a final exam. Let $P,Q$ and $R$ be the following propositions: $P:$ You get an $A$ on the final exam. $Q:$ You do every exercise in the book. $R:$ You get an $A$ in the class. Translate the following assertions into ... . You get an $A$ on the final, but you don't do every exercise in this book; nevertheless, you get an $A$ in this class.
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Others
May 8, 2021
82
views
cmi2020-datascience
0
votes
79
CMI-2020-DataScience-B: 11
Two friends Amar and Prem wish to meet at a theme party between $5$ p.m and $6$. p.m (They are said to meet if they are in the room at the same time or if one of them leaves as the other enters). Once they enter, they stay for exactly ... interval of _______ minutes. What is the probability that Amar and Prem will meet? (Hint: Plot the arrival times on the x- and y-axes).
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Others
May 8, 2021
126
views
cmi2020-datascience
0
votes
80
CMI-2020-DataScience-B: 12
Let $f$ be a continuous function on the closed interval $[a,b]$ and differentiable on the open interval $(a,b),$ where $a<b.$ It is known that there exists $c$ in $(a,b)$ such that $f^{‘}(c)= \frac{f(b)-f(a)}{b-a}$ Determine $c$ for $f(x)=2x^3-3x^2+7x-2$ on [a,b] with $a=1$ and $b=6.$
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Others
May 8, 2021
61
views
cmi2020-datascience
0
votes
81
CMI-2020-DataScience-B: 13
Let $R$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $R$ at random. What is the probability that the chosen relation is symmetric?
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Others
May 8, 2021
170
views
cmi2020-datascience
0
votes
82
CMI-2020-DataScience-B: 14
Peppa and her friends Suzy and Emily are making $3$ masks: a knight mask, a pirate mask and an elf mask. The one wearing the knight mask must always tell the truth, the one wearing the pirate mask must always lie and the one wearing the elf mask could sometimes lie ... $\text{Emily : I am not wearing an elf mask.}$ What kind of mask is each one wearing?
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Others
May 8, 2021
90
views
cmi2020-datascience
0
votes
83
CMI-2020-DataScience-B: 15
For the function $f(x)=\text{ln}(x)/x$, show that the maximum value of $f(x)$ occurs when $x=e$. Use this to show that $x^e<e^x$ for all positive values of $x$.
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Others
May 8, 2021
60
views
cmi2020-datascience
0
votes
84
CMI-2020-DataScience-B: 16
Given the set of letters $\text{\{a,b,c,d,e,f,g,h,i,j,k,l,m\}},$ ... $\text{bcjameflkihgd}$
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Others
May 8, 2021
372
views
cmi2020-datascience
0
votes
85
CMI-2020-DataScience-B: 17
Consider the following code, where $A$ is an array of integers of size $\text{size(A)}$ with values $A[0] \;to\;A[\text{size(A)-1}]$, and $\text{reverse(A,i,j)}$ reverses the segment $\text{A[i]}$ to $\text{A[j]}$ if $\text{i<=j}$ and has ... this code on an input array $A$? Suppose $\text{size(A)}$ is $1000$. How many times is the test $\text{A[i]>A[p]}$ executed?
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Others
May 8, 2021
67
views
cmi2020-datascience
0
votes
86
CMI-2020-DataScience-B: 18
Eight students are to be seated around a circular table in a circular room. Two seatings are regarded as defining the same arrangements if each student has the same student on his or her right in both seatings: it does not matter which way they face. How ... of these $8$ students are there with $2$ chosen students, say student $A$ and student $B$, always sitting together?
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Others
May 8, 2021
117
views
cmi2020-datascience
0
votes
87
CMI-2020-DataScience-B: 19
Let $f$ be a continuous bijection from closed unit interval $[0,1]$ onto itself. (Recall the Intermediate Value Theorem: let $f$ be a real valued continuous function on an interval $[a,b]$. Let $c,d\in [a,b]$ ... point. Give an example of such a function where in the fixed point is unique and an example of a function with more than one fixed point.
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Others
May 8, 2021
171
views
cmi2020-datascience
0
votes
88
CMI-2020-DataScience-B: 20
A multi-national conglomerate sells soap products for five different market segments, namely (i) Women, (ii) Men, (iii) Kids, (iv) Sports, and (v) Luxury. The sales of these five segments (in lakh number of packs) during $2012$ and $2017$ ... sales of the Men segment in $2017$? During the period $2012-2017$, which segment experienced the minimum rate of increase in sales?
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in
Quantitative Aptitude
May 8, 2021
166
views
cmi2020-datascience
bar-graph
data-interpretation
descriptive
1
vote
89
CMI-2020-DataScience-B: 3
The following graph shows the performance of students in an exam. The marks scored by every student are a multiple of five. The $j^{th}$-percentile $u^*$ for a discrete data $x_1,x_2, ,x_n$ ... in the graph, answer the following questions. Compute the $10^{th}$ percentile of marks. Is the median score higher than the mean score?
answered
in
Quantitative Aptitude
May 8, 2021
174
views
cmi2020-datascience
line-graph
data-interpretation
0
votes
90
CMI-2020-DataScience-B: 2
Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$
answered
in
Linear Algebra
May 8, 2021
379
views
cmi2020-datascience
linear-algebra
matrix
descriptive
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