GATE EE 2007 | GATE EE Year Wise Previous Years Questions

GATE EE 2007

MCQ (Single Correct Answer)

-0.3

Let a signal $${a_1}\,\sin \left( {{\omega _1}t + {\phi _1}} \right)$$ be applied to a stable linear time-invariant system. Let the corresponding steady state output be represented as $${a_2}F\left( {{\omega _2}t + {\phi _2}} \right).$$ Then which of the following statements is true?

$$F$$ is not necessarily a ''sine'' or ''cosine'' function but must be periodic with $${\omega _1} = {\omega _2}.$$

$$F$$ must be a ''sine'' or ''cosine'' function with $${a_1} = {a_2}.$$

$$F$$ must be a ''sine'' function with $${\omega _1} = {\omega _2}.$$ and $${\phi _1} = {\phi _2}.$$

$$F$$ must be a ''sine'' or ''cosine'' function with $${\omega _1} = {\omega _2}.$$

GATE EE 2007

MCQ (Single Correct Answer)

-0.6

If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t)*r(t) their convolution, then the function u(t+1)*r(t-2) is given by

(1/2)(t-1)(t-2)

(1/2)(t-1)²u(t-1)

none of the above

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