GATE ECE 2009 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in steady state. The output is sampled at a rate $${\omega _s}\,\,rad/s$$ to obtain the final output {y(k)}. Which of the following is true?

y(.) is zero for all sampling frequencies $${\omega _s}$$

y(.) is nonzero for all sampling frequencies $${\omega _s}$$

y(.) is nonzero for $${\omega _s}$$ > 2, but zero for $${\omega _s}$$ < 2

y(.) is zero for $${\omega _s}$$ > 2, but nonzero for $${\omega _s}$$ < 2

GATE ECE 2009

MCQ (Single Correct Answer)

-0.3

The ROC of Z-transform of the discrete time sequence
x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over 2}} \right)^{ n}}\,u( - n - 1)$$ is

$${1 \over 3} < \left| {z\,} \right| < {1 \over 2}$$

$$\left| {z\,} \right| > {1 \over 2}$$

$$\left| {z\,} \right| < {1 \over 2}$$

$$2 < \left| {z\,} \right| < 3$$

GATE ECE 2009

MCQ (Single Correct Answer)

-0.3

The Fourier series of a real periodic function has only

P. Cosine terms if it is even

Q. Sine terms if it is even

R. Cosine terms if it odd

S. Sine terms if it is odd

Which of the above statement are correct?

P and S

P and R

Q and S

Q and R

GATE ECE 2009

MCQ (Single Correct Answer)

-0.3

A function is given by f(t) = sin²t +cos2t . Which of the following is true?

f has frequency components at 0 and $$1/2\mathrm\pi$$ Hz

f has frequency components at 0 and $$1/\mathrm\pi$$ Hz

f has frequency components at $$1/2\mathrm\pi$$ and $$1/\mathrm\pi$$ Hz

f has frequency components at 0, $$1/2\mathrm\pi$$ and $$1/\mathrm\pi$$ Hz

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