# Electronics and Communication Engg - GATE 2013 Paper Solution

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles

Consider a vector field $\stackrel{\to }{A}\left(\stackrel{\to }{r}\right)$ . The closed loop line integral $\int \stackrel{\to }{A}·\stackrel{\to }{dl}$ can be expressed as

Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

In a forward biased pn junction diode, the sequence of events that best describes the mechanism of current flow is

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces

The maximum value of $\theta$ until which the approximation $\mathrm{sin}\theta \approx \theta$ holds to within 10% error is

The divergence of the vector field $\stackrel{\to }{A}=x{\stackrel{^}{a}}_{x}+y{\stackrel{^}{a}}_{y}+z{\stackrel{^}{a}}_{z}$ is

The impulse response of a system is $h\left(t\right)=tu\left(t\right)$.For an input $u\left(t-1\right)$ , the output is

The Bode plot of a transfer function G(s) is shown in the figure below. The gain is 32 dB and -8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G(s) is

In the circuit shown below what is the output voltage (Vout) if a silicon transistor Q and an ideal op-amp are used? Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of For 8085 microprocessor, the following program is executed.
MVI A, 05H;
MVI B, 05H;
DCR B;
JNZ PTR;
HLT;

At the end of program, accumulator contains

The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is

For a periodic signal $v\left(t\right)=30\mathrm{sin}100t+10\mathrm{cos}300t+6\mathrm{sin}\left(500t+\mathrm{\pi }/4\right)$, the fundamental frequency in rad/s is

In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain k is increased? A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is

In a MOSFET operating in the saturation region, the channel length modulation effect causes

The minimum eigenvalue of the following matrix is $\left[\begin{array}{ccc}3& 5& 2\\ 5& 12& 7\\ 2& 7& 5\end{array}\right]$
A polynomial $f\left(x\right)={a}_{4}{x}^{4}+{a}_{3}{x}^{3}+{a}_{2}{x}^{2}+{a}_{1}x-{a}_{0}$ with all coefficients positive has