GATE EC question library

In the circuit shown in the figure , the channel length modulation of all transistors is non-zero $(\lambda\neq0)$. Also, all transistors operate in saturation and have negligible body effect .The ac small signal voltage gain ($V_o/V_{in}$) of the circuit is _________

In the circuit shown in the figure, transistor $M1$ is in saturation and has transconductance $g_m = 0.01$ siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation $\lambda$ to be zero,the small signal input pole frequency (in $kHz$) is _________

Following is the K-map of a Boolean function of five variables $P,Q,R,S$ and $X$. The minimum sum-of-product (SOP) expression for the function is

For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are $2$ ns, $1.5$ ns and $1$ ns, respectively. If all the inputs $P, Q, R, S$ and $T$ are applied at the same time instant, the maximum propagation delay (in ns) of the circuit is _________

For the circuit shown in the figure, the delay of the bubbled NAND gate is $2\:ns$ and that of the counter is assumed to be zero. If the clock (Clk) frequency is $1\:GHz$, then the counter behaves as a

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as $$\begin{array}{|c|cc} \hline s^3 & 1 &(2K+3) \\ s^2 & 2K & 4 \end{array}$$ The range of $K$ for which the system is stable is

A second-order linear time-invariant system is described by the following state equations $$\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$$ $$\frac{d}{dt}x_2(t)+x_2(t)=u(t)$$ where $x_1(t)$ and $x_2(t)$ are the two state variables and $u(t)$ denotes the input. If the output $c(t)=x_1(t)$, then the system is

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $$G(s)=\frac{K(s+2)}{s^2+2s+2}\;\text{and}\hspace{0.3cm}H(s)=1,$$ respectively. If the variable parameter $K$ is real positive, then the location of the breakaway point on the root locus diagram of the system is …

A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$, then the autocorrelation function $R_Y(\tau)$ of the output $Y(t)$ is equal to

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of $4.0\:kHz$ and two-sided noise power spectral density ${\large\frac{\eta}{2}}=2.5\times10^{-5}Watt\:per\:Hz$. If information at the rate of $52\:kbps$ is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit-energy $E_b$ …

The bit error probability of a memoryless binary symmetric channel is $10^{-5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bit will be in error is _______

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. At $10 \:GHz$ operating frequency, the value of the propagation constant (per meter) of the corresponding propagation mode is _______

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. The increasing order of the cut-off frequencies for different modes is

A radar operating at $5\:GHz$ uses a common antenna for transmission and reception. The antenna has a gain of $150$ and is aligned for maximum directional radiation and reception to a target $1\:km$ away having radar cross-section of $3\:m^2$. If it transmits $100\:kW$, then the received power (in $\mu W)$ is _______

Consider the charge profile shown in the figure. The resultant potential distribution is best described by