CMI Masters in Data Science 2023 Question Paper with Solutions: 40 Questions, Answer Key & Section-wise Analysis

$FA,DE,BC,CD,AB,FA$

$AB,BC,DE,EF,EF,DE$

$AB,CD,BC,EF,DE,EF$

$AB,CD,FA,BC,AB,DE$

The function $f$ has a removable discontinuity at 1 and $g$ has it at 0.

Only $g$ is continuous everywhere.

As $x$ tends to $\infty$, $f(x)$ also tends to $\infty$.

The range of $g$ is bounded.

$n$ has to be even.

3 does not divide $n$

7 divides $n$

5 does not divide $n$

For every positive integer $n$, there is a triple of numbers $a_i<a_j<a_k$ which are in geometric progression with ratio $n$, i.e. $a_j=a_{i}n,a_k=a_{j}n$.

If $i<j$ then $a_i$ divides $a_j$.

There are only finitely many $n$ for which there are infinitely many triples $i<j<k$ with $a_i,a_j,a_k$ in arithmetic progression with common difference $n$.

Integers $a_{10},a_{30},a_{90}$ are in geometric progression.

Rank of $A$ is 12.

Rank of $A$ and $B$ are not related.

If $v$ is a vector such that $Av=0$ then $Bv$ is also 0.

Rank of $B$ is at most 11.

If $x_0$ is a flex point of $f$ then $f^{\prime \prime }(x_0)=0$.

If $f^{\prime }(x_0)=0$ then $x_0$ is a turning point of $f$.

If $f^{\prime \prime }(x_0)=0$ then $x_0$ is a flex point of $f$.

If $x_0$ is a flex point of $f$ then $f^{\prime }(x_0)\ne 0$.