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1531
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...
soujanyareddy13
118
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Jan 29, 2021
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cmi2019-datascience
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1532
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...
soujanyareddy13
112
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Jan 29, 2021
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cmi2019-datascience
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1533
CMI-2019-DataScience-B: 13
How many positive integers are factors of 2310?
How many positive integers are factors of 2310?
soujanyareddy13
144
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cmi2019-datascience
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1534
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...
soujanyareddy13
176
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Jan 29, 2021
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cmi2019-datascience
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1535
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; ...
soujanyareddy13
156
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Jan 29, 2021
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cmi2019-datascience
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1536
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...
soujanyareddy13
126
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Jan 29, 2021
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1537
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...
soujanyareddy13
156
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soujanyareddy13
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Jan 29, 2021
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cmi2019-datascience
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1538
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...
soujanyareddy13
163
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Jan 29, 2021
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cmi2019-datascience
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1539
CMI-2020-DataScience-A: 2
Consider the matrices ... of the following hold true? $|A|=|B|$ $\text{trace}(A)=\text{trace}(B)$ $|A|=-|B|$ $\text{trace}(AB)=\text{trace}(BA)$
Consider the matrices$A=\begin{pmatrix} 0 & 0 & 0 & 0 & 15 \\ 0 & 0 & 0 & 13 &14 \\ 0 & 0 & 10 & 11 & 12 \\ 0 & 6 & 7 & 8 & 9 \\ 1 & 2 & 3 & 4 & 5 \end{pmatrix} \text{ an...
soujanyareddy13
281
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Jan 29, 2021
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cmi2020-datascience
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1540
CMI-2020-DataScience-A: 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 = ... = result+(remainder*i); i = i * 10; } return result; } What is $g(25)?$ $11001$ $10011$ $11011$ $10101$
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 div...
soujanyareddy13
328
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soujanyareddy13
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Jan 29, 2021
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1541
CMI-2020-DataScience-A: 4
Which of the following limits are correct? $\displaystyle \lim_{x\rightarrow 0} \frac{x^2+2x}{2x}=1$ $\displaystyle \lim_{x\rightarrow 1/2 }\frac{2x^2+x-1}{2x-1}=\frac{3}{2}$ $\displaystyle \lim_{x\rightarrow \infty } 18x^3 – 12x^2 +1=\infty$ $\displaystyle \lim_{x\rightarrow -\infty} 8x^3 – 12x^2 +1=-\infty$
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...
soujanyareddy13
228
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soujanyareddy13
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Jan 29, 2021
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cmi2020-datascience
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1542
CMI-2020-DataScience-A: 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$ ... average is an average of a subset of data points. Choose the best answer. $900$ $9,000$ $9,00,000$ $90,00,000$
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 ...
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381
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soujanyareddy13
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Jan 29, 2021
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1543
CMI-2020-DataScience-A: 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 ... $Ax = c$ also does not admit a solution. Then the vector $c$ is a constant multiple of the vector $b$
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 s...
soujanyareddy13
240
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soujanyareddy13
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Jan 29, 2021
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cmi2020-datascience
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1544
CMI-2020-DataScience-A: 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
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 s...
soujanyareddy13
157
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soujanyareddy13
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Jan 29, 2021
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cmi2020-datascience
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1545
CMI-2020-DataScience-A: 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$
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$...
soujanyareddy13
130
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cmi2020-datascience
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1546
CMI-2020-DataScience-A: 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$ ... $\mathbb E(X^2 )= \frac {\alpha}{\beta}(\frac {1+\alpha}{\beta })$ $\mathbb E(X^2 )=18$
$\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 }...
soujanyareddy13
335
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1547
CMI-2020-DataScience-A: 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 $[ \int^8_0 \frac{\beta^{\alpha}}{\Gamma (\alpha)} e^{-\beta x} x^{\alpha -1} dx ] \times 100\%$ ... $[ \int^8_0 \frac{x \beta^{\alpha}}{\Gamma (\alpha)} e^{-\beta x} x^{\alpha -1} dx ] \times 100\%$
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 (\a...
soujanyareddy13
150
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soujanyareddy13
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Jan 29, 2021
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cmi2020-datascience
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1548
CMI-2020-DataScience-A: 12
How many squares are there on a $7\times 7$ chessboard? $49$ $204$ $203$ $140$
How many squares are there on a $7\times 7$ chessboard?$49$$204$$203$$140$
soujanyareddy13
171
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soujanyareddy13
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Jan 29, 2021
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1549
CMI-2020-DataScience-A: 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 ... in this row, in such a way that two students from the same course do not sit next to each other? $36$ $48$ $72$ $96$
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 Mon...
soujanyareddy13
222
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Jan 29, 2021
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1550
CMI-2020-DataScience-A: 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 ... $\frac {1}{14}$, respectively $\frac {1}{36}, \frac {1}{16} $, and $\frac {1}{12}$, respectively
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...
soujanyareddy13
189
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soujanyareddy13
asked
Jan 29, 2021
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cmi2020-datascience
probability
dice-rolling
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