GATE ECE 2008 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2008

MCQ (Single Correct Answer)

-0.6

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is

[exp(-2t) + exp(-4t)]u(t)

[-4exp(-2t) + 12exp(-4t) - exp(-t)]u(t)

[-4exp(-2t) + 12exp(-4t)]u(t)

[-0.5exp(-2t) + 1.5exp(-4t)]u(t)

GATE ECE 2008

MCQ (Single Correct Answer)

-0.6

A signal flow graph of a system is given below. GATE ECE 2008 Control Systems - State Space Analysis Question 29 English

The set of equations that correspond to this signal flow graph is

$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ \beta & { - \gamma } & 0 \cr \gamma & \alpha & 0 \cr { - \alpha } & { - \beta } & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 1 & 0 \cr 0 & 0 \cr 0 & 1 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$

$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ 0 & \alpha & \gamma \cr 0 & { - \alpha } & { - \gamma } \cr 0 & \beta & { - \beta } \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 0 & 0 \cr 0 & 1 \cr 1 & 0 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$

$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ { - \alpha } & \beta & 0 \cr { - \beta } & { - \gamma } & 0 \cr \alpha & \gamma & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr 0 & 0 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$

$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ { - \gamma } & 0 & \beta \cr \gamma & 0 & \alpha \cr { - \beta } & 0 & { - \alpha } \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 0 & 1 \cr 0 & 0 \cr 1 & 0 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$

GATE ECE 2008

MCQ (Single Correct Answer)

-0.3

The pole-zero plot given below corresponds to a GATE ECE 2008 Control Systems - Compensators Question 22 English

Low pass filter

High pass filter

Band pass filter

notch filter

GATE ECE 2008

MCQ (Single Correct Answer)

-0.6

The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function.

The frequency response H(ω) of the system in terms of angular frequency 'ω' is given by h( ω)

$${1 \over {1 + j2\omega }}$$

$${{\sin \omega } \over \omega }$$

$${1 \over {2 + j\omega }}$$

$${{j\omega } \over {2 + j\omega }}$$

PREVIOUS NEXT

GATE ECE Papers

All year-wise previous year question papers

2026