# GATE EC 2017 SET-1

 Question 1
The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 $\mu s$, then the number of T-states needed for executing the instruction is
 A 1 B 6 C 7 D 8
Microprocessors   Instructions of 8085 Microprocessor
Question 1 Explanation:
Given than,
$f_{\mathrm{CLK}}=5 \mathrm{MHz}$
Execution time $=1.4 \mu \mathrm{s}$
Execution time $=n(T-\text { state })$
$n=$ number of T-states required to execute the instruction
T- state (or) $T_{\mathrm{CLK}}=\frac{1}{f_{\mathrm{CLK}}}=0.2 \mu \mathrm{s}$
So, $\quad n=\frac{1.4 \mu \mathrm{s}}{T_{\mathrm{CLK}}}=\frac{1.4}{0.2}=7$
 Question 2
Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
$y[n]=\left\{\begin{matrix} n|x[n]| & for 0\leq n\leq 10\\ x[n]-x[n-1] & othrwise \end{matrix}\right.$
Which one of the following statements is true about the system?
 A It is causal and stable B It is causal but not stable C It is not causal but stable D It is neither causal nor stable
Signals and Systems   Basics of Signals and Systems
Question 2 Explanation:
Since present output does not depend upon future values of input, the system is causal and also every bounded input produces bounded output, so it is stable.
 Question 3
Consider the following statement about the linear dependence of the real valued functions $y_{1}=1, \; y_{2}=x \; and \; y_{3}=x^{2}$ , over the field of real numbers.
I. $y_{1}, \; y_{2} \; and \; y_{3}$ are linearly independent on $-1 \leq x \leq 0$
II. $y_{1}, \; y_{2} \; and \; y_{3}$ are linearly dependent on $0 \leq x \leq 1$
III. $y_{1}, \; y_{2} \; and \; y_{3}$ are linearly independent on $0 \leq x \leq 1$
IV. $y_{1}, \; y_{2} \; and \; y_{3}$ are linearly dependent on $-1 \leq x \leq 0$
Which one among the following is correct ?
 A Both I and II are true B Both I and III are true C Both II and IV are true D Both III and IV are true
Engineering Mathematics   Calculus
Question 3 Explanation:
Any of the given three functions cannot be written as the linear combination of other two functions. Hence, the statements I and III are correct
 Question 4
Consider the 5 x 5 matrix
A=$\begin{bmatrix} 1 &2 &3 & 4 & 5\\ 5 & 1& 2& 3& 4\\ 4& 5&1 & 2&3 \\ 3 & 4 & 5 & 1 & 2\\ 2&3 & 4&5 & 1 \end{bmatrix}$
It is given that A has only one real eigen value. Then the real eigen value of A is
 A -2.5 B 0 C 15 D 25
Engineering Mathematics   Linear Algebra
Question 4 Explanation:
\begin{aligned} |A-\lambda I|&=0 \\ \begin{array}{|ccccc|} 1-\lambda & 2 & 3 & 4 & 5 \\ 5 & 1-\lambda & 2 & 3 & 4 \\ 4 & 5 & 1-\lambda & 2 & 3 \\ 3 & 4 & 5 & 1-\lambda & 2 \\ 2 & 3 & 4 & 5 & 1-\lambda \end{array}&=0\\ \end{aligned}
sum of all elements in every one row must be zero.
\begin{aligned} \text{i.e. }\quad 15-\lambda&=0\\ \lambda&=15 \end{aligned}
 Question 5
The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V(\iota )=e^{-y \iota +j\omega t}$ volts, Where $\iota$ is the distance along the length of the cable in meters. $\gamma =(0.1+j40)m^{-1}$ is the complex propagation constant, and $\omega = 2\pi \times 10^{9} rad/ s$ is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.
 A 0.5 B 0.86 C 0.34 D 0.94
Electromagnetics   Transmission Lines
Question 5 Explanation:
\begin{aligned} V(l) &=V_{O} e^{-\alpha l} e^{-j\beta l} e^{j\omega t} \\ \text { Attenuation } &=\frac{\mid \text { Input } \mid}{\mid \text { Output } \mid}=\frac{\left|V_{O}(0)\right|}{\left|V_{o}(l)\right|} \end{aligned}
Attenuation per meter $=\frac{\left|V_{0}\right|}{\left|V_{0}(1 \mathrm{m})\right|}=e^{\alpha}$
Attenuation in $\mathrm{dB} / \mathrm{m}=\left(20 \log e^{\alpha}\right) \mathrm{dB} / \mathrm{m}$
$=20(0.1) \log e=0.868 \mathrm{dB} / \mathrm{m}$
 Question 6
A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statement is true?
 A Silicon atoms act as p-type dopants in Arsenic sites and n-type dopants in Gallium sites B Silicon atoms act as n-type dopants in Arsenic sites and p-type dopants in Gallium sites C Silicon atoms act as p-type dopants in Arsenic as well as Gallium sites D Silicon atoms act as n-type dopants in Arsenic as well as Gallium sites
Electronic Devices   Basic Semiconductor Physics
Question 6 Explanation:
Si acts as p-type dopant GA sites.
Si acts as n-type dopant GA sites.
 Question 7
The rank of the matrix M=$\begin{bmatrix} 5 & 10 &10 \\ 1& 0 &2 \\ 3 & 6&6 \end{bmatrix}$ is
 A 0 B 1 C 2 D 3
Engineering Mathematics   Linear Algebra
Question 7 Explanation:
\begin{aligned} &M=\left[\begin{array}{lll} 5 & 10 & 10 \\ 1 & 0 & 2 \\ 3 & 6 & 6 \end{array}\right]\\ &R_{1} \leftrightarrow R_{2}:\\ &\left[\begin{array}{lll} 1 & 0 & 2 \\ 5 & 10 & 10 \\ 3 & 6 & 6 \end{array}\right]\\ &R_{2} \leftarrow R_{2}-5 R_{1} \text { and } R_{3} \leftarrow R_{3}-3 R_{1}\\ &\left[\begin{array}{lll} 1 & 0 & 2 \\ 0 & 10 & 0 \\ 0 & 6 & 0 \end{array}\right]\\ &R_{3} \leftarrow R_{3}-\frac{6}{10} R_{2}\\ &\left[\begin{array}{lll} 1 & 0 & 2 \\ 0 & 10 & 0 \\ 0 & 0 & 0 \end{array}\right] \end{aligned}
Which is in Echelon form
Rank of matrix M is,
$\rho (M) = 2$
 Question 8
For a narrow base PNP BJT, the excess minority carrier concentration ($\Delta n_{E}$ for emitter, $\Delta p_{E0}$ for base. $\Delta n_{c}$ for collector) normalized to equilibrium minority carrier concentration ($n_{E0}$ for emmiter, $p_{B0}$ for base, $n_{C0}$ for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in ? A Forward active B Saturation C Inverse active D Cutoff
Electronic Devices   BJT and FET Basics
Question 8 Explanation:
Emitter-base junction $(J_{E})$ is in RB
Collector-base junction $(J_{C})$ is in FB
Hence, inverse active mode.
 Question 9
The Miller effect in the context of a Common Emitter amplifier explains
 A an increase in the low-frequency cutoff frequency B an increase in the high-frequency cutoff frequency C a decrease in the low-frequency cutoff frequency D a decrease in the high-frequency cutoff frequency
Analog Circuits   Frequency Response of Amplifier
Question 9 Explanation:
Miller effect increases input capacitance and thereby decreases the higher cut-off frequent
 Question 10
Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1. The duty cycle at the output latch in percentage is___________. A 20 B 25 C 30 D 35
Digital Circuits   Sequential Circuits
Question 10 Explanation: Duty cycle of output
$=\frac{\frac{T_{\mathrm{CLK}}}{2}-\frac{T_{\mathrm{CLK}}}{5}}{T_{\mathrm{CK}}} \times 100=\frac{3}{10} \times 100=30 \%$
There are 10 questions to complete.