Recent questions tagged cmi2018-datascience

If $P$ is an invertible matrix and $A=PBP^{-1},$ then which of the following statements are necessarily true?$B=P^{-1}AP$$|A|=|B|$$A$ is invertible if and only if $B$ is ...

Let $A=\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}, B=\begin{bmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{bmatrix}, C=\begin{bmatrix} 4 & 5 & 6...

Let $x=\begin{bmatrix} 3& 1 & 2 \end{bmatrix}$. Which of the following statements are true?$x^Tx$ is a $3\times 3$ matrix$xx^T$ is a $3\times 3$ matrix$xx^T$ is a $1\time...

A $n\times n$ matrix $A$ is said to be $symmetric$ if $A^T=A$. Suppose $A$ is an arbitrary $2\times 2$ matrix. Then which of the following matrices are symmetric (here $0...

$\text{Description for the following question:}$If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then$$\...

In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only $20\%$ candidates think t...

There are $n$ songs segregated into $3$ play lists. Assume that each play list has at least one song.The number of ways of choosing three songs consisting of one song fro...

Consider the following functions defined from the interval $(0,1)$ to real numbers. Which of these functions attain their maximum value in the interval $(0,1)?$$f(x)=\fra...

A farmer owns $50$ papaya trees. Each tree produces $600$ papayas in a year. For each additional tree planted in the orchard, the output of each tree (including the pre-e...

Let $a,b$ be numbers between $1$ and $2$ and let $c,d$ be numbers between $3$ and $4$. Let $u=a^{-1},v=b^{-1},w=c^{-1}$ and $x=d^{-1}$. Say which of the following inequal...

In the code fragment below, $\text{start}$ and $\text{end}$ are integer values and $\text{square(x)}$ is a function that returns $\text{Ture}$ if $\text{x}$ is a perfect ...

Given the following definition of the function $foo$, what does $foo(1037,2)$ return? Note that $a//b$ denotes the quotient (integer part) of $a\div b$, for integers $a$ ...

A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet three inhabitants: Ramesh, Bharath and Menak...

There are $7$ switches on a switchboard, some of which are $on$ and some of which are $off$. In one move, you pick any $2$ switches and toggle each of them—if the switch ...

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=\...

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 ...

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^...

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...

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...

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...

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...

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{...

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...

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...