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125
Let $X$ be a random variable which takes values $1$ and $-1$ with probability $1 / 2$ each. Suppose $Y=X+N$, where $N$ is a random variable independent of $X$ with the fo...
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128
For a time-invariant system, the impulse response completely describes the system if the system iscausal and non-linearnon-causal and non-linearcausal and linearAll of th...
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132
What is the following passive circuit?Low-pass filterHigh-pass filterBand-pass filterBand-stop filterAll-pass filter
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136
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137
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138
For $x>0$, for which range of values of $\alpha$ is the following inequality true?\[x \log _{e}(x) \geq x-\alpha\]$\alpha \geq 1 / 2$$\alpha \geq 0$$\alpha \leq 2$$\alpha...
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139
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144
Evaluate the limit\[\lim _{n \rightarrow \infty}\left(2 n^{4}\right)^{\frac{1}{3 n}} .\]$e$$1$$2^{\frac{1}{3}}$$0$None of the above
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145
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146
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147
The matrix\[A=\left(\begin{array}{ccc}1 & a_{1} & a_{1}^{2} \\1 & a_{2} & a_{2}^{2} \\1 & a_{3} & a_{3}^{2}\end{array}\right)\]is invertible when$a_{1}>a_{2}>a_{3}$$a_{1}...
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152
Consider the two quadrature amplitude modulation $\text{(QAM)}$ constellations below. Suppose that the channel has additive white Gaussian noise channel and no intersymbo...
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158