GATE ECE 2004 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2004

MCQ (Single Correct Answer)

-0.6

A causal LTI system is described by the difference equation $$2y\left[ n \right] = ay\left[ {n - 2} \right] - 2x\left[ n \right] + \beta x\left[ {n - 1} \right].$$ The system is stable only if

$$\left| \alpha \right| = 2,\,\left| \beta \right| < 2$$

$$\left| \alpha \right| > 2,\,\left| \beta \right| > 2$$

$$\left| \alpha \right| < 2$$, any value of $$\beta $$

$$\left| \beta \right| < 2,$$ any value of $$\alpha $$

GATE ECE 2004

MCQ (Single Correct Answer)

-0.3

The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$ = u\left[ {n + 3} \right] + u\left[ {n - 2} \right] - 2\,u\left[ {n - 7} \right],$$ where $$u\left[ n \right]$$ is the unit step sequence. The above system is

stable but not causal.

stable and causal.

causal but unstable.

unstable and not causal.

GATE ECE 2004

MCQ (Single Correct Answer)

-0.6

Consider the sequence

$$x[n] = [ - \,4 - \,j5,\,\mathop {1 + j2}\limits_ \uparrow ,\,\,4]$$

The conjugate anti-symmetric part of the sequence is

$$\left[ {\matrix{ { - 4 - j\,\,2.5} & {j\,2} & {4 - j\,\,2.5} \cr } } \right]$$

$$\left[ {\matrix{ { - j\,\,2.5} & 1 & { - j\,\,2.5} \cr } } \right]$$

$$\left[ {\matrix{ { - j\,\,5} & {j\,2} & 0 \cr } } \right]$$

$$\left[ {\matrix{ { - 4} & 1 & 4 \cr } } \right]$$

GATE ECE 2004

MCQ (Single Correct Answer)

-0.6

A causal system having the transfer function H(s) = $${1 \over {s + 2}}$$, is excited with 10 u(t). The time at which the output reaches 99% of its steady state value is

2.7 sec

2.5 sec

2.3 sec

2.1 sec

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