GATE EC question library

The state and output equations for a control system are: $$\begin{array}{c} \dot{x}=\left[\begin{array}{cc} -4 & -1.5 \\ 4 & 0 \end{array}\right] x+\left[\begin{array}{l} 2 \\ 0 \end{array}\right] u \\ y=\left[\begin{array}{ll} 1.5 & 0.625 \end{array}\right] x \end{array}$$ Which of the following expressions correctly represents the transfer …

The address of the first location of a $256$ kilo byte $(\mathrm{KB})$ memory is $(2500)_{\mathrm{H}}$. Choose the correct address of the last location of the memory.

Consider a real signal $x(t),-\infty < t < \infty$, such that $x(t) = 0\quad\text{for}\quad t <0, x(t) =2 \quad\text{for} \quad0 \leq t < 1\quad \text{and}\quad x(t) = 0\quad \text{for} \quad t \geq 1$. Let $E[x(t)]=\int_{-\infty}^{\infty}[x(t)]^{2} d t$. Which of the following options correctly represents the ratio, …

A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an $E_{b} / N_{o}=8.4 \mathrm{~dB}$ at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator. Assume the complimentary error function …

What is the $10^{\prime} s$ complement of $(47)_{10}?$

Consider a real baseband signal $x(t)=e^{-2 t}$, for $t$ (in seconds) $\geq 0$. If $99 \%$ of energy of $x(t)$ lies within $B \mathrm{~Hz}$, then which of the following options is TRUE for the value of ${B}?$

Consider the discrete time system (S) with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_{1}[n]$ and $h_{2}[n]$ are linear and time invariant. Which of the following statements is necessarily TRUE?

A Boolean function, $f(x, y, z)$ with $x$ as MSB and $z$ as LSB is realized by $4: 1$ multiplexer (MUX) with select lines, $\mathrm{S}_{1}$ and $\mathrm{S}_{0}\left(\mathrm{~S}_{1}\right.$ is MSB, $\mathrm{S}_{0}$ is LSB) and inputs, $\mathrm{I}_{0}, \mathrm{I}_{1}, \mathrm{I}_{2}, \mathrm{I}_{3}$ as shown in the Figure. Which of the …

A shift-left Shift Register (SR) and a D flip-flop are connected to a synchronized clock as shown in the Figure. Assume that the SR and D flip-flops are initially cleared and the XOR gate has no propagation delay. Which of the following options gives the correct binary representation $\left(b_{7} b_{6} b_{5} b_{4} b_{3} b_{2} b_{1} b_{0}\right)$ of the …

A small signal source, $V_{i}(t)=A \cos \left(10^{5} t\right)+B \sin \left(10^{7} t\right)$ is applied to a BJT circuit as shown in the Figure. Assume zero source resistance, $V_{B E}=0.7 \mathrm{~V}, \beta_{d c}=99$, Early voltage $=100 \mathrm{~V}$ and Thermal voltage $=25 \mathrm{mV}$. Effect of internal parasitic capacitances of the BJT may be …

Consider the two-port network as shown in the Figure. Which of the following options provides the correct set of values of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\text{D}$ parameters?

A complex load (in $\Omega$ ) is represented as $\Gamma_{L}=0.5 \angle 30^{\circ}$ on the Smith chart. A co-axial cable with a characteristic impedance of $50 ~\Omega$ is connected to the load. The new input impedance of the load now moves to a diametrically opposite point on the same $\Gamma$ circle on the Smith chart. Which option is the nearest …

A circuit using an ideal $\text{OP-AMP}$ is shown in the Figure. Which of the following options gives the correct value of the current $I_{X}$?

Consider an LED based on a direct bandgap semiconductor material with energy bandgap $1.3$ eV. Given: Plank's constant, $h=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}$ and speed of light in free space is $3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$. In which of the following wavelength ranges the LED will NOT emit?

Let the relevant bandwidth $(B)$ of a digital communication system be $1 ~\text{MHz}$ and $k T=-174 \mathrm{~dBm} / \mathrm{Hz}$, where $k$ is Boltzmann's constant and '$T$' is equivalent noise temperature of the receiver. The power $(S)$ of signal received through an additive Gaussian channel is $-80 ~\text{dBm}.$ Which of the following …

Consider the four-variable Boolean function, $f(w, x, y, z)=\sum m(0,2,5,7,8,10,13,14,15)$ with '$w$' as MSB and '$z$' as LSB. Which of the following expressions is/are the valid form(s) of $f(w, x, y, z)?$

Consider a real, narrowband signal $x(t)=A(t) \cos \left[2 \pi f_{c} t+\theta(t)\right]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_{M}$ and $f_{c}\left(=1000 f_{M}\right)$, respectively. Which of the following statements is/are correct for $-\infty < t < \infty ?$

Let $x_{1}(t)=\cos (2 \pi n t)$ and $x_{2}(t)=2 \sin (4 \pi n t)$ represent two sinusoids for a positive integer $n$ and $-\infty < t < \infty$. Which of the following statements about $x_{1}(t)$ and $x_{2}(t)$ is/are valid?

Consider the unity negative feedback control system shown in the Figure. The value of gain $K(>0)$ at which the given system will remain marginally stable is $\_\_\_\_$. (Answer in integer)

An $n$-channel MOSFET is connected as shown in the Figure. Assume $V_{T H}=1 \mathrm{~V}, V_{D D}=5 \mathrm{~V}$, and $\mu C_{o x}\left(\frac{W}{L}\right)=2 \mathrm{~mA} \mathrm{~V}^{-2}$ and neglect channel length modulation effects. The gate voltage ( $V_{G}$ ) of the $n$-channel $\text{MOSFET}$ (in Volt) is $\_\_\_\_$. (rounded off to two …