1
GATE ECE 2008
+2
-0.6
Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions

Group I $$P=\frac{25}{s^2+25}\;\;\;\;\;Q=\frac{36}{s^2+20s+36}$$$$$R=\frac{36}{s^2+12s+36}\;\;\;\;\;S=\frac{49}{s^2+7s+49}$$$

Group II

A
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;1\;\;\;\;\;4\;\;\;\;\;2\end{array}$$
B
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;2\;\;\;\;\;4\;\;\;\;\;1\end{array}$$
C
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\2\;\;\;\;\;1\;\;\;\;\;4\;\;\;\;\;3\end{array}$$
D
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;4\;\;\;\;\;1\;\;\;\;\;2\end{array}$$
2
GATE ECE 2007
+2
-0.6
The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}$$ .The step response of the system is:
A
$$5\left(1\;-\;e^{-5t}\right)u\left(t\right)$$
B
$$5\left(1\;-\;e^{-\frac15}\right)u\left(t\right)$$
C
$$\frac15\;\left(1\;-\;e^{-5t}\right)u\left(t\right)$$
D
$$\frac15\;\left(1\;-\;e^{-\frac15}\right)u\left(t\right)$$
3
GATE ECE 2007
+2
-0.6
The transfer function of a plant is $$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$The second-order approximation of T (s) using dominant pole concept is: A $$\frac1{\left(s+5\right)\left(s+1\right)}$$ B $$\frac5{\left(s+5\right)\left(s+1\right)}$$ C $$\frac5{\left(s^2+s+1\right)}$$ D $$\frac1{\left(s^2+s+1\right)}$$ 4 GATE ECE 2006 MCQ (Single Correct Answer) +2 -0.6 The unit impulse response of a system is: $$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state value of the output for unit step input is equal to
A
-1
B
$$0$$
C
1
D
$$\infty$$
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