Questions by Arjun / GO Instrumentation

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81

GATE2019 IN: GA-6
Since the last one year after a $125$ basis point reduction in repo rate by the Reserve Bank Of India, banking institutions have been making a demand to reduce interest rates on small saving schemes. Finally, the government announced yesterday a reduction in interest rates on small saving schemes to bring them on par ... rates on small saving scheme A reduction in interest rates on small savings scheme follow only after a reduction in repo rate by the Reserve Bank Of India

Since the last one year after a $125$ basis point reduction in repo rate by the Reserve Bank Of India, banking institutions have been making a demand to reduce interest r...

asked Feb 10, 2019

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82

GATE2019 IN: GA-7
In a country of $1400$ million population, $70\%$ own mobile phones. Among the mobile phone owners, only $294$ million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country? $10.50$ $14.70$ $15.00$ $50.00$

In a country of $1400$ million population, $70\%$ own mobile phones. Among the mobile phone owners, only $294$ million access the Internet. Among these Internet users, on...

asked Feb 10, 2019

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83

GATE2019 IN: GA-8
The nomenclature of Hindustani music has changed over the countries. Since the medieval period, dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and instrumental styles, respectively. With the institutionalization of music education, the term gharana became acceptable. ... including disciples and grand disciples. Which one of the following pairings is NOT correct? dhrupad, baani gayaki, vocal baaj, institution gharana, lineage

The nomenclature of Hindustani music has changed over the countries. Since the medieval period, dhrupad styles were identified as baanis. Terms like gayaki and baaj were ...

asked Feb 10, 2019

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84

GATE2019 IN: GA-9
two trains started at $7$AM from the same point. The first train travelled north at a speed of $80$km/h and the second train travelled south at a speed of $100$km/h. The time at which they were $540$ km apart is ________ AM. $9$ $10$ $11$ $11.30$

two trains started at $7$AM from the same point. The first train travelled north at a speed of $80$km/h and the second train travelled south at a speed of $100$km/h. The ...

asked Feb 10, 2019

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85

GATE2019 IN: GA-10
“I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in his own community.” Based on the paragraph above, the prestige of a head-hunter depended upon ______________ the prestige of the kingdom the prestige of the heads the number of taxes he could levy the number of heads he could gather

“I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the pr...

asked Feb 10, 2019

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86

GATE2019 IN: 1
$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\widehat{k}}$ and $\overrightarrow{b}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ – ${\widehat{k}}$, the vector $\overrightarrow{c}$ is parallel to $\widehat{i}+2\widehat{j}+3\widehat{k}$ $2\widehat{i} + \widehat{j}$ $2\widehat{i} – \widehat{j}$ $4\widehat{k}$

$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\wi...

asked Feb 10, 2019

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87

GATE2019 IN: 2
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightarrow{\bigtriangledown}$ x $\overrightarrow{A}$| is -1 0 1 $\infty$

The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightar...

asked Feb 10, 2019

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88

GATE2019 IN: 3
A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is 4/15 7/16 ½ 8/15

A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and...

asked Feb 10, 2019

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89

GATE2019 IN: 4
In the Figures (a) and (b) shown below, the transformers are identical and ideal ,except that the transformer in Figure (b) is centre -tapped. Asssuming ideal diodes, the ratio of the root mean-square (RMS) voltage across the resistor R in Figure (a) to that in figure (b) is $\sqrt{2}$: 1 2: 1 2$\sqrt{2}$ : 1 4:1

In the Figures (a) and (b) shown below, the transformers are identical and ideal ,except that the transformer in Figure (b) is centre -tapped. Asssuming ideal diodes, the...

asked Feb 10, 2019

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90

GATE2019 IN: 5
The output y(t) of a system is related to its input x(t) as y(t) = ${\displaystyle \int^t_0}$x(t – 2)dt, where, x(t) =0 and y(t) = 0 for t $\le$ 0. The transfer function of the system is $\frac{1}{s}$ $\frac{(1-e^{-2s})}{s}$ $\frac {e^{-2s}}{s}$ $\frac{1}{s} – e^{-2s}$

The output y(t) of a system is related to its input x(t) asy(t) = ${\displaystyle \int^t_0}$x(t – 2)dt, where, x(t) =0 and y(t) = 0 for t $\le$ 0. The transfer function...

asked Feb 10, 2019

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91

GATE2019 IN: 6
The input x[n] and output y[n] of a discrete-time system are related as y[n] = $\alpha$y[n – 1] + x[n]. The condition of $\alpha$ for which the system is Bounded-Input Bounded-Output (BIBO) stable is |$\alpha$| < 1 |$\alpha$| = 1 |$\alpha$| > 1 |$\alpha$| < 3/2

The input x[n] and output y[n] of a discrete-time system are related as y[n] = $\alpha$y[n – 1] + x[n]. The condition of $\alpha$ for which the system is Bounded-Input...

asked Feb 10, 2019

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92

GATE2019 IN: 7
In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant $\tau${_1}$. Similarly, the closed loop transfer function of the outer loop may be assumed to have a single time constant $\tau${_2}$. The desired relationship between $\tau${_1}$ and $\tau${_2}$ in a well-designed control system is ... $\tau${_1}$ is equal to $\tau${_2}$ $\tau${_1}$ is much greater than $\tau${_2}$ $\tau${_1}$ is independent of $\tau${_2}$

In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant $\tau$${_1}$. Similarly, the closed loop tr...

asked Feb 10, 2019

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93

GATE2019 IN: 8
The loop-gain function L(s) of a control system with unity feedback is given to be L(s) = $\frac{k}{(s + 1)(s + 2)(s + 3)}$, where k >0. If the gain cross-over frequency of the loop-gain function is less than its phase cross-over frequency, the closed-loop system is unstable marginally stable conditionally stable stable

The loop-gain function L(s) of a control system with unity feedback is given to be L(s) = $\frac{k}{(s + 1)(s + 2)(s + 3)}$, where k >0. If the gain cross-over frequency...

asked Feb 10, 2019

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94

GATE2019 IN: 9
If each of the values of inductance, capacitance and resistance of a series LCR circuit are doubled, the Q-factor of the circuit would reduce by a factor $\sqrt{2}$ reduce by a factor 2 increase by a factor $\sqrt{2}$ increase by a factor 2

If each of the values of inductance, capacitance and resistance of a series LCR circuit are doubled, the Q-factor of the circuit wouldreduce by a factor $\sqrt{2}$reduce ...

asked Feb 10, 2019

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95

GATE2019 IN: 10
In the circuit shown below, the input voltage V${_i}{_n}$ is positive. The current (I) – voltage(V) characteristics of the diode can be assumed to be I = I${_0}$e$^{v/vr}$ under the forward bias condition, where V${_T}$ is the thermal voltage and I${_0}$ is the reverse saturation current. Assuming an ideal op-amp, the output voltage v${_o}{_u}{_t}$ of the circuit is proportional to log${_e}$(V${_i}{_n}/V{_T}$) 2V${_i}{_n}$ e$^{V}{_i}{_n}/^{V}{T}$ V$^{2}{_i}{_n}$

In the circuit shown below, the input voltage V${_i}{_n}$ is positive. The current (I) – voltage(V) characteristics of the diode can be assumed to be I = I${_0}$e$^{v/v...

asked Feb 10, 2019

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96

GATE2019 IN: 11
The correct biasing conditions for typical operation of light emitting diodes, photodiodes, Zener diodes are, respectively forward bias, reverse bias, reverse bias reverse bias, reverse bias, forward bias forward bias, forward bias, reverse bias reverse bias, forward bias, reverse bias

The correct biasing conditions for typical operation of light emitting diodes, photodiodes, Zener diodes are, respectivelyforward bias, reverse bias, reverse biasreverse ...

asked Feb 10, 2019

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97

GATE2019 IN: 12
The circuit shown in the figure below uses ideal positive edge-triggered synchronous J-K flip flops with outputs X and Y. If the initial state of the output is X =0 and Y =0 just before the arrival of the first clock pulse, the state of the output just before the arrival of the second clock pulse is X=0, Y=0 X=0, Y=1 X=1, Y=0 X=1, Y=1

The circuit shown in the figure below uses ideal positive edge-triggered synchronous J-K flip flops with outputs X and Y. If the initial state of the output is X =0 and Y...

asked Feb 10, 2019

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98

GATE2019 IN: 13
Thermocouples measure temperature based on Photoelectric effect Seebeck effect Hall effect Thermal expansion

Thermocouples measure temperature based on Photoelectric effectSeebeck effectHall effectThermal expansion

asked Feb 10, 2019

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99

GATE2019 IN: 14
Four strain gauges in a Wheatstone bridge configuration are connected to an instrumentation amplifier as shown in the figure. From the choices given below, the preferred value for the common mode rejection ratio(CMRR) of the amplifier, in dB, would be -20 0 3 100

Four strain gauges in a Wheatstone bridge configuration are connected to an instrumentation amplifier as shown in the figure. From the choices given below, the preferred ...

asked Feb 10, 2019

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100

GATE2019 IN: 15
In a single-mode optical fiber, the zero-dispersion wavelength refers to the wavelength at which the material dispersion is zero. waveguide dispersion is zero. sum of material dispersion and waveguide dispersion is zero. material dispersion and waveguide dispersion are simultaneously zero.

In a single-mode optical fiber, the zero-dispersion wavelength refers to the wavelength at which the material dispersion is zero.waveguide dispersion is zero.sum of mater...

asked Feb 10, 2019

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101

GATE2019 IN: 16
A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.

A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.

asked Feb 10, 2019

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102

GATE2019 IN: 17
In the circuit shown below, maximum power is transferred to the load resistance R${_L}$, when R${_L}$ = $\_\_\_\_$ $\Omega$.

In the circuit shown below, maximum power is transferred to the load resistance R${_L}$, when R${_L}$ = $\_\_\_\_$ $\Omega$.

asked Feb 10, 2019

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103

GATE2019 IN: 18
Consider a circuit comprising only resistors with constant resistance and ideal independent DC voltage sources. If all the resistances are scaled down by a factor 10, and all source voltages are scaled up by a factor 10, the power dissipated in the circuit scles up by a factor of $\_\_\_\_\_\_$.

Consider a circuit comprising only resistors with constant resistance and ideal independent DC voltage sources. If all the resistances are scaled down by a factor 10, an...

asked Feb 10, 2019

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104

GATE2019 IN: 19
In the circuit shown below, initially the switch S${_1}$ is open, then capacitor C1 has a charge of 6 coulomb, and the capacitor C2 has 0 coulomb. After s${_1}$ is closed, the charge on C2 in steady state is $\_\_\_\_\_$ coulomb.

In the circuit shown below, initially the switch S${_1}$ is open, then capacitor C1 has a charge of 6 coulomb, and the capacitor C2 has 0 coulomb. After s${_1}$ is closed...

asked Feb 10, 2019

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105

GATE2019 IN: 20
An 8-bit weighted resistor digital-to-analog converter(DAC) has the smallest resistance of 500 $\Omega$. The largest resistance has a value $\_\_\_\_$ k$\Omega$.

An 8-bit weighted resistor digital-to-analog converter(DAC) has the smallest resistance of 500 $\Omega$. The largest resistance has a value $\_\_\_\_$ k$\Omega$.

asked Feb 10, 2019

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106

GATE2019 IN: 21
The total number of Boolean functions with distinct truth-tables that can be defined over 3 Boolean variables is $\_\_\_\_$.

The total number of Boolean functions with distinct truth-tables that can be defined over 3 Boolean variables is $\_\_\_\_$.

asked Feb 10, 2019

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107

GATE2019 IN: 22
The figure below shows the i $^{th}$ full-adder block of a binary adder circuit. C${_i}$ is the input carry and C${_i}{_+}{_1}$ is the output carry of the circuit. Assume that each logic gate has a delay of 2 nanosecond, with no additional time delay due to the interconnecting wires. If the inputs A${_i}$,B${_i}$ are ... stable throughout the carry propogation, the maximum time taken for an input C${_i}$ to produce a steady-state output C${_i}{_+}{_1}$ is $\_\_\_\_$ nanosecond.

The figure below shows the i $^{th}$ full-adder block of a binary adder circuit. C${_i}$ is the input carry and C${_i}{_+}{_1}$ is the output carry of the circuit. Assume...

asked Feb 10, 2019

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108

GATE2019 IN: 23
The resistance of a resistor is measured using a voltmeter and an ammeter. The voltage measurements have a mean value of 1 V and standard deviation of 0.12 V while current measurements have a mean value of 1 mA with standard deviation of 0.05 mA. Assuming that the errors in voltage and current measurements are independent, the standard deviation of the calculated resistance value is $\_\_\_\_$ $\Omega$.

The resistance of a resistor is measured using a voltmeter and an ammeter. The voltage measurements have a mean value of 1 V and standard deviation of 0.12 V while curren...

asked Feb 10, 2019

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109

GATE2019 IN: 24
A pitot-static tube is used to estimate the velocity of an incompressible fluid of density 1 kg/m$^{3}$. If the pressure differences measured by the tube is 200 N/m$^{2}$, the velocity of the fluid, assuming the pitot-tube coefficient to be 1.0, is $\_\_\_\_$m/s.

A pitot-static tube is used to estimate the velocity of an incompressible fluid of density 1 kg/m$^{3}$. If the pressure differences measured by the tube is 200 N/m$^{2}$...

asked Feb 10, 2019

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110

GATE2019 IN: 25
A signal cos(2$\pi$f${_m}$t) modulates a carrier cos(2$\pi$f${_c}$t) using the double -sideband-with-carrier (DSDWC) scheme to yield a modulated signal cos(2$\pi$f${_c}$t) + 0.3 cos(2$\pi$f${_m}$t) cos2$\pi$f${_c}$t. The modulation index is $\_\_\_\_\_$ .(Answer should br rounded off to one decimal place)

A signal cos(2$\pi$f${_m}$t) modulates a carrier cos(2$\pi$f${_c}$t) using the double -sideband-with-carrier (DSDWC) scheme to yield a modulated signal cos(2$\pi$f${_c}$t...

asked Feb 10, 2019

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111

GATE2019 IN: 26
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional to x$^{-1}$ x$^{2}$ x$^{3}$ x$^{4}$

The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional tox$^{-1}$x$^{2}$x$^{3}...

asked Feb 10, 2019

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112

GATE2019 IN: 27
The function p(x) is given by p(x) = A/x$^\mu$ where A and $\mu$ are constants with $\mu$ > 1 and 1 $\le$ x <$\infty$ and p(x) = 0 for -$\infty$ < x <1. For p(x) to be a probability density function, the value of A should be equal to $\mu$ – 1 $\mu$ + 1 1/($\mu$ – 1) 1/($\mu$ +1)

The function p(x) is given by p(x) = A/x$^\mu$ where A and $\mu$ are constants with $\mu$ 1 and 1 $\le$ x <$\infty$ and p(x) = 0 for -$\infty$ < x <1. For p(x) to be a ...

asked Feb 10, 2019

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113

GATE2019 IN: 28
The dynamics of the state $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ of a sytem is governed by the differential equation $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ = $\begin{bmatrix}1 & 2 \\-3 & -4\end{bmatrix}$\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ + $ ... is $\begin{bmatrix}-30 \\-40\end{bmatrix}$ $\begin{bmatrix}-20 \\-10\end{bmatrix}$ $\begin{bmatrix}5\\-15\end{bmatrix}$ $\begin{bmatrix}50 \\-35\end{bmatrix}$

The dynamics of the state $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ of a sytem is governed by the differential equation $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ = ...

asked Feb 10, 2019

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114

GATE2019 IN: 29
A complex function f(z) = u(x,y) + i v(x,y) and its complex conjugate f*(z) = u(x,y) – i v(x,y) are both analytic in the entire complex plane, where z = x + i y and i = $\sqrt{-1}$. The function f is then given by f(z) = x + i y f(z) = x$^{2}$ – y$^{2}$ + i 2xy f(z) = constant f(z) = x$^{2}$ + y$^{2}$

A complex function f(z) = u(x,y) + i v(x,y) and its complex conjugate f*(z) = u(x,y) – i v(x,y) are both analytic in the entire complex plane, where z = x + i y and i =...

asked Feb 10, 2019

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115

GATE2019 IN: 30
In a control system with unity gain feedback, the plant has the transfer function P(s) = 3/s. Assuming that a controller of the form C(s) = K/(s + p) is used, where K is a positive constant, the value of p for which the root-locus of the closed-loop system passes through the points -3$\pm$j3$\sqrt{3}$ where j = $\sqrt{-1}$, is 3 3$\sqrt{3}$ 6 9

In a control system with unity gain feedback, the plant has the transfer function P(s) = 3/s. Assuming that a controller of the form C(s) = K/(s + p) is used, where K is ...

asked Feb 10, 2019

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116

GATE2019 IN: 31
The forward path transfer function L(s) of the control system shown in Figure(a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d(t) is given by d(t) = 0.1 sin($\omega$t) where $\omega$ = 5 rad/s, the steady-state amplitude of the output y(t) is 1.00x10$^{-3}$ 2.50x10$^{-3}$ 5.00x10$^{-3}$ 10.00x10$^{-3}$

The forward path transfer function L(s) of the control system shown in Figure(a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d(t) is given by d(t...

asked Feb 10, 2019

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117

GATE2019 IN: 32
In the control system shown in the figure below, a reference signal $r(t)=t^2$ is applied at time $t=0$. The control system employs a $PID$ controller $C(s)=K_p+K_1/s+K_Ds$ and the plant has a transfer function $P(s)=3/s.$ If $K_p=10,K_1=1 and K_D=2$, the steady state value of $e$ is $0$ $2/3$ $1$ $\infty$

In the control system shown in the figure below, a reference signal $r(t)=t^2$ is applied at time $t=0$. The control system employs a $PID$ controller $C(s)=K_p+K_1/s+K_D...

asked Feb 10, 2019

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118

GATE2019 IN: 33
A voltage amplifier is constructed using enhancement mode $MOSFETs$ labeled $M_1,M_2,M_3$ and $M_4$ in the figure below. $M_1,M_2$ and $M_4$ are n-channel MOSFETs and $M_3$ is a p-channel $MOSFET$. All $MOSFETs$ operate in saturation mode and channel length modulation can be ignored. The low frequency, small signal input and ooutput voltages are $v_{in}$ and $V_{out}$ respectively ... $-g_{mn}/g_{mp}$ $-g_{mn}(g_{mn}+g_{mp})^{-1}$ $+g_{mn}/g_{mp}$ $g_{mn}(g_{mn}+g_{mp})^{-1}$

A voltage amplifier is constructed using enhancement mode $MOSFETs$ labeled $M_1,M_2,M_3$ and $M_4$ in the figure below. $M_1,M_2$ and $M_4$ are n-channel MOSFETs and $M_...

asked Feb 10, 2019

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119

GATE2019 IN: 34
In the circuit shown below, assume that the comparators are ideal and all components have zero propagation delay. In one period of the input signal $V_{in}=6 \sin(\omega t)$, the fraction of the time for which the output $OUT$ is in logic state $HIGH$ is $1/12$ $1/2$ $2/3$ $5/6$

In the circuit shown below, assume that the comparators are ideal and all components have zero propagation delay. In one period of the input signal $V_{in}=6 \sin(\omega ...

asked Feb 10, 2019

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120

GATE2019 IN: 35
$X=X_1X_0 \;and\;Y=Y_1Y_0$ are 2-bit binary numbers. The Boolean function $S$ that satisfies the condition “If $X>Y$, then $S=1”$, in its minimized form, is $X_1Y_1+X_0Y_0$ $X_1\overline Y_1+X_0\overline Y_0\overline Y_1+X_0\overline Y_0 X_1$ $X_1\overline Y_1X_0Y_0$ $X_1Y_1+X_0\overline Y_0Y_1+X_0\overline Y_0\overline X_1$

$X=X_1X_0 \;and\;Y=Y_1Y_0$ are 2-bit binary numbers. The Boolean function $S$ that satisfies the condition “If $X>Y$, then $S=1”$, in its minimized form, is$X_1Y_1+X_...

asked Feb 10, 2019