# Electronics and Communication Engg - GATE 2009 Paper Solution

The order of the differential equation $\frac{{d}^{2}\mathrm{y}}{d{\mathrm{t}}^{2}}+{\left(\frac{d\mathrm{y}}{d\mathrm{t}}\right)}^{3}+{\mathrm{y}}^{4}={\mathrm{e}}^{-\mathrm{t}}$ is

The Fourier series of a real periodic function has only

P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cosine terms if it is odd
S. Sine terms if it is odd

Which of the above statements are correct?

A function is given f(t) = sin2t + cos2t. Which of the following is true?

A fully charged mobile phone with a 12V battery is good for a 10minute talk-time. Assume that, during the talk-time, the battery delivers a constant current of 2A and its voltage drops linearly from 12 V to 10V as shown in the figure. How much energy does the battery deliver during this talk-time?

In an n-type silicon crystal at room temperature, which of the following can have a concentration of 4×1019 cm-3?

The full form of the abbreviations TTL and CMOS in reference to logic families are

The ROC of Z-transform of the discrete time sequence $x\left(n\right)={\left(\frac{1}{3}\right)}^{n}u\left(n\right)-{\left(\frac{1}{2}\right)}^{n}u\left(-n-1\right)$ is

The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensators has such a magnitude plot?

A white noise process X(t) with two-sided power spectral density 1×10-10 W/Hz is input to a filter whose magnitude squared response is shown below

The power of the output process Y(t) is given by

Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?

A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

If the power spectral density of stationary random process is a sine-squared function of frequency, the shape of its autocorrelation is

If $f\left(z\right)={c}_{0}+{c}_{1}{z}^{-1}$, then ${\Large{\underset{circle}{\underset{unit}{\oint}}\frac{1+f\left(z\right)}zdz}}$ is given by

In the interconnection of ideal sources shown in the figure, it is known that the 60 V source is absorbing power

Which of the following can be the value of the current source I ?

The ratio of the mobility to the diffusion coefficient in a semiconductor has the units

In a microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed or rejected. Such an interrupt is

If the transfer function of the following network is $\frac{{V}_{0}\left(s\right)}{{V}_{i}\left(s\right)}=\frac{1}{2+sCR}$,

The value of the load resistance RL is

Consider the system $\frac{dx}{dt}=Ax+Bu$ with $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{c}p\\ q\end{array}\right]$ where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?
For a message signal $m\left(t\right)=\mathrm{cos}\left(2\pi {f}_{\mathit{m}}t\right)$ and carrier of frequency fc, which of the following represents a single side band (SSB) signal?