For the circuit shown in the figure, R₁ = R₂ = R₃ = 1 Ω, L = 1 µH and C = 1 µF. If the input V_in = cos(10⁶t) , then the overall voltage gain (V_out /V_in) of the circuit is __________.

For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in MHz) is _________.

A wide sense stationary random process $$X(t)$$ passes through the $$LTI$$ system shown in the figure. If the autocorrelation function of $$X(t)$$ is $${R_x}\left( \tau \right),$$ then the autocorrelation function $${R_x}\left( \tau \right),$$ of the output $$Y(t)$$ is equal to

The bit error probability of a memoryless binary symmetric channel is $${10^{ - 5}}$$. If $${10^{ - 5}}$$ bits are sent over this channel, then the probability that not more than one bit will be in error is ________________