GATE ECE 2002 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2002

MCQ (Single Correct Answer)

-0.3

The differential equation for the current i(t) in the circuit of Fig. is

GATE ECE 2002 Network Theory - Network Elements Question 37 English

$$2\;\frac{\operatorname d^2\mathrm i}{\operatorname d\mathrm t^2}+\;2\;\frac{\operatorname d\mathrm i}{\mathrm{dt}}\;+\;\mathrm i(\mathrm t)\;=\sin\left(\mathrm t\right)$$

$$\frac{\operatorname d^2\mathrm i}{\operatorname d\mathrm t^2}+\;2\;\frac{\operatorname d\mathrm i}{\mathrm{dt}}\;+\;2\mathrm i(\mathrm t)\;=\cos\left(\mathrm t\right)$$

$$2\;\frac{\operatorname d^2\mathrm i}{\operatorname d\mathrm t^2}+\;2\;\frac{\operatorname d\mathrm i}{\mathrm{dt}}\;+\;\mathrm i(\mathrm t)\;=\cos\left(\mathrm t\right)$$

$$\frac{\operatorname d^2\mathrm i}{\operatorname d\mathrm t^2}+\;2\;\frac{\operatorname d\mathrm i}{\mathrm{dt}}\;+\;2\mathrm i(\mathrm t)\;=\sin\left(\mathrm t\right)$$

GATE ECE 2002

MCQ (Single Correct Answer)

-0.3

The Fourier transform F $$\left\{ {{e^{ - t}}u(t)} \right\}$$ is equal to $${1 \over {1 + j2\pi f}}$$. Therefore, $$F\left\{ {{1 \over {1 + j2\pi t}}} \right\}$$ is

$${e^f}u(f)$$

$${e^{ - f}}$$ u(f)

$${e^f}u(f)$$

$${e^{ - f}}$$u(-f)

GATE ECE 2002

MCQ (Single Correct Answer)

-0.6

The Laplace transform of a continuous - time signal x(t) is $$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If the Fourier transform of tyhis signal exists, then x(t) is

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

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

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

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

GATE ECE 2002

MCQ (Single Correct Answer)

-0.3

Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to

$$X\left( {t - 12} \right)$$

$$X\left( {t + 12} \right)$$

$$X\left( {t - 2} \right)$$

$$X\left( {t + 2} \right)$$

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