GATE EE 2009 | GATE EE Year Wise Previous Years Questions

GATE EE 2009

MCQ (Single Correct Answer)

-0.3

A linear Time Invariant system with an impulse response $$h(t)$$ produces output $$y(t)$$ when input $$x(t)$$ is applied. When the input $$x\left( {t - \tau } \right)$$ is applied to a system with response $$h\left( {t - \tau } \right)$$, the output will be

$$y\left( t \right)$$

$$y\left( {2\left( {t - \tau } \right)} \right)$$

$$y\left( {t - \tau } \right)$$

$$y\left( {t - 2\tau } \right)$$

GATE EE 2009

MCQ (Single Correct Answer)

-0.6

The Fourier Series coefficients, of a periodic signal $$x\left( t \right),$$ expressed as $$x\left( t \right) = \sum {_{k = - \infty }^\infty {a_k}{e^{j2\pi kt/T}}} $$ are given by
$${a_{ - 2}} = 2 - j1;\,\,{a_{ - 1}} = 0.5 + j0.2;\,\,{a_0} = j2;$$
$${a_1} = 0.5 - j0.2;\,\,{a_2} = 2 + j1;\,\,$$ and
$${a_k} = 0;$$ for $$|k|\,\, > 2.$$

Which of the following is true?

$$x(t)$$ has finite energy because only finitely many coefficients are non $$-$$ zero

$$x(t)$$ has zero average value because it is periodic

the imaginary part of $$x(t)$$ is constant

The real part of $$x(t)$$ is even

GATE EE 2009

MCQ (Single Correct Answer)

-0.6

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

each system in the cascade is individually casual and unstable

at least one system is unstable and atleast one system is casual

at least one system is casual and all systems are unstable

the majority are unstable and the majority are casual

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