CMI Masters in Data Science 2024 Question Paper with Solutions: 60 Questions, Answer Key & Section-wise Analysis

Suppose that $A$ is an $n\times n$ matrix with $n\ge 6$. For an $n\times 1$ vector $b$ consider the equations

Which of the following inequalities are correct?

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

Let $x$ be a variable that takes real values, and let $f(x),g(x),h(x)$ be three polynomials with real-valued coefficients. Further, let $f(x)$ be a polynomial of degree 1, $g(x)$ a polynomial of degree 2, and $h(x)$ a polynomial of degree 3. Which of the following statements is/are always true for any three polynomials of these types?

A spherical ball of ice of radius $20m$ is dropped in a vat of hot water. The ice melts in such a way that (i) the shape of the ball remains spherical, and (ii) the radius of the ball decreases at a constant rate of $0.5m{s}^{-1}$. At what rate does the volume of the ice ball decrease, when the radius of the ball is $15m$?

Let $x$ be a real-valued variable. What is the range of the function $f(x)={\sin }^{2}x-\sin x+2$?

In the following code, $A$ is an array indexed from 0 whose elements are all positive integers, and $n$ is the number of elements in $A$. It is given that $n$ is at least 2. The operator $\ast$ denotes multiplication.

In the following code, $A$ is an array indexed from 0 whose elements are all positive integers, and $n$ is the number of elements in $A$.

A prominent newspaper conducted a survey among a carefully chosen sample of 1,00,000 voters under the age of 25. A randomly chosen subset of 60% of this sample were asked the following question: "Have you ever voted in a general election?" The remaining 40% were asked the following, different question: "Is it true that you have never voted in a general election?"