Recent questions tagged tifrece2017

Consider a system which in response to input $x(t)$ outputs\[y(t)=2 x(t-2)+x(2 t-1)+1 .\]Which of the following describes the system?linear, time-invariant, causallinear,...

Suppose a $1 \mu \mathrm{H}$ inductor and a $1 \Omega$ resistor are connected in series to a $1 \mathrm{ V}$ battery. What happens to the current in the circuit?The curre...

What is the maximum average power that can be dissipated by a load connected to the output terminals of the following circuit with an alternating current source?$23 \math...

A Schmitt trigger circuit is a comparator circuit with a hysteresis. Consider the Schmitt trigger circuit in the figure implemented using an opamp. What are the trigger l...

Consider the inequality\[n-\frac{1}{n} \geq \sqrt{n^{2}-1},\]where $n$ is an integer $\geq 1$. Which of the following statements is $\text{TRUE?}$This inequality holds fo...

Let $a, b \in\{0,1\}$. Consider the following statements where $*$ is the $\text{AND}$ operator, $\oplus$ is $\text{EXCLUSIVE-OR,}$ and ${ }^{c}$ denotes the complement f...

A circulant matrix is a square matrix whose each row is the preceding row rotated to the right by one element, e.g., the following is a $3 \times 3$ circulant matrix.\[\l...

Consider the two positive integer sequences, defined for a fixed positive integer $c \geq 2$\[f(n)=\frac{1}{n}\left\lfloor\frac{n}{c}\right\rfloor, \quad g(n)=n\left\lflo...

Recall that for a random variable $X$ which takes values in $\mathbb{N}$, the set of natural numbers, its entropy in bits is defined as\[H(X)=\sum_{n=1}^{\infty} p_{n} \l...

Consider a single coin where the probability of heads is $p \in(0,1)$ and probability of tails is $1-p$. Suppose that this coin is flipped an infinite number of times. Le...

Consider a unit length interval $[0,1]$ and choose a point $X$ on it with uniform distribution. Let $L_{1}=X$ and $L_{2}=1-X$ be the length of the two sub-intervals creat...

Consider a signal $X$ that can take two values, $-1$ with probability $p$ and $+1$ with probability $1-p$. Let $Y=X+N$, where $N$ is mean zero random noise that has proba...

Let $A$ be an $n \times n$ matrix. Consider the following statements.$A$ can have full-rank even if there exists two vectors $v_{1} \neq v_{2}$ such that $A v_{1}=A v_{2}...

Consider the positive integer sequence\[x_{n}=n^{50} e^{-(\log (n))^{3 / 2}}, \quad n=1,2,3, \ldots\]Which of the following statements is $\text{TRUE?}$For every $M>0$, t...

Suppose that $f(x)$ is a real valued continuous function such that $f(x) \rightarrow \infty$ as $x \rightarrow \infty$. Further, let\[a_{n}=\sum_{j=1}^{n} 1 / j\]and\[b_{...