CMI Masters in Data Science 2019 Question Paper with Solutions: 36 Questions, Answer Key & Section-wise Analysis

Let $X=\{x_1,x_2,\dots ,x_n\}$ and $Y=\{y_1,y_2\}$. The number of surjective functions from $X$ to $Y$ equals

If $P(A\cup B)=0.7$ and $P(A\cup B^c)=0.9$ then find $P(A)$.

Which of the following statements are true for all $n\times n$ matrices $A$, $B$:

Let $A=\left[\begin{array}{ccc}1& 1& 1\\ 0& 2& 2\\ 0& 0& 3\end{array}\right]$, $B=\left[\begin{array}{ccc}5& 5& 5\\ 0& 10& 10\\ 0& 0& 15\end{array}\right]$, $C=\left[\begin{array}{ccc}3& 0& 0\\ 3& 6& 0\\ 3& 6& 9\end{array}\right]$. Which of the following statements are true?

Consider the polynomials $p(x)=(5x^2+6x+1)(x+1)(2x+3)$ and $q(x)=(5x^2-9x-2)(2x^2+5x+3)$. The set of common divisors of $p(x)$ and $q(x)$ is:

Let $R$ denote the set of real numbers and let $A=\{x\in R:x\ne 3\}$. For $x\in A$, let $f(x)=\frac{2x+1}{x-3}$. Let $B$ denote the range of $f$. Then