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41
GATE2020: 6
A phase lead network has the transfer function $G(S)=\frac{1+0.2s}{1+0.05s}$. The angular frequency at which the maximum phase shift for the network occurs is _____________ $10\;rad/s$ $20\;rad/s$ $100\;rad/s$ $200\;rad/s$
A phase lead network has the transfer function $G(S)=\frac{1+0.2s}{1+0.05s}$. The angular frequency at which the maximum phase shift for the network occurs is ___________...
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42
GATE2020: 7
If the diodes in the circuit shown are ideal and the breakdown voltage $V_z$ of the Zener diode is $5\;V$ the power dissipated in the $100\;\Omega$ resistor (in watts) is __________. $0$ $1$ $25/100$ $225/100$
If the diodes in the circuit shown are ideal and the breakdown voltage $V_z$ of the Zener diode is $5\;V$ the power dissipated in the $100\;\Omega$ resistor (in watts) is...
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44
GATE2020: 9
A $Q$ meter is best suited for the measurement of the ___________ Quality factor of a capacitance Distributed capacitance of a coil quality factor of piezoelectric sensor Turns-ratio of a transformer
A $Q$ meter is best suited for the measurement of the ___________Quality factor of a capacitanceDistributed capacitance of a coilquality factor of piezoelectric sensorTur...
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47
GATE2020: 12
The boolean operation performed by the following circuit at the output O is _______ $O=S_1\oplus S_0$ $O=S_1\bullet \overline{S_0}$ $O=S_1+S_0$ $O=S_0\bullet \overline{S_1}$
The boolean operation performed by the following circuit at the output O is _______$O=S_1\oplus S_0$$O=S_1\bullet \overline{S_0}$$O=S_1+S_0$$O=S_0\bullet \overline{S_1}$
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48
GATE2020: 13
Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $ The period of this signal $x[n]$ is ___________. $4$ $3$ $2$ $1$
Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $The period of this signal $x[n...
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49
GATE2020: 14
The closed loop transfer function of a control system is given by $\frac{C(s)}{R(s)}=\frac{1}{s+1}$. for the input $r(t)=\sin\;t$ the steady state response $c(t)$ is ___________ $1$ $\frac{1}{\sqrt{2}} \cos t$ $\frac{1}{\sqrt{2}} \sin (t+\frac{\pi}{4})$ $\frac{1}{\sqrt{2}} \sin (t-\frac{\pi}{4})$
The closed loop transfer function of a control system is given by $\frac{C(s)}{R(s)}=\frac{1}{s+1}$. for the input $r(t)=\sin\;t$ the steady state response $c(t)$ is ____...
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50
GATE2020: 15
Let $f(z)=\frac{1}{z+a},a>0.$ the value of the integral $\oint f(z)dz$ over a circle $C$ with center $(-a,0)$ and radius $R>0$ evaluated in the anti-clockwise direction is ____________ $0$ $2\pi i$ $-2\pi i$ $4\pi i$
Let $f(z)=\frac{1}{z+a},a>0.$ the value of the integral $\oint f(z)dz$ over a circle $C$ with center $(-a,0)$ and radius $R>0$ evaluated in the anti-clockwise direction i...
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52
GATE2020: 17
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
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53
GATE2020: 18
Three $400\;\Omega$ resistors are connected in delta and powered by a $400\;V\;(rms), \;50\;Hz,$ balanced symmetrical $R-Y-B$ sequence, three-phase three-wire mains. The rms value of the line current $\text{(in amperes, rounded off to one decimal place)}$ is __________.
Three $400\;\Omega$ resistors are connected in delta and powered by a $400\;V\;(rms), \;50\;Hz,$ balanced symmetrical $R-Y-B$ sequence, three-phase three-wire mains. The ...
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54
GATE2020: 19
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
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55
GATE2020: 20
A second order system has closed loop poles located at $s=-3\pm j4$. The time t at which the maximum value of the step response occurs (in seconds, rounded off to two decimal places) is ________
A second order system has closed loop poles located at $s=-3\pm j4$. The time t at which the maximum value of the step response occurs (in seconds, rounded off to two dec...
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56
GATE2020: GA: 1
He is known for his unscrupulous ways. He always sheds ___________ tears to deceive people. fox’s crocodile’s crocodile fox
He is known for his unscrupulous ways. He always sheds ___________ tears to deceive people.fox’scrocodile’scrocodilefox
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57
GATE2020: GA: 2
Jofra Archer, the England fast bowler, is _____________ than accurate. more fast faster less faster more faster
Jofra Archer, the England fast bowler, is _____________ than accurate.more fastfasterless fastermore faster
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58
GATE2020: GA: 3
Select the word that fits the analogy: $\text{Build : Building :: Grow :}$ _______________ Grown Grew Growth Growed
Select the word that fits the analogy:$\text{Build : Building :: Grow :}$ _______________GrownGrewGrowthGrowed
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60
GATE2020: GA: 5
Define $[x]$ as the greatest integer less than or equal to $x$, for each $x \; \in \; [-\infty,\infty]$. If $y=[x],$ then area under $y$ for $x \; \in \; [1,4]$ is ____________. $1$ $3$ $4$ $6$
Define $[x]$ as the greatest integer less than or equal to $x$, for each $x \; \in \; [-\infty,\infty]$. If $y=[x],$ then area under $y$ for $x \; \in \; [1,4]$ is _____...
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63
GATE2020: GA: 8
The sum of the first $n$ terms in the sequence $\text{8, 88, 888, 8888,$\dots$}$ is __________. $\frac{81}{80}(10^n-1)+\frac{9}{8}n$ $\frac{81}{80}(10^n-1)-\frac{9}{8}n$ $\frac{80}{81}(10^n-1)+\frac{8}{9}n$ $\frac{80}{81}(10^n-1)-\frac{8}{9}n$
The sum of the first $n$ terms in the sequence $\text{8, 88, 888, 8888,$\dots$}$ is __________.$\frac{81}{80}(10^n-1)+\frac{9}{8}n$$\frac{81}{80}(10^n-1)-\frac{9}{8}n$$\f...
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64
GATE2020: GA: 9
Select the graph that schematically represents $\text{BOTH} \;y=x^m$ and $y=x^{1/m}$ properly in the interval $0\leq x\leq 1$, for integer values of $m$, where $m>1$.
Select the graph that schematically represents $\text{BOTH} \;y=x^m$ and $y=x^{1/m}$ properly in the interval $0\leq x\leq 1$, for integer values of $m$, where $m>1$.
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65
GATE2020: GA: 10
The bar graph shows the data of the students who appeared and passes in an examination for four schools $\text{P, Q, R and S.}$ The average of success rates (in percentage) of these four schools is _________. $58.5\%$ $58.8\%$ $59.0\%$ $59.3\%$
The bar graph shows the data of the students who appeared and passes in an examination for four schools $\text{P, Q, R and S.}$ The average of success rates (in percentag...
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66
GATE2017: 31
A series $R-L-C$ circuit is excited with an a.c. voltage source. The quality factor $(Q)$ of the circuit is given as $Q=30$. The amplitude of current in $\text{ampere}$ at upper half-power frequency will be _________.
A series $R-L-C$ circuit is excited with an a.c. voltage source. The quality factor $(Q)$ of the circuit is given as $Q=30$. The amplitude of current in $\text{ampere}$ a...
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67
GATE2017: 32
In the circuit diagram, shown in the figure, $S_1$ was closed and $S_2$ was open for a very long time. At $t=0,\;S_1$ is opened and $S_2$ is closed. The voltage across the capacitor, in volt, at $t=5\mu s$ is _________.
In the circuit diagram, shown in the figure, $S_1$ was closed and $S_2$ was open for a very long time. At $t=0,\;S_1$ is opened and $S_2$ is closed. The voltage across th...
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68
GATE2017: 33
Consider two discrete-time signals: $x_1(n)$={1,1} and $x_2(n)$={1,2} , for $n=0,1$. The Z-transform of the convoluted sequence $x(n)=x_1(n)^*x_2(n)$ is $1+2z^{-1}+3z^{-2}$ $z^2+3z+2$ $1+3z^{-1}+2z^{-2}$ $z^{-2}+3z^{-3}+2z^{-4}$
Consider two discrete-time signals:$x_1(n)$={1,1} and $x_2(n)$={1,2} , for $n=0,1$.The Z-transform of the convoluted sequence $x(n)=x_1(n)^*x_2(n)$ is$1+2z^{-1}+3z^{-2}$$...
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69
GATE2017: 34
Three $DFT$ coefficients, out of five $DFT$ coefficients of a five-point reall sequence are given as: $X(0)=4$, $X(1)=1-j1$ and $X(3)=2+j2$. The zeroth value of the sequence $x(n), \;x(0)$,is $1$ $2$ $3$ $4$
Three $DFT$ coefficients, out of five $DFT$ coefficients of a five-point reall sequence are given as: $X(0)=4$, $X(1)=1-j1$ and $X(3)=2+j2$. The zeroth value of the seque...
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70
GATE2017: 35
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
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71
GATE2017: 36
The block diagram of a closed-loop control system is shown in the figure. The values of $K$ and $K_p$ are such that the system has a damping ratio of $0.8$ and an undamped natural frequency $\omega_n$ of $\text{4 rad/s}$ respectively. The value of $K_p$ will be__________________.
The block diagram of a closed-loop control system is shown in the figure. The values of $K$ and $K_p$ are such that the system has a damping ratio of $0.8$ and an undampe...
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72
GATE2017: 37
The loop transfer function of a closed-loop system is given by $G(s)H(s)=\frac{K(s+6)}{s(s+2)}$. The breakaway point of the root-loci will be ___________.
The loop transfer function of a closed-loop system is given by $G(s)H(s)=\frac{K(s+6)}{s(s+2)}$. The breakaway point of the root-loci will be ___________.
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73
GATE2017: 38
A closed-loop system is shown in the figure. The system parameter $\alpha$ is not known. The condition for asymptotic stability of the closed loop system is $\alpha<-0.5$ $-0.5<\alpha<0.5$ $0<\alpha<0.5$ $\alpha>0.5$
A closed-loop system is shown in the figure. The system parameter $\alpha$ is not known. The condition for asymptotic stability of the closed loop system is $\alpha<-0.5$...
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75
GATE2017: 40
Assuming the opamp shown in the figure to be ideal, the frequency at which the magnitude of $V_\circ$ will be $95\%$ of the magnitude of $V_{in}$ is ______________$kHz$.
Assuming the opamp shown in the figure to be ideal, the frequency at which the magnitude of $V_\circ$ will be $95\%$ of the magnitude of $V_{in}$ is ______________$kHz$.
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76
GATE2017: 41
In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by $I_D=\frac{1}{2}(V_{GS}-1)^2$ $mA$, where $V_{GS}$ is in $V$. If $V_s=+5V$, then the value of $R_s$ in $K\Omega$ is _______________.
In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by $I_D=\frac{1}{2}(V_{GS}-1)^2$ $mA$, whe...
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77
GATE2017: 42
The two-input voltage multiplier, shown in the figure, has a scaling factor of $1$ and produces voltage output. If $V_1=+15\;V$ and $V_2=+3\;V$, the value of $V_\circ$ in $\text{volt}$ is _______________.
The two-input voltage multiplier, shown in the figure, has a scaling factor of $1$ and produces voltage output. If $V_1=+15\;V$ and $V_2=+3\;V$, the value of $V_\circ$ in...
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78
GATE2017: 43
The two inputs $A$ and $B$ are connected to an $R-S$ latch via two $AND$ gates as shown in the figure. If $A=1$ and $B=0$, the output $Q\overline{Q}$ is $00$ $10$ $01$ $11$
The two inputs $A$ and $B$ are connected to an $R-S$ latch via two $AND$ gates as shown in the figure. If $A=1$ and $B=0$, the output $Q\overline{Q}$ is$00$$10$$01$$11$
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79
GATE2017: 44
The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between $\pm7\;V$. The width of the hysteresis band is ______________$V$.
The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between $\pm7\;V$. The width of the hysteresis band is _________...
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