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31
CMI-2018-DataScience-B: 14
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar charts ... in the same proportion across the five states, then what are the sales of chocolate in Tamil Nadu, in lakhs of rupees?
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues ...
275
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answered
May 8, 2021
Others
cmi2018-datascience
pie-chart
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32
CMI-2018-DataScience-B: 13
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar ... the detail of breakdown for strawberry flavor by states in lakhs of rupees. What are the total sales of the chocolate flavor?
$\text{Description for the following question:}$An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (...
345
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May 8, 2021
Others
cmi2018-datascience
pie-chart
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33
CMI-2018-DataScience-B: 12
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar ... detail of breakdown for strawberry flavor by states in lakhs of rupees. What is the total revenue of the ice cream company?
$\text{Description for the following question:}$An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (...
236
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May 8, 2021
Others
cmi2018-datascience
pie-chart
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0
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34
CMI-2018-DataScience-B: 11
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar ... the detail of breakdown for strawberry flavor by states in lakhs of rupees. What are the total sales of the strawberry flavor?
$\text{Description for the following question:}$An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (...
276
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answered
May 8, 2021
Others
cmi2018-datascience
pie-chart
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0
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35
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 $Rs. 100,000?$
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.$\text{D...
198
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May 8, 2021
Others
cmi2018-datascience
probability
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36
CMI-2018-DataScience-B: 9
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\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?
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.$\text{D...
210
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May 8, 2021
Others
cmi2018-datascience
probability
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37
CMI-2018-DataScience-B: 8
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\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.
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. $\text{...
242
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May 8, 2021
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cmi2018-datascience
probability
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38
CMI-2018-DataScience-B: 7
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\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$?$
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 comput...
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May 8, 2021
Others
cmi2018-datascience
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39
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 $abcd$.
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 $4$-di...
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May 8, 2021
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cmi2018-datascience
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40
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.
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 functi...
264
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May 8, 2021
Others
cmi2018-datascience
set-theory
discrete-mathematics
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41
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?
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 compu...
333
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May 8, 2021
Others
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
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42
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.
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 $A^...
165
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cmi2018-datascience
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43
CMI-2018-DataScience-B: 2
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\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
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 ...
329
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answered
May 8, 2021
Others
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
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44
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.
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=\...
204
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May 8, 2021
Others
cmi2018-datascience
discrete-mathematics
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45
CMI-2019-DataScience-B: 18
$\text{Description of the following question:}$ The break-up of the colour of cars sold by an Indian company in a given year is provided in the pie-chart, see the Figure(1). The bar chart shows the number of grey coloured cars sold in ... cars were sold in Chennai. What is the largest possible percentage of brown cars sold in Chennai, rounded off to the nearest integer?
$\text{Description of the following question:}$The break-up of the colour of cars sold by an Indian company in a given year is provided in the pie-chart, see the Figure(1...
158
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May 8, 2021
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cmi2019-datascience
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46
CMI-2019-DataScience-B: 17
$\text{Description of the following question:}$ The break-up of the colour of cars sold by an Indian company in a given year is provided in the pie-chart, see the Figure(1). The bar chart shows the number of grey coloured cars sold in different cities ... grey cars sold in Delhi is the same as the proportion of red cars sold in Delhi, how many red cars were sold in Delhi?
$\text{Description of the following question:}$The break-up of the colour of cars sold by an Indian company in a given year is provided in the pie-chart, see the Figure(1...
147
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May 8, 2021
Others
cmi2019-datascience
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47
CMI-2019-DataScience-B: 16
$\text{Description of the following question:}$ The break-up of the colour of cars sold by an Indian company in a given year is provided in the pie-chart, see the Figure(1). The bar chart shows the number of grey coloured cars sold in different cities, see the Figure(2). How many blue cars were sold in that year?
$\text{Description of the following question:}$The break-up of the colour of cars sold by an Indian company in a given year is provided in the pie-chart, see the Figure(1...
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May 8, 2021
Others
cmi2019-datascience
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48
CMI-2019-DataScience-B: 15
Consider the following pseudocode for a function that operates on an $N$ element array $A[1],A[2],\dots,A[N]$ of integers. function mystery (A[1...N]) { int i,j,position,tmp; for i=1 to N { position=i; for j=i+1 to N { if(A[j]<A[ ... Explain what effect the function has on the input array $A$. If $N=100$, how many times is the comparison $A[i]<A[position]$ checked?
Consider the following pseudocode for a function that operates on an $N$ element array $A ,A ,\dots,A[N]$ of integers.function mystery (A[1...N]) { int i,j,position,tmp; ...
144
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cmi2019-datascience
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49
CMI-2019-DataScience-B: 14
A thief picks a wallet and starts running at a speed of $5\; m/s$ with zero acceleration. In $5$ seconds, a policewoman notices the alarm and starts following the thief with a speed of $3\; m/s$ with a uniform acceleration of $1\; m/s^2$. How many seconds ... $v_0$ m/s and uniform acceleration $a\; m/s^2$ will cover a distance of $(at^2/2+v_0t)$ meters in $t$ seconds.)
A thief picks a wallet and starts running at a speed of $5\; m/s$ with zero acceleration. In $5$ seconds, a policewoman notices the alarm and starts following the thief w...
157
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May 8, 2021
Others
cmi2019-datascience
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50
CMI-2019-DataScience-B: 13
How many positive integers are factors of 2310?
How many positive integers are factors of 2310?
129
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May 8, 2021
Others
cmi2019-datascience
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51
CMI-2019-DataScience-B: 12
Let $n,k$ be positive integers. The expansion of $(x_1+\dots+x_k)^n$ is given by $(x_1+\dots+x_k)^n=\sum\frac{n!}{n_1!n_2!\dots n_k!}x_1^{n_1}x_2^{n_2}\dots x_k^{n_k},$ where the sum is taken over all sequences $n_1,n_2,\dots,n_k$ of non-negative integers such that $n_1,n_2+\dots+n_k=n$. What is the coefficient of $x^5$ in the expansion of $(1+3x+2x^2)^4$?
Let $n,k$ be positive integers. The expansion of $(x_1+\dots+x_k)^n$ is given by$$(x_1+\dots+x_k)^n=\sum\frac{n!}{n_1!n_2!\dots n_k!}x_1^{n_1}x_2^{n_2}\dots x_k^{n_k},$$w...
108
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May 8, 2021
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cmi2019-datascience
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52
CMI-2019-DataScience-B: 11
A thin piece of metal of length $20$ cm and width $16$ cm is to be used to construct an open-topped box. A square will be cut from each corner and the sides will be folded up. What size corner should be cut so that the volume of the box is maximized?
A thin piece of metal of length $20$ cm and width $16$ cm is to be used to construct an open-topped box. A square will be cut from each corner and the sides will be folde...
109
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May 8, 2021
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cmi2019-datascience
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53
CMI-2019-DataScience-B: 10
Let $p(x)$ be a polynomial with integer coefficients. Let $n$ be a positive integer and suppse $a$ and $b$ are two integers such that $a \equiv b(\text{mod}\;n)$. Is it true that $p(a)\equiv p(b)(\text{mod}\;n)$? Justify your answer.
Let $p(x)$ be a polynomial with integer coefficients. Let $n$ be a positive integer and suppse $a$ and $b$ are two integers such that $a \equiv b(\text{mod}\;n)$. Is it t...
112
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May 8, 2021
Others
cmi2019-datascience
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54
CMI-2019-DataScience-B: 9
Show that among any set of $7$ distinct integers there must exist $2$ integers whose sum or difference is divisible by $10$.
Show that among any set of $7$ distinct integers there must exist $2$ integers whose sum or difference is divisible by $10$.
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May 8, 2021
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cmi2019-datascience
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55
CMI-2019-DataScience-B: 8
A small circular fire is spreading with its radius increasing at the rate of $1.5$ meters per minute. When the radius of the fire is $5$ metres, how fast is the burned area growing?
A small circular fire is spreading with its radius increasing at the rate of $1.5$ meters per minute. When the radius of the fire is $5$ metres, how fast is the burned ar...
215
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May 8, 2021
Others
cmi2019-datascience
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56
CMI-2019-DataScience-B: 7
Ani is training for the olympics with Usain Bolt. After a few days of training Usain challenges Ani to catch him. Usain sets off running very slowly with a view to encourage Ani. He covers $\text{70m}$ the first minute, $\text{100m}$ the ... at an integral multiple of a minute. How many minutes did Ani run before catching up with Usain. What were their respective speeds?
Ani is training for the olympics with Usain Bolt. After a few days of training Usain challenges Ani to catch him. Usain sets off running very slowly with a view to encour...
287
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May 8, 2021
Others
cmi2019-datascience
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57
CMI-2019-DataScience-B: 6
Let $\theta=\log_e(2).$ For $-\theta\leq x\leq\theta,$ let $f(x)=\frac{\exp(x)}{1+\exp(x)}$. Compute $\alpha$ and $\beta$ where $\alpha=\displaystyle \max_{-\theta\leq x\leq\theta}f(x)\;\text{and}\; \beta=\displaystyle \min_{-\theta\leq x\leq\theta}f(x).$ Justify your answers.
Let $\theta=\log_e(2).$ For $-\theta\leq x\leq\theta,$ let $f(x)=\frac{\exp(x)}{1+\exp(x)}$. Compute $\alpha$ and $\beta$ where$$\alpha=\displaystyle \max_{-\theta\leq x\...
115
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May 8, 2021
Others
cmi2019-datascience
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58
CMI-2019-DataScience-B: 5
If the lines $2x+y=2,-5x+3y=4$ and $ax+by=1$ are concurrent then prove that the line $9x-10y=1$ passes through $(a,b).$
If the lines $2x+y=2,-5x+3y=4$ and $ax+by=1$ are concurrent then prove that the line $9x-10y=1$ passes through $(a,b).$
103
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May 8, 2021
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cmi2019-datascience
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59
CMI-2019-DataScience-B: 4
Four friends attending an opera leave their coats at the checkroom. When they return each one is handed a coat that does not belong to her. In how many ways can this happen?
Four friends attending an opera leave their coats at the checkroom. When they return each one is handed a coat that does not belong to her. In how many ways can this happ...
192
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May 8, 2021
Others
cmi2019-datascience
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60
CMI-2019-DataScience-B: 3
Suppose $X$ is a continuous distribution with probability density function $f(x)=k(x-x^2),\;0\leq x\leq 1,$ where $k$ is the normalizing constant. Find the value of $k$ and the expected value of the distribution.
Suppose $X$ is a continuous distribution with probability density function$$f(x)=k(x-x^2),\;0\leq x\leq 1,$$where $k$ is the normalizing constant. Find the value of $k$ a...
178
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May 8, 2021
Others
cmi2019-datascience
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