Recent questions tagged gate2009-ec

The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is$1$$2$$3$$4$

The Fourier series of a real periodic function has onlycosine terms if it is evensine terms if it is evencosine terms if it is oddsine terms if it is oddWhich of the abov...

A function is given by $f(t)=\sin ^{2} t+\cos 2 t$. Which of the following is true?$f$ has frequency components at 0 and $1 / 2 \pi \; \mathrm{Hz}$$f$ has frequency compo...

A fully charged mobile phone with a $12 \mathrm{~V}$ battery is good for a $10$ minute talk-time. Assume that, during the talk-time, the battery delivers a constant curre...

In an n-type silicon crystal at room temperature, which of the following can have a concentration of $4 \times 10^{19} \mathrm{~cm}^{-3}$ ?Silicon atomsHolesDopant atomsV...

The full forms of the abbreviations $\text{TTL}$ and $\text{CMOS}$ in reference to logic families areTriple Transistor Logic and Chip Metal Oxide SemiconductorTristate Tr...

The $\text{ROC}$ of $\text{Z}$-transform of the discrete time sequence $\quad x(n)=\left(\dfrac{1}{3}\right)^{n} u(n)-\left(\dfrac{1}{2}\right)^{n} u(-n-1) \quad$ is$\fra...

The magnitude plot of a rational transfer function $G(s)$ with real coefficients is shown below. Which of the following compensators hás such a magnitude plot?Lead compen...

A white noise process $X(t)$ with two-sided power spectral density $1 \times 10^{-10} \mathrm{~W} / \mathrm{Hz}$ is input to a filter whose magnitude squared response is ...

Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?Only $\text{P}$ has no cutoff-frequencyOnly $\text{Q}$ has no cu...

A fair coin is tossed $10$ times. What is the probability that $\text{ONLY}$ the first two tosses will yield heads?$\left(\frac{1}{2}\right)^{2}$${ }^{10} C_{2}\left(\fra...

If the power spectral density of stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is

If $f(z) = c_{0} + c_{1} z^{-1},$ then $\displaystyle{} \oint_{\text{unit circle}} \frac{1+f(z)}{z} dz$ is given by$2 \pi c_{1}$$2 \pi\left(1+c_{0}\right)$$2 \pi j c_{1}$...

In the interconnection of ideal sources shown in the figure, it is known that the $60 \mathrm{~V}$ source is absorbing power.Which of the following can be the value of th...

The ratio of the mobility to the diffusion coefficient in a semiconductor has the units$\mathrm{V}^{-1}$$\mathrm{cm} \cdot \mathrm{V}^{-1}$$\mathrm{V} \cdot \mathrm{cm}^{...

In a microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed o...

If the transfer function of the following network is $\dfrac{V_{o}(s)}{V_{i}(s)}=\dfrac{1}{2+s C R}.$the value of the load resistance $R_{L}$ is$R / 4$$R / 2$$R$$2 R$

Consider the system $\dfrac{d x}{d t}=A x+B u$ with $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}p \\ q\end{array}\right]$ whe...

For a message signal $m(t)=\cos \left(2 \pi f_{m} t\right)$ and carrier of frequency $f_{c}$ which of the following represents a single-side-band (SSB) signal?$\cos \left...

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the $y-z$ plane and parallel to the $y$-axis. The other wire is in the $x-y$ p...

Consider two independent random variables $X$ and $Y$ with identical distributions. The variables $X$ and $Y$ take values $0,1$ and $2$ with probabilities $\frac{1}{2}, \...

The Taylor series expansion of $\dfrac{\sin x}{x-\pi}$ at $x=\pi$ is given by$1+\frac{(x-\pi)^{2}}{3 !}+\ldots$$-1-\frac{(x-\pi)^{2}}{3 !}+\ldots$$1-\frac{(x-\pi)^{2}}{3 ...

If a vector field $ \displaystyle{} \vec{V}$ is related to another vector field $ \displaystyle{} \vec{A}$ through $ \displaystyle{} \vec{V}=\nabla \times \vec{A}$, which...

Given that $F(s)$ is the one-sided Laplace transform of $f(t),$ the Laplace transform of $\displaystyle{}\int_{0}^{t} f(\tau) d \tau$ is$s F(s)-f(0)$$\dfrac{1}{s} F(s)$$\...

Match each differential equation in $\text{Group I}$ to its family of solution curves from $\text{Group II.}$$$\begin{array}{llll} & \textbf{Group I} & & \textbf{Group II...

The eigen values of the following matrix are\[ \left[\begin{array}{ccc}-1 & 3 & 5 \\-3 & -1 & 6 \\0 & 0 & 3\end{array}\right] \]$3,3+5 j, 6-j$$-6+5 j, 3+j, 3-j$$3+j, 3-j,...

An $\text{AC}$ source of $\text{RMS}$ voltage $20 \mathrm{~V}$ with internal impedance $Z_{s}=(1+2 j) \Omega$ feeds a load of impedance $Z_{L}=(7+4 j) \Omega$ in the figu...

The switch in the circuit shown was on position $a$ for a long time, and is moved to position $b$ at time $t=0$. The current $i(t)$ for $t>0$ is given by$0.2 e^{-125 t} u...

In the circuit shown, what value of $R_{L}$ maximizes the power delivered to $R_{L}$ ?$2.4 \; \Omega$$\frac{8}{3} \; \Omega$$4 \; \Omega$$6 \; \Omega$

In the circuit below, the diode is ideal. The voltage $V$ is given by$\min \left(V_{i}, 1\right)$$\max \left(V_{i}, 1\right)$$\min \left(-V_{i}, 1\right)$$\max \left(-V_{...