Recent questions tagged gate2014-in / GO Instrumentation

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41

GATE2014-25
In a time-of-flight mass spectrometer if $q$ is the charge and $m$ the mass of the ionized species, then the time of flight is proportional to $\frac{\sqrt m}{\sqrt q}$ $\frac{\sqrt q}{\sqrt m}$ $\frac{m}{\sqrt q}$ $\frac{q}{\sqrt m}$

In a time-of-flight mass spectrometer if $q$ is the charge and $m$ the mass of the ionized species, then the time of flight is proportional to$\frac{\sqrt m}{\sqrt q}$$\f...

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42

GATE2014-31
The resistance of a wire is given by the expression $R=\frac{4\rho L}{\pi D^2},$ where, $\rho$ is the resistivity ($\Omega$-meter), $L$ is the length (meter) and D (meter) is the diameter of the wire. The error in measurement of each of the parameters $\rho,L,$ and $D$ is $\pm 1.0\%$. Assuming that the errors are independent random variables, the percent error in measurement of $R$ is __________.

The resistance of a wire is given by the expression$$R=\frac{4\rho L}{\pi D^2},$$where, $\rho$ is the resistivity ($\Omega$-meter), $L$ is the length (meter) and D (meter...

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43

GATE2014-33
A thermistor has a resistance of $1\;k\Omega$ at temperature $298\;K$ and $465\;\Omega$ at temperature $316\;K$. The temperature sensitivity in $K^{-1}[i.e(1/R)(dR/dT),$ where $R$ is the resistance at the temperature $T(in\; K)]$, of this thermistor at $316\;K$ is ___________.

A thermistor has a resistance of $1\;k\Omega$ at temperature $298\;K$ and $465\;\Omega$ at temperature $316\;K$. The temperature sensitivity in $K^{-1}[i.e(1/R)(dR/dT),$ ...

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44

GATE2014-34
A barium titanate piezoelectric crystal with $d_{33}=150\;pC/N, C_{crystal}=25\;pF$ and $R_{crystal}=10^{10}\Omega$ is used to measure the amplitude of a step force. The voltage output is measured using a digital voltmeter with input impedance $10^{13}\Omega$ connected across the crystal. All other capacitances and ... time in milliseconds with in which the voltmeter should sample the crystal output voltage so that the drop from the peak value is no more than $0.12V$ is ____________.

A barium titanate piezoelectric crystal with $d_{33}=150\;pC/N, C_{crystal}=25\;pF$ and $R_{crystal}=10^{10}\Omega$ is used to measure the amplitude of a step force. The ...

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45

GATE2014-35
A thermopile is constructed using $10$ junctions of Chromel-Constantan ( sensitivity $60\mu V/^\circ C$ for each junction) connected in series. The output is fed to an amplifier having an infinite input impedance and a gain of $10$. The output from the amplifier is acquired using a $10-bit\;ADC$, with reference voltage of $5\;V$. The resolution of this system in units of $^{\circ}C$ is ____________.

A thermopile is constructed using $10$ junctions of Chromel-Constantan ( sensitivity $60\mu V/^\circ C$ for each junction) connected in series. The output is fed to an am...

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46

GATE2014-36
A transit time ultrasonic flowmeter uses a pair of ultrasonic transducers placed at $45^{\circ}$ angle, as shown in the figure. The inner diameter of the pipe is $0.5\;m$. The differential transit time is directly measured using a clock of frequency $5\;MHz$. The velocity of the fluid is small compared to the velocity ... of the crystals is negligible compared to the diameter of the pipe. The minimum change in fluid velocity $(m/s)$ that can be measured using this system is _________.

A transit time ultrasonic flowmeter uses a pair of ultrasonic transducers placed at $45^{\circ}$ angle, as shown in the figure.The inner diameter of the pipe is $0.5\;m$....

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47

GATE2014-37
Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance $\frac{V_0}{i}$ in $M\Omega$ of the current to voltage converter shown in the figure is ___________.

Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance $\frac{V_0}{i}$ in $M\Omega$ of the current to voltage converter shown in t...

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48

GATE2014-38
For the circuit shown in the figure, the transistor has $\beta=40, V_{BE}=0.7\;V$, and the voltage across the Zener diode is $15\;V$. The current (in mA) through the Zener diode is ____________.

For the circuit shown in the figure, the transistor has $\beta=40, V_{BE}=0.7\;V$, and the voltage across the Zener diode is $15\;V$. The current (in mA) through the Zene...

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49

GATE2014-39
In the figure, transistors $T_1$ and $T_2$ have identical characteristics. $V_{CE(sat)}$ of transistor $T_3$ is $0.1\:V$. The voltage $V_1$ is high enough to put $T_3$ in saturation. Voltage $V_{BE}$ of transistors $T_1,T_2$ and $T_3$ is $0.7 V$. The value of $(V_1-V_2)$ in $V$ is _________________.

In the figure, transistors $T_1$ and $T_2$ have identical characteristics. $V_{CE(sat)}$ of transistor $T_3$ is $0.1\:V$. The voltage $V_1$ is high enough to put $T_3$ in...

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50

GATE2014-40
The figures show an oscillator circuit having an ideal Schmitt trigger and its input-output characteristics. The time period (in ms) of $v_{\circ}(t)$ is ______________.

The figures show an oscillator circuit having an ideal Schmitt trigger and its input-output characteristics. The time period (in ms) of $v_{\circ}(t)$ is ______________.

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51

GATE2014-41
An $N-$bit, $ADC$ has an analog reference voltage $V$. Assuming zero mean and uniform distribution of the quantization error, the quantization noise power will be: $\frac{V^2}{12(2^N-1)^2}$ $\frac{V^2}{12(2^N-1)}$ $\frac{V}{12(2^N-1)}$ $\frac{V^2}{\sqrt{12} }$

An $N-$bit, $ADC$ has an analog reference voltage $V$. Assuming zero mean and uniform distribution of the quantization error, the quantization noise power will be:$\frac{...

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52

GATE2014-42
A microprocessor accepts external interrupts (Ext INT) through a Programmable Interrupt Controller as shown in the figure. Assuming vectored interrupt, a correct sequence of operations when a single extrenal interrupt (Ext INT1) is received will be : $Ext\;INT1\rightarrow INTA\rightarrow Data\;Read\rightarrow INT$ ... $Ext\;INT1\rightarrow INT \rightarrow INTA \rightarrow Address\;Write$ $Ext\;INT1\rightarrow INT\rightarrow Data\;Read\rightarrow Address\;Write$

A microprocessor accepts external interrupts (Ext INT) through a Programmable Interrupt Controller as shown in the figure. Assuming vectored interrupt, a correct sequence...

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53

GATE2014-43
The circuit in the figure represents a counter-based unipolar $ADC$. when $SOC$ is asserted the counter is reset and clock is enabled so that the counter counts up and the $DAC$ output grows. When the $DAC$ output exceeds the input sample value, the comparator switches from logic 0 to logic 1, disabling the clock ... of the analog sample value is: directly proportional to $V_{ref}$ inversely proportional to $V_{ref}$ independent of $V_{ref}$ directly proportional to clock frequency

The circuit in the figure represents a counter-based unipolar $ADC$. when $SOC$ is asserted the counter is reset and clock is enabled so that the counter counts up and th...

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54

GATE2014-44
$X(k)$ is the Discrete Fourier Transform of a 6-point real sequence $x(n).$ If $X(0)=9+j0, X(2)=2+j2, X(3)=3-j0, X(5)=1-j1, x(0)$ is $3$ $9$ $15$ $18$

$X(k)$ is the Discrete Fourier Transform of a 6-point real sequence $x(n).$If $X(0)=9+j0, X(2)=2+j2, X(3)=3-j0, X(5)=1-j1, x(0)$ is$3$$9$$15$$18$

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55

GATE2014-45
The transfer function of a digital system is given by: $\frac{b_0}{1-z^{-1}+a_2z^{-2}},\text{ where $a_2$ is real.}$ The transfer function in $BIBO$ stable if the value of $a_2$ is: $-1.5$ $-0.75$ $0.5$ $1.5$

The transfer function of a digital system is given by:$$\frac{b_0}{1-z^{-1}+a_2z^{-2}},\text{ where $a_2$ is real.}$$The transfer function in $BIBO$ stable if the value o...

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56

GATE2014-46
The transfer function of a system is given by $G(s)=\frac{e^{-s/500}}{s+500}$ The input to the system is $x(t)=\sin100\pi t$. In periodic steady state the output of the system is found to be $y(t)=A\sin(100\pi t-\phi).$ The phase angle $(\phi )$ in degree is ___________.

The transfer function of a system is given by$$G(s)=\frac{e^{-s/500}}{s+500}$$The input to the system is $x(t)=\sin100\pi t$. In periodic steady state the output of the s...

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57

GATE2014-47
In the microprocessor controlled measurement scheme shown in the figure, $R_x$ is the unknown resistance to be measured, while $R_{ref}$ and $C_{ref}$ are known. $C_{ref}$ is charged from voltage $V_L$ to $V_H$ (by a constant DC voltage source $V_s$), once through $R_{ref}$ in $T_{ref}$ seconds and then discharged to $V_L$. It is again charged from voltage ... $T_x=kT_{ref}$ then $R_x=kR_{ref}(1-\frac{V_L}{V_H})$ $R_x=kR_{ref}ln(\frac{V_H}{V_L})$ $R_x=kR_{ref}$ $R_x=kR_{ref}\;ln\;k$

In the microprocessor controlled measurement scheme shown in the figure, $R_x$ is the unknown resistance to be measured, while $R_{ref}$ and $C_{ref}$ are known. $C_{ref...

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58

GATE2014-48
Frequency of an analog periodic signal in the range of $5kHz-10kHz$ is to be measured with a resolution of $100Hz$ by measuring its period with a counter. Assuming negligible signal and transition delays the minimum clock frequency and minimum number of bits in the counter needed, respectively, are: $1\; MHz,\; 10-bits$ $10\; MHz,\; 10-bits$ $1\; MHz,\; 8-bits$ $10\; MHz,\; 8-bits$

Frequency of an analog periodic signal in the range of $5kHz-10kHz$ is to be measured with a resolution of $100Hz$ by measuring its period with a counter. Assuming neglig...

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59

GATE2014-49
The loop transfer function of a feedback control system is given by $G(s)H(s)=\frac{1}{s(s+1)(9s+1)}$ Its phase crossover frequency (in rad/s), approximated to two decimal places, is ______________.

The loop transfer function of a feedback control system is given by$$G(s)H(s)=\frac{1}{s(s+1)(9s+1)}$$Its phase crossover frequency (in rad/s), approximated to two decima...

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60

GATE2014-50
Consider a transport lag process with a transfer function $G_p(S)=e^{-s}$ The process is controlled by a purely integral controller with transfer function $G_c(S)=\frac{K_i}{S}$ in a unity feedback configuration. The value of $K_i$ for which the closed loop plant has a pole at $ s=-1$, is ___________.

Consider a transport lag process with a transfer function$$G_p(S)=e^{-s}$$The process is controlled by a purely integral controller with transfer function$$G_c(S)=\frac{K...

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61

GATE2014-51
Consider the control system shown in figure with feed forward action for rejection of a measurable disturbance $d(t)$. The value of $K$, for which the disturbance response at the output $y(t)$ is zero mean, is : $1$ $-1$ $2$ $-2$

Consider the control system shown in figure with feed forward action for rejection of a measurable disturbance $d(t)$. The value of $K$, for which the disturbance respons...

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62

GATE2014-52
A mixture contains two mutually inert solutions $’X’$ and $’Y’$ in equal volumes. The mixture is examined in a spectrophotometer using a cuvette. It is observed that the transmittance is $0.40$. With only the solution $’X’$ in the same cuvette, the transmittance is $0.20$. With only solution $’Y’$ in the cuvette the transmittance is __________.

A mixture contains two mutually inert solutions $’X’$ and $’Y’$ in equal volumes. The mixture is examined in a spectrophotometer using a cuvette. It is observed t...

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63

GATE2014-53
Monochromatic light from a step index $(n_1=1.500;n_2=1.485),$ multimode optical fiber of core diameter $100\;\mu m$ is incident through air $(n=1.000)$ onto a linear photo-detector array placed at $1\; mm$ distance from the tip of the fiber. The tip of the fiber is polished and its exit plane is ... diameter. The distance between the edges of two adjacent elements can be assumed to be zero. The number of elements illuminated by the light coming out of the fiber is __________.

Monochromatic light from a step index $(n_1=1.500;n_2=1.485),$ multimode optical fiber of core diameter $100\;\mu m$ is incident through air $(n=1.000)$ onto a linear pho...

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64

GATE2014-54
An image of the chest of a patient is taken with an $X-ray$ machine on a photographic film. The Hurter-Driffield (HD) curve of the film is shown in the figure. The highly absorbing parts of the body (e.g. bones), show up as low exposure regions(mapped near A) and the less absorbing parts (e.g. ... contrast decreases since both A and B move into the shoulder region contrast increases since A moves into the toe region contrast decreases since both A and B move into the toe region

An image of the chest of a patient is taken with an $X-ray$ machine on a photographic film. The Hurter-Driffield (HD) curve of the film is shown in the figure. The highly...

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