A cascade of 3 Liner Time Invariant systems is causal and

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A cascade of 3 Liner Time Invariant systems is causal and unstable. From this, we conclude that

1. each system in the cascade is individually causal and unstable
2. at least one system is unstable and at least one system is causal
3. at least one system is causal and all systems are unstable
4. the majority are unstable and the majority are causal

Correct Option: B

If h₁ (t), h₂ (t) and h₃ (t) are the impulse response of the three LTI-systems, then
Overall response of the system is h(t) = G₁ (t) × G₂ (t) × G₃ (t)
Assuming t₁, t₂, t₃ are the initial points of three systems,
then, by convolution theorem, initial point for The combined system t = t₁ + t₂ + t₃
As the entire system is causal, therefore h(t) > 0 for t > 0
For this condition, t > 0 to be true, at least one of the time t₁, t₂, t₃ must be greater than zero.
i.e. one of the system must be causal. As far as stability is concerned, if the system becomes unstable, the entire system will be unstable.