GATE EC 2022 Question Paper (06-Feb-2022) (Shift 1)

Consider the following partial differential equation (PDE)

$\mathrm{a}\frac{{\partial }^2\mathrm{f}(\mathrm{x},\mathrm{y})}{\partial {\mathrm{x}}^2}+\mathrm{b}\frac{{\partial }^2\mathrm{f}(\mathrm{x},\mathrm{y})}{\partial {\mathrm{y}}^2}=\mathrm{f}(\mathrm{x},\mathrm{y})$

where a and b are distinct positive real numbers. Select the combination(s) of values of the real parameters 𝜉 and 𝜂 such that f(x, y) = e${}^{(\text{ξ}x+ny)}$ is a solution of the given PDF.

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability(1 -ϵ), and flipped with probability ϵ. For each codeword transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error.

For ϵ = 0.1, the probability that a transmitted codeword is decoded correctly is _________ (rounded off to two decimal places).

An ideal OPAMP circuit with a sinusoidal input is shown in the figure. The 3 dB frequency is the frequency at which the magnitude of the voltage gain decreases by 3 dB from the maximum value. Which of the options is/are correct?

Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.

Select the correct statement(s) regarding CMOS implementation of NOT gates.