GATE EC question library

The Boolean expression $\text{AC + B} \overline{\text{C}}$ is equivalent to

$11001, 1001$ and $111001$ correspond to the $2$'s complement representation of which one of the following sets of number ?

The $8255$ Programmable Peripheral Interface is used as described below. An A/D converter is interfaced to a microprocessor through $8255.$ The conversion is initiated by a signal from the $8255$ on Port C. A signal on Port C causes data to be strobed into Port A. Two computers exchange data using a pair of $8255 \mathrm{s}$. Port A works as a …

The number of memory cycles required to execute the following $8085$ instructions $\text{LDA 3000 H}$ $\text{LXI D, FOF 1 H}$ would be

In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops. The $2$-input gate is

Consider the sequence of $8085$ instructions given below. $\text{LXI H, 9258, MOV A, M, CMA, MOV M, A}$ Which one of the following is performed by this sequence?

A Boolean function $f$ of two variables $x$ and $y$ is defined as follows: $$f(0,0)=f(0,1)=f(1,1)=1 ; \quad f(1,0)=0$$ Assuming complements of $x$ and $y$ are not available, a minimum cost solution for realizing $f$ using only $2$-input NOR gates and $2$-input OR gates (each having unit cost) would have a total cost of

It is desired to multiply the numbers $0 \mathrm{AH}$ by $0 \mathrm{BH}$ and store the result in the accumulator. The numbers are available in registers $B$ and $C$ respectively. A Part of the $8085$ program for this purpose is given below: $\qquad \qquad \text{MV1 A, 00H}$ $\text{Loop;}…....……….….$ $\qquad.…...…….....….$ …

A $1 \; \mathrm{kHz}$ sinusoidal signal is ideally sampled at $1500$ samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequencey $800 \mathrm{~Hz}$. The output signal has the frequency

A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a

A causal $\text{LTI}$ system is described by the difference equation $$2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]$$ The system is stable only if

A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state value is

The impulse response $h|n|$ of a linear time invariant system is given as $$h[n]=\left\{\begin{array}{cc} -2 \sqrt{2} & n=1,-1 \\ 4 \sqrt{2} & n=2,-2 \\ 0, & \text{ otherwise } \end{array}\right.$$ If the input to the above system is the sequence $\mathrm{e}^{j \pi n / 4}$, then the output is

Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure. Then $Y(f)$ is

A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase of the system response at $20 \mathrm{~Hz}$ is

Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is

If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ is

The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$ The range of $\mathrm{K}$ for which the system is stable is

For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is

The state variable equations of a system are: $\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$ The system is