# GATE EE 2013

 Question 1
In the circuit shown below what is the output voltage $(V_{out})$ if a silicon transistor Q and an ideal op-amp are used? A $-15 V$ B $-0.7 V$ C $+0.7 V$ D $+15 V$
Analog Electronics   Operational Amplifiers
Question 1 Explanation: Using the concept of vitual ground, V=0 $V_{out}=-0.7V$
 Question 2
The transfer function $\frac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is A $\frac{0.5s+1}{s+1}$ B $\frac{3s+6}{s+2}$ C $\frac{s+2}{s+1}$ D $\frac{s+1}{s+2}$
Control Systems   Mathematical Models of Physical Systems
Question 2 Explanation: $\frac{V_2(s)}{V_1(s)}=\frac{R+\frac{1}{Cs}}{\frac{1}{Cs}+R+\frac{1}{Cs}}$
$=\frac{1+RCs}{2+RCs}$
$=\frac{1+10 \times 10^3 \times 100 \times 10^{-6}s}{2+10 \times 10^3 \times 100 \times 10^{-6}s}$
$=\frac{s+1}{s+2}$

 Question 3
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is A u(t) B tu(t) C $\frac{t^{2}}{2}u(t)$ D $e^{-t}u(t)$
Signals and Systems   Laplace Transform
Question 3 Explanation:
\begin{aligned} Y(s)&=\frac{1}{s}U(s)=\frac{1}{s^2}\\ y(t)&=tu(t) \end{aligned}
 Question 4
The impulse response of a system is h(t)=tu(t). For an input u(t-1), the output is
 A $\frac{t^{2}}{2}u(t)$ B $\frac{t(t-1)}{2}u(t-1)$ C $\frac{(t-1)^{2}}{2}u(t-1)$ D $\frac{t^{2}-1}{2}u(t-1)$
Signals and Systems   Linear Time Invariant Systems
Question 4 Explanation:
\begin{aligned} h(t) &=tu(t) \\ H(s) &=\frac{1}{s^2} \\ \Rightarrow \; \frac{Y(s)}{U(s)} &=\frac{1}{s^2} \\ Y(s) &=\frac{1}{s^2} \frac{e^{-s}}{s}\\ \Rightarrow \; y(t) &=\frac{(t-1)^2}{2}u(t-1) \end{aligned}
 Question 5
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
 A All the poles of the system must lie on the left side of the $j \omega$ axis B Zeros of the system can lie anywhere in the s-plane C All the poles must lie within |s| = 1 D All the roots of the characteristic equation must be located on the left side of the $j \omega$ axis.
Signals and Systems   Laplace Transform
Question 5 Explanation:
All poles must lie within |Z|=1

There are 5 questions to complete.