GATE ECE 2006 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2006

MCQ (Single Correct Answer)

-0.3

A solution for the differential equation $$\mathop x\limits^. $$(t) + 2 x (t) = $$\delta (t)$$ with intial condition $$x({0^ - }) = 0$$ is

$${e^{ - 2t}}\,u(t)$$

$${e^{2t}}\,u(t)$$

$${e^{ - t}}\,u(t)$$

$${e^t}\,u(t)$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

As x is increased from $$ - \infty \,\,to\,\infty $$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$

monotonically increases

monotonically decreases

increases to a maximum value and then decreases

decreases to a minimum value and then increases

GATE ECE 2006

MCQ (Single Correct Answer)

-0.3

The Dirac delta function $$\delta (t)$$ is defined as

$$\delta (t) = \left\{ {\matrix{ {1,} & {t = 0} \cr {0,} & {otherwise} \cr } } \right.$$

$$\delta (t) = \left\{ {\matrix{ {\infty ,} & {t = 0} \cr {0,} & {otherwise} \cr } } \right.$$

$$\delta (t) = \left\{ {\matrix{ {1,} & {t = 0} \cr {0,} & {otherwise\,\,\,and\,\,\int\limits_{ - \infty }^\infty {\delta (t)\,dt = 1} } \cr } } \right.\,\,$$

$$\delta (t) = \left\{ {\matrix{ {\infty ,} & {t = 0} \cr {0,} & {otherwise\,\,\,and\,\,\int\limits_{ - \infty }^\infty {\delta (t)\,dt = 1} } \cr } } \right.\,\,$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty }^\infty {{{( - 10)}^k}\,\delta (t - 0.5x{{10}^{ - 4}}k)} $$
The resulting signal is then passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be

$${\delta (t)}$$

m(t)

m(t) $${\delta (t)}$$

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