Recent questions tagged iitb-ms-phd-test-dec

Given an array $a$ of $n$ integers which is already sorted in ascending order, a slice $a[i: j]$ consisting of elements $a[i], a[i+1] \ldots a[j]$ is called a plateau if ...

Shown below is a forwarding table at a router in the public Internet (values are in hexadecimal, for easy conversion to binary).\[\begin{array}{|l|l|}\hline\text{Destinat...

Shown below is a forwarding table at a router in the public Internet (values are in hexadecimal, for easy conversion to binary).\[\begin{array}{|l|l|}\hline\text{Destinat...

A client $\text{C}$ within a private network is downloading a large file from an external HTTP server S, via a NAT router $\text{R}$. Which of the following will NOT affe...

A network topology having $20$ nodes and $55$ links uses a link-state protocol. The periodic link-state update timer is $30$ -sec. What is the (minimum) number of LSP (li...

Consider an $n \times n$ matrix $\mathbf{A}$ whose rank is $k$. What is the rank of $\mathbf{I}-\mathbf{A}$, where $\mathbf{I}$ is the identity matrix? $\_\_\_\_\_\_$$n-k...

Suppose you are building a simple ASR (Automatic Speech Recognition) system which recognizes only four words bowl, bore, pour, poll involving five phones $p, b, o, l, r$ ...

Suppose you are building a simple ASR (Automatic Speech Recognition) system which recognizes only four words bowl, bore, pour, poll involving five phones $p, b, o, l, r$ ...

Suppose an ML model has not been trained on adequate amount of data, as well as for adequate amount of time. The item for the model is to detect if a presented input patt...

Consider the "animal hierarchy tree" below:We want to find something called the "probability of the tree" which has many applications in data science. By convention the p...

An HMM-Viterbi (HMM=Hidden Markov Model) bi-gram POS (Part-of-Speech) tagger is tested on a corpus with $100$ tokens. The tagger fails to produce any label for $20$ token...

Consider the phrase "Back to the future". Identify the phrase(s) from below which exhibit(s) the same language phenomenon as in the given phrase: $\_\_\_\_\_\_\_$.Deafeni...

In the sentence "$\mathrm{foxes}$ ${ }_{1}$ $\mathrm{foxes}$ $_{2}$ $\mathrm{fox}$ $_{3}$ $\mathrm{fox}$ $_{4}$ $\mathrm{foxes}$ $_{5}$ " (the lower suffixes indicate the...

Here is a strange POS (Part-fo-Speech) tagging situation for Finnish language. The FinnTreebank Tagset has $221$ tags. A Finnish corpus of $221$ words is taken. A strange...

Consider the following corpus:$\text{{People laugh, Children play, Rivers flow, Birds fly, Boys play, Girls laugh}}$The unique words in this corpus are then arranged rand...

Penn POS (Part-of-Speech) tagset is used as basis for the POS tagset of many languages. Typically, Penn tagset is expanded for a language by introducing new tags.Suppose ...

We are given a rod of unit length. A point is chosen uniformly randomly along its length and the rod is cut at that point to give two pieces. The expected length of the l...

A uniform random number generator $\mathcal{U}[0,1]$ is invoked twice to get random numbers $X_{1}$ and $X_{2}$. The value of $\mathbb{E}\left[\min \left\{X_{1}, X_{2}\ri...

Consider a complete graph with nodes numbered $1,2, \ldots, N$. How many distinct cycles of length $k$ are there? Nodes of a cycle can be enumerated starting from any pos...

Suppose $X$ and $Y$ are random variables having $M_{X}(t)$ and $M_{Y}(t)$, as moment generating functions, respectively. Then $X$ and $Y$ have the same probability distri...

A random variable $X$ has the density function $f(x)=\frac{1}{c\left(x^{2}+1\right)}$ where $x$ lies between $-\infty$ and $+\infty$. The value of ' $c$ ' is: $\_\_\_\_\_...

Use the z-score data sheet below for solving this question:\[\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hlinez & .00 & .01 & .02 & .03 & .04 & .05 & .06 & .07 & .08 & .09 \\\...

\[\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hlinez & .00 & .01 & .02 & .03 & .04 & .05 & .06 & .07 & .08 & .09 \\\hline-3.4 & .0003 & .0003 & .0003 & .0003 & .0003 & .0003 &...

Suppose the level of significance is fixed at $\alpha$ (alpha). Given a sample of size $36$ and mean $30$, and the standard deviation of the population as $3$, the popula...

Use the following table for this question:$\text{test-type (col), vs., and Confidence Interval (Significance level)}$ $\text{Two-Tail}$$1$ $\text{sided to +inf}$$1$ $\tex...

Suppose you are given a dataset with $n$ samples and $p$ features. Answer the following question .The total time complexity of training a linear regression model using th...

Suppose you are given a dataset with $n$ samples and $p$ features. Answer the following question .As the dataset size $n$ and dimensionality $p$ increase, which of the fo...