Recent questions without answers / GO Instrumentation

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481

GATE2016-25
Let $s(t)=rect\left(\frac{t-3}{3}\right)$ be a signal passed through an $AWGN$ (additive white Gaussian noise) channel with noise power spectral density $(PSD)$ $\frac{N_0}{2}$ to get $v(t)$. If $v(t)$ is passed through a matched-filter that is matched to s(t), then output signal-to-noise ratio $(SNR)$ of the matched-filter is $\frac{1}{N_0}$ $\frac{2}{N_0}$ $\frac{3}{N_0}$ $\frac{4}{N_0}$

Let $s(t)=rect\left(\frac{t-3}{3}\right)$ be a signal passed through an $AWGN$ (additive white Gaussian noise) channel with noise power spectral density $(PSD)$ $\frac{N_...

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482

GATE2016-26
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$

Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$

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483

GATE2016-27
An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same color. The probability of getting a red ball in the next draw is $\frac{65}{156}$ $\frac{67}{156}$ $\frac{79}{156}$ $\frac{89}{156}$

An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same co...

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484

GATE2016-28
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_\_.$

Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_...

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485

GATE2016-29
The relationship between the force $f(t)$ and the displacement $x(t)$ of a spring-mass system (with a mass $M$, viscous damping $D$ and spring constant $K$) is $M\frac{d^2x(t)}{dt^2}+D\frac{dx(t)}{dt}+Kx(t)=f(t).$ $X(s)$ and $F(s)$ are the Laplace transforms of $x(t)$ and $f(t)$ respectively. With $\text{M=0.1, D=2, K=10}$ in appropriate units, the transfer function $G(s)=\frac{X(s)}{F(s)}$ is $\frac{10}{s^2+20s+100}$ $s^2+20s+100$ $\frac{10s^2}{s^2+20s+100}$ $\frac{s}{s^2+20s+100}$

The relationship between the force $f(t)$ and the displacement $x(t)$ of a spring-mass system (with a mass $M$, viscous damping $D$ and spring constant $K$) is$$M\frac{d^...

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486

GATE2016-30
The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in the complex plane is $\_\_\_\_\_\_\_\_.$

The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in th...

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487

GATE2016-31
The current $I_X$ in the circuit given below in $\text{milliampere}$ is $\_\_\_\_\_\_\_.$

The current $I_X$ in the circuit given below in $\text{milliampere}$ is $\_\_\_\_\_\_\_.$

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488

GATE2016-32
In the circuit shown below, $V_s=101\angle 0V, R=10\Omega$ and $\omega L=100\Omega$. The current $I_s$ is in phase with $V_s$. The magnitude of $I_s$ in $\text{milliampere}$ is $\_\_\_\_\_\_\_\_.$

In the circuit shown below, $V_s=101\angle 0V, R=10\Omega$ and $\omega L=100\Omega$. The current $I_s$ is in phase with $V_s$. The magnitude of $I_s$ in $\text{milliamper...

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489

GATE2016-33
A symmetrical three-phase three-wire $RYB$ system is connected to a balanced delta-connected load. The $RMS$ values of the line current and line-to-line voltage are $\text{10 A}$ and $\text{400 V}$ respectively. The power in the system is measured using the two wattmeter method. The first wattmeter connected between $R$-line and $Y$-line reads zero. The reading of the second wattmeter (connected between $B$-line and $Y$-line) in $\text{watt}$ is ___________.

A symmetrical three-phase three-wire $RYB$ system is connected to a balanced delta-connected load. The $RMS$ values of the line current and line-to-line voltage are $\tex...

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490

GATE2016-34
In the strain gauge bridge circuit given below, $R_1=R_3=\text{R(1-x)}$ and $R_2=R_4=\text{R(1+x)}$, where $R$ is $350\Omega$. The voltage sources $v_s$ and $v_n$ represent the dc excitation and the undesired noise/interference, respectively. The value of capacitor $C$ in $\text{microfarad}$ that is required to ensure that the output across $a$ and $b$ is low-pass filtered with a cutoff frequency of $\text{150 Hz}$ is $\_\_\_\_\_\_\_$.

In the strain gauge bridge circuit given below, $R_1=R_3=\text{R(1-x)}$ and $R_2=R_4=\text{R(1+x)}$, where $R$ is $350\Omega$. The voltage sources $v_s$ and $v_n$ represe...

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491

GATE2016-35
The voltage $v(t)$ shown below is applied to the given circuit. $v(t)=3V$ for $t<0$ and $v(t)=6V$ for $t>0$. The value of current $i(t)$ at $t=1s$, in ampere is ____________.

The voltage $v(t)$ shown below is applied to the given circuit. $v(t)=3V$ for $t<0$ and $v(t)=6V$ for $t>0$. The value of current $i(t)$ at $t=1s$, in ampere is _________...

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492

GATE2016-36
For the periodic signal $x(t)$ shown below with period $T=8s$, the power in the 10th harmonic is __________. $0$ $\frac{1}{2} \left (\frac{2}{10\pi} \right)^2$ $\frac{1}{2} \left (\frac{4}{10\pi} \right)^2$ $\frac{1}{2} \left (\frac{4}{5\pi} \right)^2$

For the periodic signal $x(t)$ shown below with period $T=8s$, the power in the 10th harmonic is __________.$0$$\frac{1}{2} \left (\frac{2}{10\pi} \right)^2$$\frac{1}{2} ...

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493

GATE2016-37
The fundamental period $N_0$ of the discrete-time sinusoid $x[n]=\sin \left (\frac {301}{4}\pi n \right)$ is ____________.

The fundamental period $N_0$ of the discrete-time sinusoid $x[n]=\sin \left (\frac {301}{4}\pi n \right)$ is ____________.

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494

GATE2016-38
The transfer function $G(s)$ of a system which has the asymptotic Bode plot shown below is $10^4 \frac {(s-1)^2}{(s+100)^2}$ $10^4 \frac {(s+1)^2}{(s+100)^2}$ $10^4 \frac {(s+1)}{(s+100)^2}$ $10^4 \frac {(s-1)^2}{(s-100)^2}$

The transfer function $G(s)$ of a system which has the asymptotic Bode plot shown below is $10^4 \frac {(s-1)^2}{(s+100)^2}$$10^4 \frac {(s+1)^2}{(s+100)^2}$$10^4 \frac {...

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495

GATE2016-39
For the feedback system given below, the transfer function $G(s)=\frac{1}{(s+1)^2}$. The system $\text{CANNOT}$ be stabilized with $C(s)=1+\frac{3}{s}$ $C(s)=3+\frac{7}{s}$ $C(s)=3+\frac{9}{s}$ $C(s)=\frac{1}{s}$

For the feedback system given below, the transfer function $G(s)=\frac{1}{(s+1)^2}$. The system $\text{CANNOT}$ be stabilized with$C(s)=1+\frac{3}{s}$$C(s)=3+\frac{7}{s}$...

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496

GATE2016-40
Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below. $P(s)-(3), Q(s)-(2), R(s)-(1)$ $P(s)-(1), Q(s)-(2), R(s)-(3)$ $P(s)-(2), Q(s)-(1), R(s)-(3)$ $P(s)-(1), Q(s)-(3), R(s)-(2)$

Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below.$P(s)-(3), Q(s)-(2), R(s)-(1)$$P(s)-(1), Q(s)-(2), R(s)-(3)$$...

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497

GATE2016-41
An ideal opamp is used to realize a difference amplifier circuit given below having a gain of $10$. If $x=0.025$, the $CMRR$ of the circuit in $dB$ is $\_\_\_\_\_\_\_\_$.

An ideal opamp is used to realize a difference amplifier circuit given below having a gain of $10$. If $x=0.025$, the $CMRR$ of the circuit in $dB$ is $\_\_\_\_\_\_\_\_$....

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498

GATE2016-42
In the circuit given below, the opamp is ideal. The input $v_x$ is a sinusoid. To ensure $v_y=v_x$, the value of $C_N$ in $\text{picofarad}$ is $\_\_\_\_\_\_\_$.

In the circuit given below, the opamp is ideal. The input $v_x$ is a sinusoid. To ensure $v_y=v_x$, the value of $C_N$ in $\text{picofarad}$ is $\_\_\_\_\_\_\_$.

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499

GATE2016-43
In the circuit given below, the opamp is ideal. The value of current $I_L$ in $\text{microampere}$ is $\_\_\_\_\_\_\_\_.$

In the circuit given below, the opamp is ideal. The value of current $I_L$ in $\text{microampere}$ is $\_\_\_\_\_\_\_\_.$

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500

GATE2016-44
A $4$ to $1$ multiplexer to realize a Boolean function $F(X, Y, Z)$ is shown in the figure below. The inputs $Y$ and $Z$ are connected to the selectors of the $MUX$ ($Y$ is more significant). The canonical sum-of-product expression for $F(X, Y, Z)$ is $\Sigma m (2, 3, 4, 7)$ $\Sigma m (1, 3, 5, 7)$ $\Sigma m (0, 2, 4, 6)$ $\Sigma m (2, 3, 5, 6)$

A $4$ to $1$ multiplexer to realize a Boolean function $F(X, Y, Z)$ is shown in the figure below. The inputs $Y$ and $Z$ are connected to the selectors of the $MUX$ ($Y$ ...

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501

GATE2016-45
A synchronous counter using two J-K flip flops that goes through the sequence of states: $Q_1Q_2=00\rightarrow10\rightarrow01\rightarrow11\rightarrow00 \dots$ is required. To achive this, the inputs to the flip flops are $J_1=Q_2,\;\;\;K_1=0\;\;\;\;;\;J_2={Q_1}’, \;\;K_2=Q_1$ $J_1=1,\;\;\;\;\;K_1=1\;\;\;\;\;;\;J_2={Q_1}, \;K_2=Q_1$ $J_1=Q_2,\;\;K_1={Q_2}’\;;\;J_2=1, \;\;\;\;K_2=1$ $J_1={Q_2}’,\;K_1=Q_2\;\;;\;J_2={Q_1}, \;K_2={Q_1}’$

A synchronous counter using two J-K flip flops that goes through the sequence of states: $Q_1Q_2=00\rightarrow10\rightarrow01\rightarrow11\rightarrow00 \dots$ is required...

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502

GATE2016-46
A $1$ Kbyte memory module has to be interfaced with an $8$-bit microprocessor that has $16$ address lines.The address lines $A_0$ to $A_9$ of the processor are connected to the corresponding address lines of the memory module. The active low chip select $\overline{CS}$ of the memory module is connected to the $y_5$ output of a $3$ ... $33FF_H$ and $E000_H$ to $E3FF_H$ $1400_H$ to $17FF_H $ $5300_H$ to $53FF_H$ and $A300_H$ to $A3FF_H$ $5800_H$ to $5BFF_H$ and $D800_H$ to $D8FF_H$

A $1$ Kbyte memory module has to be interfaced with an $8$-bit microprocessor that has $16$ address lines.The address lines $A_0$ to $A_9$ of the processor are connected ...

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503

GATE2016-47
A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a capacitance of $\text{110 pF}$. When the frequency is doubled, the capacitance required for resonance is $\text{20 pF}$. The distributed capacitance of the coil in $\text{pico farad}$ is $\_\_\_\_\_\_\_\_$.

A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a capacitance of $\text{110 pF}$. When the frequency is doubled, the cap...

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504

GATE2016-48
The comparators (output=$’1’$, when input $\underline{>}$ and output=$’0’$, when input$<0$), exclusive-OR gate and the unity gain low-pass filter given in the circuit are ideal. The logic output voltages of the exclusive-OR gate are $\text{0 V}$ and $\text{5 V}$. The cutoff frequency of the low-pass filter is $\text{0.1 Hz}$. For $V_1=1 \sin (3000t+36^0)V$ and $V_2=1 \sin (3000t)V$, the value of $V_0$ in $volt$ is $\_\_\_\_\_\_\_\_.$

The comparators (output=$’1’$, when input $\underline{>}$ and output=$’0’$, when input$<0$), exclusive-OR gate and the unity gain low-pass filter given in the cir...

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505

GATE2016-49
A $\text{200 mV}$ full scale dual-slope $3\frac{1}{2}$ digit $DMM$ has a reference voltage of $\text{100 mV}$ and a first integration time of $\text{100 ms}$. For an input of $[100+10 \cos (100\pi t)]mV$, the conversion time (without taking the auto-zero phase time into consideration) in $\text{millisecond}$ is $\_\_\_\_\_\_\_$.

A $\text{200 mV}$ full scale dual-slope $3\frac{1}{2}$ digit $DMM$ has a reference voltage of $\text{100 mV}$ and a first integration time of $\text{100 ms}$. For an inpu...

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506

GATE2016-50
In the circuit below, the opamp is ideal and the sensor is an $RTD$ whose resistance $R_\theta=1000(1+0.004\;\theta)\Omega$, where $\theta$ is temperature in $^0C$. The output sensitivity in $mV/^0C$ is $\_\_\_\_\_\_\_\_$.

In the circuit below, the opamp is ideal and the sensor is an $RTD$ whose resistance $R_\theta=1000(1+0.004\;\theta)\Omega$, where $\theta$ is temperature in $^0C$. The o...

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507

GATE2016-51
The photo diode in the figure below has an active sensing area of $10 \;mm^2,$ a sensitivity of $0.5\;A/W$ and a dark current of $1\; \mu A$. The $i-to-v$ converter has a sensitivity of $100\;mV/\mu A$. For an input light intensity of $4\;W/m^2,$ the output $V_0$ in $volt$ is $\_\_\_\_\_\_\_\_\_.$

The photo diode in the figure below has an active sensing area of $10 \;mm^2,$ a sensitivity of $0.5\;A/W$ and a dark current of $1\; \mu A$. The $i-to-v$ converter has a...

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508

GATE2016-52
The velocity of flow of water (density $1000\;kg/m^3$) in a horizontal pipe is measured using the $PITOT$ tube shown below. The fluid in the U-tube manometer is mercury with a density of $13534\;kg/m^3$. Assume $g=9.81\;m/s^2$. If the height difference $(h)$ is measured as $94.1\;mm$, the velocity of flow of water in $m/s$ is $\_\_\_\_\_\_\_\_$.

The velocity of flow of water (density $1000\;kg/m^3$) in a horizontal pipe is measured using the $PITOT$ tube shown below. The fluid in the U-tube manometer is mercury w...

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509

GATE2016-53
The bandgap in $eV$ of a semiconductor material required to construct an $LED$ that emits peak power at the wavelength of $620\;nm$ is $\_\_\_\_\_\_\_.$ (Plank constant $h=4.13567\times10^{-15}\;eV\;s$ and speed of light $c=2.998\times10^8\;m/s$).

The bandgap in $eV$ of a semiconductor material required to construct an $LED$ that emits peak power at the wavelength of $620\;nm$ is $\_\_\_\_\_\_\_.$(Plank constant $h...

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510

GATE2016-54
The signal $m(t)=\frac{\sin(100\;\pi t)}{100\; \pi t}$ is frequency modulated $(FM)$ with an $FM$ Modulator of frequency deviation constant of $30\;kHz/V$. Using Carson’s rule, the approximate bandwidth of the modulated wave in $\text{kilohertz}$ is $\_\_\_\_\_\_\_\_$.

The signal $m(t)=\frac{\sin(100\;\pi t)}{100\; \pi t}$ is frequency modulated $(FM)$ with an $FM$ Modulator of frequency deviation constant of $30\;kHz/V$. Using Carson�...

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511

GATE2016-55
A signal $m(t)$ varies from $-3.5\;V$ to $+3.5\;V$ with an average power of $3\;W$. The signal is quantized using a midtread type quantizer and subsequently binary encoded. With the codeword of length $3$, the signal to quantization noise ratio in $dB$ is $\_\_\_\_\_\_\_\_.$

A signal $m(t)$ varies from $-3.5\;V$ to $+3.5\;V$ with an average power of $3\;W$. The signal is quantized using a midtread type quantizer and subsequently binary encode...

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512

GATE2015-1
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Apparent lifelessness $\_\_\_\_\_\_\_\_\_\_\_\_$ dormant life. harbours leads to supports affects

Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:Apparent lifelessness $\_\_\_\_\_\_\_\_\_\_\_\_$ dormant life....

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513

GATE2015-2
$\text{Fill in the blank with the correct idiom/phase}$. That boy from the town was a $\_\_\_\_\_\_\_\_\_\_\_\_$ in the sleepy village. dog out of herd sheep from the heap fish out of water bird from the flock

$\text{Fill in the blank with the correct idiom/phase}$.That boy from the town was a $\_\_\_\_\_\_\_\_\_\_\_\_$ in the sleepy village.dog out of herdsheep from the heapfi...

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514

GATE2015-3
Choose the statement where underlined word is used correctly. When the teacher eludes to different authors, he is being $\underline{elusive.}$ When the thief keeps eluding the police, he is being $\underline{elusive}.$ Matters that are difficult to understand, identify or remember are $\underline{allusive.}$ Mirages can be $\underline{allusive,}$ but a better way to express them is illusory.

Choose the statement where underlined word is used correctly.When the teacher eludes to different authors, he is being $\underline{elusive.}$When the thief keeps eluding ...

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515

GATE2015-4
Tanya is older than Eric. Cliff is older than Tanya Eric is older than cliff. If the first two statements are true, then the third statement is: True False Uncertain Data insufficient

Tanya is older than Eric.Cliff is older than TanyaEric is older than cliff.If the first two statements are true, then the third statement is:TrueFalseUncertainData insuff...

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516

GATE2015-5
Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete the league round of matches? $20$ $10$ $8$ $5$

Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to c...

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517

GATE2015-6
Select the appropriate option in place of underlined part of the sentence. $\underline{\text{Increased productivity necessary}}$ reflects greater efforts made by the employees. Increase in productivity necessary Increase productivity is necessary Increase in productivity necessarily No improvement required

Select the appropriate option in place of underlined part of the sentence.$\underline{\text{Increased productivity necessary}}$ reflects greater efforts made by the emplo...

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518

GATE2015-7
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. $\text{Statements:}$ No manager is a leader. All leaders are executives. $\text{Conclusions:}$ No manager is an executive. No executive is a manager. Only conclusion I follows Only conclusion II follows Neither conclusion I nor II follows Both conclusions I and II follow

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.$\text{Statements:}$No manager is a l...

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519

GATE2015-8
In the given figure angle $Q$ is a right angle, $PS:QS=3:1, RT:QT=5:2$ and $PU:UR=1:1$. If area of triangle $QTS$ is $20\; cm^2$, then the area of triangle $PQR$ in $cm^2$ is $\_\_\_\_\_\_\_\_\_\_\_.$

In the given figure angle $Q$ is a right angle, $PS:QS=3:1, RT:QT=5:2$ and $PU:UR=1:1$. If area of triangle $QTS$ is $20\; cm^2$, then the area of triangle $PQR$ in $cm^2...

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520

GATE2015-9
Right triangle $PQR$ is to be constructed in the xy-plane so that the right angle is at $P$ and line $PR$ is parallel to the x-axis. The $x$ and $y$ coordinates of $P, Q$ and $R$ are to be integers that satisfy the inequalities: $-4\leq x\leq 5$ and $6\leq y\leq 16$. How many different triangles could be constructed with these properties? $110$ $1,100$ $9,900$ $10,000$

Right triangle $PQR$ is to be constructed in the xy-plane so that the right angle is at $P$ and line $PR$ is parallel to the x-axis. The $x$ and $y$ coordinates of $P, Q$...

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