Recent questions tagged cmi2020-datascience

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$

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...

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...

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...

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 ...

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...

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 Calc...

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...

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 $A,B,A\Delta B=(A^c\cap B)\cup (A\cap B^c))$.$A$...

$\text{Description for the following question:}$The lifespan of a battery in a car follows Gamma distribution with probability density function$$f(x)=\frac{\beta^\alpha }...

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...

How many squares are there on a $7\times 7$ chessboard?$49$$204$$203$$140$

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...

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...

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 derivat...

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}$

The identity$$\frac{1}{(1-2r)}=\displaystyle\sum^{\infty} _{k=0} (2r)^k $$is trueif and only if $r\neq \frac{1}{2}$if and only if $0\leq r < \frac{1}{2}$if and only if $-...

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 $-19$

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 h...

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 $x$

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 $...

Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$

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 d...

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 $ABC?$

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)} & {\sigm...

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)...

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”), a...

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 viruse...

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 gam...

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.$...