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GATE Signals and systems questions

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1) Which of the following signal is not periodic?
a) sin 10\pit
b) sin 31t
c)sin 10\pit + sin 31t
d) sin(10\pit +31)

2) The value of the integral \int_{0}^{\infty} e^{-\alpha*t^2} \delta(t+10) dt is
a) 0
b) e^{-100 \alpha}
c) e^{10 \alpha}
d) e^{100 \alpha}

3) A system is defined by its input and output relationship y(t)=5x(t+3)+2 where y(t) and x(t) are the output and input respectively. The system is
a) Linear and Casual
b)Linear and non-casual
c) non-linear and casual
d) non-linear and non-casual

4) If the input-output relation of a system is y(t)=\int_{-\infty}^{2t} x(\tau) d\tau then the system is
a) Linear, time invariant and unstable
b) linear ,non-causal and unstable
c) linear, causal and time invariant
d) non-causal, time invariant and unstable

5) Evaluate te function \int_{0}^{\infty} t^2 \delta(t-3) dt
a) e^{-t^2}
b) t^3/3
c) t^2(t-3)
d) 9

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