GATE EC question library

A connection is made consisting of resistance A in series with a parallel combination of resistances $B$ and $C$. Three resistors of value $10 Ω, 5 Ω, 2 Ω$ are provided. Consider all possible permutations of the given resistors into the positions $A, B, C$, and identify the configurations with maximum possible overall resistance, and also the ones …

An LTI system with unit sample response $h[n]=5\delta [n]-7\delta [n-1]+7\delta [n-3]-5\delta [n-4]$ is a

The input $x(t)$ and the output $y(t)$ of a continuous –time system are related as $$y(t)=\int_{t-T}^{t}x(u) du.$$ The system is

An n-channel enhancement mode MOSFET is biased at $V_{GS}$ >$V_{TH}$ and $V_{DS}$ > $(V_{GS}-V_{TH})$, where $V_{GS}$ is the gate-to-source voltage, $V_{DS}$ is the drain-to-source voltage and $V_{TH}$ is the threshold voltage. Considering channel length modulation effect to be significant, the MOSFET behaves as a

An $npn$ bipolar junction transistor (BJT) is operating in the active region. If the reverse bias across the base-collector junction is increased, then

Consider an $n$-channel MOSFET having width $W$, length $L$, electron mobility in the channel $\mu _{n}$ and oxide capacitance per unit area $C_{ox}$. If gate-to-source $V_{GS}=0.7$ V, drain-to-source voltage $V_{DS}=0.1 V$, $\mu _{n}C_{ox}=100 \mu A/V^{2}$, threshold voltage $V_{TH}=0.3V$ and $(W/L)=50$, then the transconductance …

The output $V_0$ of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the diode, is _________________.

In the figure, $D1$ is a real silicon $pn$ junction diode with a drop of $0.7V$ under forward bias condition and $D2$ is a Zener diode breakdown voltage of $-6.8V$. The input $V_{in}(t)$ is a periodic square wave of period $T$, whose one period is shown in the figure. Assuming $10 \tau < < T$, where $\tau$ is the time constant of the …

Consider the circuit shown in the figure. Assume base-to-emitter voltage $V_{BE}=0.8 V$ and common-base current gain ($\alpha$) of the transistor is unity. The value of the collector-to-emitter voltage $V_{CE}$ (in volt) is ____________

For the circuit shown in the figure, P and Q are the inputs and Y is the output. The logic implemented by the circuit is

Consider the circuit shown in the figure. The Boolean expression $F$ implemented by the circuit is

In a DRAM,

For the system shown in the figure, $Y(s)/X(s)$ = ___________

Consider the state space realization $\begin{bmatrix} \dot{x_1}(t)\\ \dot{x_2}(t) \end{bmatrix}=\begin{bmatrix} 0 &0 \\ 0&-9 \end{bmatrix}\begin{bmatrix} x_1(t)\\ x_2(t) \end{bmatrix}+\begin{bmatrix} 0\\ 45 \end{bmatrix} u(t)$ , with the initial condition $\begin{bmatrix} x_1(0)\\ x_2(0) \end{bmatrix}=\begin{bmatrix} 0\\ 0 \end{bmatrix}$ , where …

Which of the following statements is incorrect?

Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memoryless binary symmetric channel with crossover probability $p$ ?

Consider the random process $X(t)=U+Vt,$ Where $U$ is a zero-mean Gaussian random variable and V is a random variable uniformly distributed between $0$ and $2$. Assume that $U$ and $V$ are statistically independent. The mean value of the random process at $t = 2$ is ________

A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is $40$ dB. The minimum number of bits per sample needed to achieve the desired SQNR is __________

Two conducting spheres $S1$ and $S2$ of radii $a$ and $b$ ($b>a$) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure. For some charge placed on this structure, the potential and surface electric field on $S1$ are $V_a$ and $E_a$ and that on S2 are $V_b$ and $E_b$, respectively. …

A two-wire transmission line terminates in a television set. The VSWR measured on the line is $5.8$. The percentage of power that is reflected from the television set is _________