Recent questions tagged isi2025-mcs-pcb

Consider the following function job(), which takes two positive integers $x$ and $y$, and returns another integer.int job(int x, int y) {if (x y) return x;else if (x y) ...

Suppose $X=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ is an array of numbers (not necessarily integers) sorted in the ascending order, and $Y=\left(y_{1}, y_{2}, \ldots, y...

Let $f: \mathbb{R} \rightarrow(0, \infty)$ be a function satisfying $f(x+y)=f(x) f(y)$ for all $x, y \in \mathbb{R}$.Prove that if $f$ is continuous at 0 , then $f$ is co...

The map below shows all the routes connecting the locations $A, B, C$ and $D$. However, there are many bridges, each indicated with a (?) mark. Each bridge is open with p...

Let $p(x)=(x-1)(x-2) \cdots(x-n+1)(x-n)-1$ be a polynomial where $n \geq 1$. Suppose $p(x)=f(x) g(x)$ where $f$ and $g$ are both polynomials with integer coefficients.Sho...

Let $L$ be a language over an alphabet $\{a, b\}$ such that the empty string does not belong to $L$ and the first and the last letters of every string in $L$ are the same...

Using JK flip-flops and a minimal number of combinatorial logic gates, design a sequential circuit that takes a stream of bits as input and outputs $1$ whenever three con...

Suppose $X=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ is an array of numbers (not necessarily integers) sorted in the ascending order, and $Y=\left(y_{1}, y_{2}, \ldots, y...

For a graph $G=(V, E)$ and a subset $X \subseteq V$ of the vertices, the induced subgraph $G[X]$ is defined as $G[X]=\left(X, E^{\prime}\right)$, where $E^{\prime}=\{u v ...

Using JK flip-flops and a minimal number of combinatorial logic gates, design a sequential circuit that takes a stream of bits as input and outputs $1$ whenever three con...

Let $L$ be a language over an alphabet $\{a, b\}$ such that the empty string does not belong to $L$ and the first and the last letters of every string in $L$ are the same...

Consider that node $X$ is sending packets to node $Y$. The path from $X$ to $Y$ has a bandwidth of $B_{X Y}=5000$ bytes/second and a propagation delay of $P_{X Y}=100$ mi...