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Recent questions tagged cmi2022-datascience
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31
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 ...
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 coa...
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32
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)
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)
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33
CMI-2022-DataScience-A: 11
Which of the following plots correspond to a bijective function? (i) and (ii) (ii) and (iii) (i) and (iv) (iii) and (iv)
Which of the following plots correspond to a bijective function? (i) and (ii)(ii) and (iii)(i) and (iv)(iii) and (iv)
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34
CMI-2022-DataScience-A: 12
A relation $R$ on the set $A=\{a, b, c, d\}$ is defined by reading the columns of the following table from top to bottom. If a column in the table reads $(x, y, 1)$ it means $x$ is related to $y$ in $R$. If a column in the table reads $(x, y, 0)$ it means $x$ is not ... $(z, y) \in R$ hold. Which of the following pairs are in $S?$ $(a, a)$ $(b, b)$ $(c, c)$ $(d, d)$
A relation $R$ on the set $A=\{a, b, c, d\}$ is defined by reading the columns of the following table from top to bottom. If a column in the table reads $(x, y, 1)$ it me...
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Jul 23, 2022
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35
CMI-2022-DataScience-A: 13
We say that a subset $S$ of a finite set $U$ is large if $|S|>|U \backslash S|$. Here $U \backslash S$ denotes the elements of $U$ which are not in $S$ and the notation $|T|$ denotes the number of elements in a set $T$. Let $x$ be the number of large subsets ... $x=260, y=256$ $x=386, y=256$ $x=386, y=130$ $x=512, y=256$
We say that a subset $S$ of a finite set $U$ is large if $|S|>|U \backslash S|$. Here $U \backslash S$ denotes the elements of $U$ which are not in $S$ and the notation $...
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Jul 23, 2022
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36
CMI-2022-DataScience-A: 14
A ternary tree starts with a single root node at the top of the tree. Each node in the tree can have up to three nodes as its children. No node in the tree is the child of two different nodes. A node which has no children is called a leaf node. The children of a node are drawn below it, ... $2^{11}-1$ $\frac{2^{10}+2}{3}$ $\frac{3^{10}-1}{2}$ $\frac{3^{10}+1}{2}$
A ternary tree starts with a single root node at the top of the tree. Each node in the tree can have up to three nodes as its children. No node in the tree is the child o...
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Jul 23, 2022
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37
CMI-2022-DataScience-A: 15
Which of the following expressions take integral values for all integers $n>100?$ $\frac{3^{n}-1}{2}$ $\frac{4^{n}-1}{2}$ $\frac{4^{n}-1}{3}$ $\frac{5^{n}-1}{2}$
Which of the following expressions take integral values for all integers $n>100?$ $\frac{3^{n}-1}{2}$$\frac{4^{n}-1}{2}$$\frac{4^{n}-1}{3}$$\frac{5^{n}-1}{2}$
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Jul 23, 2022
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38
CMI-2022-DataScience-A: 16
At a conference attended by $1235$ people, some attendees shake hands with other attendees. As a part of the local $\text{COVID-19}$ ... multiple of $2$ $\mathcal{N}$ is always a multiple of $3$ $\mathcal{N}$ is always a multiple of $5$
At a conference attended by $1235$ people, some attendees shake hands with other attendees. As a part of the local $\text{COVID-19}$ tracing protocol the organizers ask e...
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39
CMI-2022-DataScience-A: 17
Let $n$ be a positive integer and let $k$ be a positive integer which is greater than $1.$ Then $n$ can be represented as $ n=n_{t} k^{t}+n_{t-1} k^{t-1}+\cdots+n_{1} k+n_{0} $ for a unique set of positive integers $n_{0}, \ldots n_{t}$. This ... $\left(\begin{array}{lllll}2 & 2 & 0 & 2 & 0 \end{array}\right)_{3}$
Let $n$ be a positive integer and let $k$ be a positive integer which is greater than $1.$ Then $n$ can be represented as $$ n=n_{t} k^{t}+n_{t-1} k^{t-1}+\cdots+n_{1} k+...
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Jul 23, 2022
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40
CMI-2022-DataScience-A: 18
There are two villages $X$ and $Y$ in a faraway land. It is known that each person from village $X$ always tells the truth, and that each person from village $Y$ always lies. You meet three people $A, B, C$ who are from these villages. You are told ... $Y$ and $C$ is from village $X$. The given information is insufficient to infer the villages to which $A, B, C$ belong.
There are two villages $X$ and $Y$ in a faraway land. It is known that each person from village $X$ always tells the truth, and that each person from village $Y$ always l...
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Jul 23, 2022
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41
CMI-2022-DataScience-A: 19
A stick is fixed on the ground at an angle of $60$ degrees as shown in Figure $1.$ The part of the stick which is above the ground-which is the part that is shown in Figure $1$-has a length of $10$ metres. At a certain time $T_{1}$ during the day, the sun ... $5$ metres and $10 \sqrt{3}$ metres $5$ metres and $10$ metres $5 \sqrt{3}$ metres and $10$ metres
A stick is fixed on the ground at an angle of $60$ degrees as shown in Figure $1.$ The part of the stick which is above the ground-which is the part that is shown in Figu...
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Jul 23, 2022
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42
CMI-2022-DataScience-A: 20
A park in Chennai has walkways as depicted in the figure. The straight path from $A$ to $B$ is $100$ metres long. The curved part is a semicircle whose centre coincides with the midpoint of line segment $A B$. A woman and her dog take a walk in this park, both ... The average speed of the dog's walk is between $0.27 \text{ ms}^{-1}$ and $0.30 \text{ ms}^{-1}$
A park in Chennai has walkways as depicted in the figure. The straight path from $A$ to $B$ is $100$ metres long. The curved part is a semicircle whose centre coincides w...
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Jul 23, 2022
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