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

A computer monitor displays images by outputting voltages whose values are of the form $v=c r^{\gamma}$ where $r$ is the input intensity, and $c>0, \gamma>0$ are properti...

Consider a Gaussian kernel $G_{\sigma}(x, y)$ with mean 0 and standard deviation $\sigma$. The Laplacian of Gaussian operator $\nabla^{2} G_{\sigma}$ operator acting on a...

Consider a kernel $k_{1}=\left(\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right)$. Consider another kernel $k_{2}=\frac{1}{9} k_{1}$. Consider a gra...

Consider a Gaussian probability density function $P_{1}\left(x ; \mu_{1}, \sigma_{1}^{2}\right)$ with finite mean $\mu_{1}$ and variance $\sigma_{1}^{2}>0$. Consider anot...

Consider a 1D image function $f(x)$ that is real-valued function of the realvalued coordinate $x \in(-\infty,+\infty)$. Let us define $f(x):=x$. Consider a Gaussian convo...

Consider a $n \times n$ matrix $\boldsymbol{A}$ with eigendecomposition $\boldsymbol{A}=\boldsymbol{V} \boldsymbol{\Lambda} \boldsymbol{V}^{-1}$ where the eigenvalue matr...

Part 1: Consider the following code snippet for bubble sort on integer array arr with $n>0$ elements:for(i=0; i { ... for(j=0; j { ... if(arr[j]>arr[j+1]) { ... int temp ...

Consider a $3 \times 3$ rotation matrix $\boldsymbol{R}$ associated with an axis of rotation $\boldsymbol{v}$ and an angle of rotation $\theta$. Answer the following ques...

Consider a $3 \times 3$ rotation matrix $\boldsymbol{R}$ associated with an axis of rotation $\boldsymbol{v}$ and an angle of rotation $\theta$. Answer the following ques...

Consider a $3 \times 3$ rotation matrix $\boldsymbol{R}$ associated with an axis of rotation $\boldsymbol{v}$ and an angle of rotation $\theta$. Answer the following ques...

For integers $m$ and $n$ such that $2<n<m$, let $H_{m, n}:\left\{ 0,1 \right\}^{m}\rightarrow \left\{ 0, 1\right\}^{n}$ be a function.A pair of inputs $x_{1}, x_{2}\epsil...

For integers $m$ and $n$ such that $2<n<m$, let $H_{m, n}:\left\{ 0,1 \right\}^{m}\rightarrow \left\{ 0, 1\right\}^{n}$ be a function.A pair of inputs $x_{1}, x_{2}\epsil...

Now, let's consider "multi-collisions": for an integer $k>1$, a $k$-tuple of pairwise-distinct inputs $x_{1}, \cdots, x_{k} \in\{0,1\}^{m}$ is said to be an $k$-collision...

Now, let's consider "multi-collisions": for an integer $k>1$, a $k$-tuple of pairwise-distinct inputs $x_{1}, \cdots, x_{k} \in\{0,1\}^{m}$ is said to be an $k$-collision...

Consider the directed graph in the Figure $1$. Suppose we do a random walk as follows: we start from the vertex $s$; when we are at any vertex, we choose one of the outgo...

Which of the following problems can be proven conclusively to be in NP, under standard complexity assumptions? Marks only if all correct options are chosen and no incorre...

Which all of the following are true? Marks only if all correct options are chosen and no incorrect option is chosen.If a problem is in $\mathrm{NP}$, it is unlikely to be...

Suppose you are given two functions $f, g: \mathbb{N} \rightarrow \mathbb{N}$. Which of the following options DOES NOT hold. You are supposed to select only one option. (...

Order the following functions so that for all $i, j$, if $f_{i}$ comes before $f_{j}$ in the order then $f_{i}=O\left(f_{j}\right)$.$f_{1}(n)=3^{n}$$f_{2}(n)=n^{1 / 3}$$f...

You are given two functions $f, g: \mathbb{N} \rightarrow \mathbb{N}$. Say $f(n)=2^{n!}$ and $g(n)=\left(2^{n}\right)!$. Which of the following options holds? You are sup...

Solve the following modular arithmetic equations for $x$ and $y$ and write out your answers in the space provided.$9 x+5=7 \bmod 13$. Your Answer: $x=$ $\_\_\_\_$$13^{202...

Consider a directed graph $G=(V, E)$ with non-negative weights on the edges. Answer the following questions based on different graph algorithms and their properties.Which...

Consider a directed graph $G=(V, E)$ with non-negative weights on the edges. Answer the following questions based on different graph algorithms and their properties.Which...

Consider a directed graph $G=(V, E)$ with non-negative weights on the edges. Answer the following questions based on different graph algorithms and their properties.In th...

Answer each part with a number (either integer or float up to two decimals).In answering a question on a multiple-choice test, a student either knows the answer or guesse...