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Recent questions tagged cmi2020-datascience

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2 answers
1
Consider the following program. Assume that $x$ and $y$ are integers. f(x, y) { if (y != 0) return (x * f(x,y-1)); else return 1; } What is $f(6,3)?$ $243$ $729$ $125$ $216$
asked Jan 29 in Algorithms soujanyareddy13 92 views
0 votes
1 answer
2
Consider the matrices ... $|A|=|B|$ $\text{trace}(A)=\text{trace}(B)$ $|A|=-|B|$ $\text{trace}(AB)=\text{trace}(BA)$
asked Jan 29 in Others soujanyareddy13 33 views
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1 answer
3
Consider the following program. Assume that all variables are integers. Note that $x\%y$ computes the remainder after dividing $x$ and $y$. The division is an integer division. For example, $1/3$ will return zero while $10/3$ will return $3$. g(n) { result = 0; i = 1; repeat until( ... 2; result = result+(remainder*i); i = i * 10; } return result; } What is $g(25)?$ $11001$ $10011$ $11011$ $10101$
asked Jan 29 in Others soujanyareddy13 35 views
0 votes
1 answer
4
Which of the following limits are correct? $\displaystyle \lim_{x\rightarrow 0} \frac{x^2+2x}{2x}=1$ $\displaystyle \lim_{x\rightarrow 1/2 }\frac{2x^2+x-1}{2x-1}=\frac{3}{2}$ $\displaystyle \lim_{x\rightarrow \infty } 18x^3 – 12x^2 +1=\infty$ $\displaystyle \lim_{x\rightarrow -\infty} 8x^3 – 12x^2 +1=-\infty$
asked Jan 29 in Others soujanyareddy13 32 views
0 votes
1 answer
5
As per the data released by the US Department of Health, Education and Welfare, the number of Ph.D. degrees conferred in Earth Sciences from the year $1948$ to $1954$ is as given in Table $5$ ... or a rolling average is an average of a subset of data points. Choose the best answer. $900$ $9,000$ $9,00,000$ $90,00,000$
asked Jan 29 in Others soujanyareddy13 24 views
0 votes
1 answer
6
Suppose that $A$ is an $n \times n$ matrix with $n=10$ and $b$ is an $n \times 1$ vector. Suppose that the equation $Ax=b$ for an $n \times 1$ vector does not admit any solution. Which of the following conclusions can be drawn from the given information? $A^{-1}$ ... $n\times 1$ vector such that $Ax = c$ also does not admit a solution. Then the vector $c$ is a constant multiple of the vector $b$
asked Jan 29 in Others soujanyareddy13 16 views
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2 answers
7
Consider the following bar chart: Which of the following are true? Number of students who scored $A$ in Algebra is higher than the number of students who scored $A$ in Calculus Percentage of students who scored $A$ or $B$ in algebra is lower than the percentage of ... or $B$ in calculus Calculus is easier than algebra Considering this data, the average percentage of students scoring $A$ is $12\%$
asked Jan 29 in Quantitative Aptitude soujanyareddy13 45 views
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1 answer
8
Let $A=((a_{ij}))$ be a $7\times7$ matrix with $a_{i,i+1}=1$ for $1\leq i \leq 6$, $a_{7,1}=1$ and all the other elements of the matrix are zero. Which of the following statements are true? $|A|=1$ $\text{trace(A)}=0$ $A^{-1}=A$ $A^7 =I$, where $I$ is the identity matrix
asked Jan 29 in Others soujanyareddy13 13 views
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1 answer
9
Let $A$ and $B$ be events such that $P(A)=0.4, P(B)=0.5$ and $P(A\cup B)=0.7$. Which of the following are true? (For sets $A,B,A\Delta B=(A^c\cap B)\cup (A\cap B^c))$. $A$ and $B$ are mutually exclusive $A$ and $B$ are independent $P(A\Delta B)= 0.1$ $P(A^c \cup B^c)=0.8$
asked Jan 29 in Others soujanyareddy13 15 views
0 votes
1 answer
10
$\text{Description for the following question:}$ The lifespan of a battery in a car follows Gamma distribution with probability density function $f(x)=\frac{\beta^\alpha }{\Gamma(\alpha) } e^{-\beta x}x^{\alpha -1}, 0<x< \infty ,$ where $\alpha >0$ and $\beta >0$. The mean and variance of a ... $\beta =2$ $\mathbb E(X^2 )= \frac {\alpha}{\beta}(\frac {1+\alpha}{\beta })$ $\mathbb E(X^2 )=18$
asked Jan 29 in Others soujanyareddy13 14 views
0 votes
1 answer
11
Out of a large number of cars produced by the automaker, the percentage of batteries that will last for more than $8$ years is $[ \int^8_0 \frac{\beta^{\alpha}}{\Gamma (\alpha)} e^{-\beta x} x^{\alpha -1} dx ] \times 100\%$ ... $[ \int^8_0 \frac{x \beta^{\alpha}}{\Gamma (\alpha)} e^{-\beta x} x^{\alpha -1} dx ] \times 100\%$
asked Jan 29 in Others soujanyareddy13 16 views
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1 answer
12
How many squares are there on a $7\times 7$ chessboard? $49$ $204$ $203$ $140$
asked Jan 29 in Others soujanyareddy13 16 views
0 votes
1 answer
13
It is mid-semester exam week at $CMI$ and first-year students from both $M.Sc.$ Data Science $(DS)$ and $M.Sc.$ Computer Science $(CS)$ have their exams scheduled for Monday from $10$ a.m. to $1$ p.m. in Lecture Hall $1$. The first row in Lecture hall $1$ has six ... - be seated in this row, in such a way that two students from the same course do not sit next to each other? $36$ $48$ $72$ $96$
asked Jan 29 in Others soujanyareddy13 15 views
0 votes
1 answer
14
Suppose you roll two six-sided fair dice with faces numbered from $1$ to $6$ and take the sum of the two numbers that turn up. What is the probability that: the sum is $12;$ the sum is $12$, given that the sum is even; the sum is $12$, given that the sum is an even number greater than ... $\frac {1}{14}$, respectively $\frac {1}{36}, \frac {1}{16} $, and $\frac {1}{12}$, respectively
asked Jan 29 in Others soujanyareddy13 19 views
0 votes
1 answer
15
Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivative $f^ (x) $ changes sign at $x_0$ ... point $x_0 =6$ is the only inflection point $x_0 =0$ and $x_0 =6$, both are inflection points The function does not have an inflection point
asked Jan 29 in Others soujanyareddy13 12 views
0 votes
1 answer
16
Which of the following are true? $\frac {2019}{2020} < \frac {2020}{2021}$ $x+\frac{1}{x} \geq 2$ for all $x>0$ $2^{60} >5^{24}$ $2^{314} <31^{42}$
asked Jan 29 in Others soujanyareddy13 14 views
0 votes
1 answer
17
The identity $\frac{1}{(1-2r)}=\displaystyle\sum^{\infty} _{k=0} (2r)^k $ is true if and only if $r\neq \frac{1}{2}$ if and only if $0\leq r < \frac{1}{2}$ if and only if $-\frac{1}{2} \leq r<\frac{1}{2}$ if and only if $-\frac{1}{2}<r<\frac{1}{2}$
asked Jan 29 in Others soujanyareddy13 11 views
0 votes
2 answers
18
The sum and product of the roots of the polynomial $9x^2+171x-81$ are, respectively: $-19$ and $-9$ $19$ and $9$ $-9$ and $19$ $9$ and $-19$
asked Jan 29 in Others soujanyareddy13 22 views
0 votes
1 answer
19
Choose the conclusions that follow logically from the statements given below. Nobody who really appreciates A.R.Rahman fails to subscribe to his YouTube channel. Owls are hopelessly ignorant of music. No one who is hopelessly ignorant of music ever subscribes to A.R ... Rahman Owls are not really appreciated by A.R.Rahman Anyone who really appreciates A.R.Rahman is not hopelessly ignorant of music
asked Jan 29 in Others soujanyareddy13 15 views
0 votes
1 answer
20
Which of the following inequalities are true? $e^x\geq(1+x)$ for $x\geq 0$ $e^x\leq(1+x)$ for $x<0$ $\text{In}(x)<(1+x)$ for $x>0$ $e^x<x^2$ for all real numbers $x$
asked Jan 29 in Others soujanyareddy13 13 views
1 vote
1 answer
21
For any string $\text{str, length(str)}$ returns the length of the string, $\text{append(str1, str2)}$ concatenates $\text{str1}$ with another string $\text{str2}$, and $\text{trim(str)}$ removes any spaces that exist at the end of the string $\text{str}$. The function $\text{reverse(str, i, j)}$ ... n; i=i+1) { if(str[i] is ' ') { reverse(str, j, i-1); j = i + 1; } } trim(str); return str; }
asked Jan 29 in Algorithms soujanyareddy13 50 views
1 vote
2 answers
22
Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$
asked Jan 29 in Linear Algebra soujanyareddy13 93 views
0 votes
1 answer
23
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 $x_1,x_2, ,x_n$ ... presented in the graph, answer the following questions. Compute the $10^{th}$ percentile of marks. Is the median score higher than the mean score?
asked Jan 29 in Quantitative Aptitude soujanyareddy13 28 views
0 votes
1 answer
24
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 $ABC?$
asked Jan 29 in Quantitative Aptitude soujanyareddy13 37 views
0 votes
1 answer
25
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2,\dots ,n\}$ to itself. We denote it using the notation $\begin{pmatrix}1 & 2 & & n \\ {\sigma(1)} & {\sigma(2)} &\dots & {\sigma(n)} \end{pmatrix},$ e.g. if $n=3$ ... $\sigma =\begin{pmatrix} 1 & 2 & 3&4&5&6 \\ 2& 3&4&5&1&6 \end{pmatrix}, \; \tau=\begin{pmatrix} 1 & 2 & 3&4&5&6 \\ 4& 1&3&2&6&5 \end{pmatrix}$
asked Jan 29 in Others soujanyareddy13 22 views
0 votes
1 answer
26
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2, ,n\}$ to itself. We denote it using the notation $\begin{pmatrix}1 & 2 & & n \\ {\sigma(1)} & {\sigma(2)} & & {\sigma(n)} \end{pmatrix},$ ... $|A_{\sigma} |$ and $|A_\tau|?$ Can you relate these with the signs of permutations $\sigma$ and $\tau ?$
asked Jan 29 in Others soujanyareddy13 18 views
0 votes
1 answer
27
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 $CFR$ of ... probability that an elderly Pandamic-$20$ patient in Gondwanaland survives the disease if they were put on a ventilator as part of the treatment?
asked Jan 29 in Others soujanyareddy13 10 views
0 votes
2 answers
28
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 the machine ... probability that among the first one crore $(10^7)$ masks that the machine produces, there is at least one mask which is not effective?
asked Jan 29 in Others soujanyareddy13 26 views
0 votes
1 answer
29
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 at $9$ a.m. on ... of Week $3,$ there are at least two players who would have completed the same number of games in the tournament till that point.
asked Jan 29 in Others soujanyareddy13 15 views
0 votes
1 answer
30
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 propositional formulas ... final. 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.
asked Jan 29 in Others soujanyareddy13 14 views
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