Transfer function and Laplace Transform:
In control systems, the transfer function is a mathematical representation of the relationship between the input and output of a system. It is usually denoted by H(s), where 's' represents the complex frequency variable. The Laplace Transform is a mathematical tool used to analyze dynamic systems in the frequency domain.

Given Block Transfer Function:
The given block has a transfer function of a-2s. This means that when the Laplace Transform of the input signal r(t) is taken, it is multiplied by a-2s.

Modified Output:
When the input signal r(t) is passed through the given block, the Laplace Transform of the modified output signal c(t) can be calculated. Let's denote the Laplace Transform of c(t) as C(s).

Laplace Transform of the Input Signal:
The Laplace Transform of the input signal r(t) is denoted as R(s).

Effect of the Block Transfer Function on the Input Signal:
When the input signal R(s) is multiplied by a-2s (block transfer function), the resulting Laplace Transform is A-2sR(s).

Modified Output Signal:
The modified output signal C(s) can be obtained by multiplying the Laplace Transform of the input signal R(s) by the block transfer function a-2s. Therefore, C(s) = A-2sR(s).

Inverse Laplace Transform:
To obtain the modified output signal c(t), the inverse Laplace Transform of C(s) needs to be taken. Since the Laplace Transform of a signal represents its frequency domain representation, the inverse Laplace Transform brings the signal back to the time domain.

Modified Output Signal in Time Domain:
Taking the inverse Laplace Transform of C(s) = A-2sR(s), we get the modified output signal c(t) = a(t - 2)u(t - 2), where a(t - 2) represents a delayed version of the original signal by 2 units of time, and u(t - 2) represents the unit step function that accounts for the delay.

Correct Answer:
Therefore, the correct answer is option 'A' - c(t - 2)u(t - 2). The modified output signal c(t) is a delayed version of the original signal r(t) by 2 units of time, and it is multiplied by the unit step function to account for the delay.