5.
Consider a message signal whose spectrum is given by $$M\left( f \right) = 1 - \frac{{\left| f \right|}}{{{{10}^4}}},\,\left| f \right| \leqslant {10^4}$$     and zero elsewhere. The message signal amplitude modulates a carrier fc = 1 MHz. The bandwidth of the modulated signal is:

6.
A probability density function is given by $$P\left( x \right) = K\exp \left( { - \frac{{{x^2}}}{2}} \right),\, - \infty < x < \infty $$
The value of K should be

7.
A uniformly distributed random variable X with probability density function $${f_x}\left( x \right) = \frac{1}{{10}}\left( {u\left( {x + 5} \right) - u\left( {x - 5} \right)} \right)$$
Where u(⋅) is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable Y would be
Communication Systems mcq question image

8.
Consider the following statements regarding signals:
1. Deterministic signal is a signal about which there is no uncertainty with respect to its value at any time.
2. Each signal within the ensemble has a certain probability of occurrence and the ensemble of signals is referred to as a random process.
3. EEG signal is an example of random signal.
Which of the above statements are correct?

10.
A carrier of frequency 1 MHz is amplitude modulated by a signal of frequency 1 kHz to a depth of 60%. This is passed through a filter of characteristics shown in the given Figure-I and Figure-II. If the filter output is fed to an envelope detector, the detector output will be
Communication Systems mcq question image

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