Questions by gatecse / GO Instrumentation

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1

GATE2018IN: 55
A multi-mode optical fiber with a large core diameter has a core refractive index $n_1 = 1.5$ and cladding refractive index $n_2 = 1.4142.$ The maximum value of $\theta_A$ (in degrees) for which the incident light from air will be guided in the optical fiber is $\pm$ _______________.

A multi-mode optical fiber with a large core diameter has a core refractive index $n_1 = 1.5$ and cladding refractive index $n_2 = 1.4142.$ The maximum value of $\theta_A...

asked Feb 20, 2018

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2

GATE2018IN: 54
A Michelson Interferometer using a laser source of wavelength $\lambda_0 = 500\; nm$, with both the mirrors $(M_1$ & $M_2)$ fixed and positioned equidistant from the splitter/combiner is shown in the figure. When a dielectric plate of refractive index $n = 1.5$, of thickness $t$ ... position of the mirrors $M_1$ & $M_2$, a bright fringe is observed on the detector. The minimum thickness $t$ (in $nm$) of the dielectric is ______________.

A Michelson Interferometer using a laser source of wavelength $\lambda_0 = 500\; nm$, with both the mirrors $(M_1$ & $M_2)$ fixed and positioned equidistant from the spl...

asked Feb 20, 2018

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3

GATE2018IN: 53
The sampling rate for Compact Discs $(CDs)$ is $44,000\; samples/s$. If the samples are quantized to $256$ levels and binary coded, the corresponding bit rate (in bits per second) is ____________.

The sampling rate for Compact Discs $(CDs)$ is $44,000\; samples/s$. If the samples are quantized to $256$ levels and binary coded, the corresponding bit rate (in bits pe...

asked Feb 20, 2018

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4

GATE2018IN: 52
Assuming ideal opamp, the $RMS$ voltage (in mV) in the output $V{_o}$ only due to the $230V,\; 50\; Hz$ interference is (up to one decimal place) __________.

Assuming ideal opamp, the $RMS$ voltage (in mV) in the output $V{_o}$ only due to the $230V,\; 50\; Hz$ interference is (up to one decimal place) __________.

asked Feb 20, 2018

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5

GATE2018IN: 51
A $1000\;\Omega$ strain gage $(R_g$) has a gage factor of $2.5$. It is connected in the bridge as shown in figure. The strain gage is subjected with a positive strain of $400\; \mu m/m.$ The output $V_0$ (in $mV$) of the bridge is(up to two decimal places) $\_\_\_\_\_\_\_$.

A $1000\;\Omega$ strain gage $(R_g$) has a gage factor of $2.5$. It is connected in the bridge as shown in figure. The strain gage is subjected with a positive strain of ...

asked Feb 20, 2018

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6

GATE2018IN: 50
The average velocity $v$ of flow of clear water in a $100\; cm$ (inner) diameter tube is measured using the ultrasonic flow meter as shown in the figure. The angle $\theta$ is $45^\circ$. The measured transit times are $t_1 = 0.9950\;ms$ and $t_2 = 1.0000\; ms$. The velocity $v$ (in m/s) in the pipe is (up to one decimal place) $\_\_\_\_\_$.

The average velocity $v$ of flow of clear water in a $100\; cm$ (inner) diameter tube is measured using the ultrasonic flow meter as shown in the figure. The angle $\thet...

asked Feb 20, 2018

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7

GATE2018IN: 49
The inductance of a coil is measured using the bridge shown in the figure. Balance $(D = 0)$ is obtained with $C_1= 1\; nF, R_1 = 2.2\; M\Omega, R_2 = 22.2\; k\Omega, R_4 = 10\; k\Omega$. The value of the inductance $L_x$ (in $\text{mH} $ is $\_\_\_\_\_\_$

The inductance of a coil is measured using the bridge shown in the figure. Balance $(D = 0)$ is obtained with $C_1= 1\; nF, R_1 = 2.2\; M\Omega, R_2 = 22.2\; k\Omega, R...

asked Feb 20, 2018

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8

GATE2018IN: 48
A high $Q$ coil having distributed (self) capacitance is tested with a Q-meter. First resonance at $\omega_1$ = $10^6$ rad/s is obtained with a capacitance of $990\; pF$. The second resonance at $\omega_2 = 2 \times 10^6\;rad/s$ is obtained with $240\; pF$ capacitance. The value of the inductance (in $mH$) of the coil is (up to one decimal place) $\_\_\_\_\_\_$.

A high $Q$ coil having distributed (self) capacitance is tested with a Q-meter. First resonance at $\omega_1$ = $10^6$ rad/s is obtained with a capacitance of $990\; pF$....

asked Feb 20, 2018

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9

GATE2018IN: 47
The voltage and current drawn by a resistive load are measured with a $300\; V$ voltmeter of accuracy $\pm1\%$ of full scale and a $5 \;A$ ammeter of accuracy $\pm 0.5\%$ of full scale. The readings obtained are $200\; V$ and $2.5\; A$. The limiting error (in $\%$) in computing the load resistance is (up two decimal places) $\_\_\_\_\_\_\_$.

The voltage and current drawn by a resistive load are measured with a $300\; V$ voltmeter of accuracy $\pm1\%$ of full scale and a $5 \;A$ ammeter of accuracy $\pm 0.5\%$...

asked Feb 20, 2018

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10

GATE2018IN: 46
The Boolean function $F(X, Y)$ realized by the given circuit is $\overline{X} Y + X \overline{Y}$ $\overline{X} \;\overline{Y}+ X Y$ $X + Y$ $\overline{X}\cdot \overline{Y}$

The Boolean function $F(X, Y)$ realized by the given circuit is $\overline{X} Y + X \overline{Y}$$\overline{X} \;\overline{Y}+ ...

asked Feb 20, 2018

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11

GATE2018IN: 45
A portion of an assembly language program written for an 8-bit microprocessor is given below along with explanations. The code is intended to introduce a software time delay. The processor is driven by a $5\; MHz$ clock. The time delay (in $\mu$s) introduced by the program is _____________. $\text{MVI B, 64H}$ : Move ... : Jump to address with Label LOOP if zero flag is not set. Takes $10$ clock periods when jump is performed and $7$ clock periods when jump is not performed.

A portion of an assembly language program written for an 8-bit microprocessor is given below along with explanations. The code is intended to introduce a software time de...

asked Feb 20, 2018

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12

GATE2018IN: 44
A 2-bit synchronous counter using two $J-K$ flip flops is shown. The expressions for the inputs to the $J-K$ flip flops are also shown in the figure. The output sequence of the counter starting from $Q_1Q_2 = 00$ is $00 \rightarrow 11 \rightarrow 10 \rightarrow 01 \rightarrow 00 …$ $00 \rightarrow 01 \rightarrow 10 \rightarrow 11 \rightarrow 00…$ $00 \rightarrow 01 \rightarrow 11 \rightarrow 10 \rightarrow 00…$ $00 \rightarrow 10 \rightarrow 11 \rightarrow 01 \rightarrow 00 ...$

A 2-bit synchronous counter using two $J-K$ flip flops is shown. The expressions for the inputs to the $J-K$ flip flops are also shown in the figure. The output sequence ...

asked Feb 20, 2018

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13

GATE2018IN: 43
The product of sum expression of a Boolean function F(A, B, C) of three variables is given by $F(A, B, C) = (A + B + \overline{C}) \cdot(A + \overline{B} + \overline{C}) \cdot (\overline{A} + B + C) \cdot(\overline{A} + \overline{B} + \overline{C}$) The canonical sum product expression of $F(A, B, C)$ ... $\overline{A}\; \overline{B}\; \overline{C} + \overline{A} B C + A B \overline{C} + A B C$

The product of sum expression of a Boolean function F(A, B, C) of three variables is given by$F(A, B, C) = (A + B + \overline{C}) \cdot(A + \overline{B} + \overline{C}) \...

asked Feb 20, 2018

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14

GATE2018IN: 42
The circuit given uses ideal opamps. The current $I$ (in $\mu$A) drawn from the source v$_s$ is (up to two decimal places) $\_\_\_\_\_$.

The circuit given uses ideal opamps. The current $I$ (in $\mu$A) drawn from the source v$_s$ is (up to two decimal places) $\_\_\_\_\_$.

asked Feb 20, 2018

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15

GATE2018IN: 41
An opamp that is powered from a $\pm\; 5V$ supply is used to build a non-inverting amplifier having a gain of $15$. The slew rate of the opamp is $0.5 \times 10^6 \;V/s.$ For a sinusoidal input with ampitude of $0.3V,$ the maximum frequency (in $\text{kHz}$) up to which it can be operated without any distortion is (up to one decimal place) _______.

An opamp that is powered from a $\pm\; 5V$ supply is used to build a non-inverting amplifier having a gain of $15$. The slew rate of the opamp is $0.5 \times 10^6 \;V/s.$...

asked Feb 20, 2018

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16

GATE2018IN: 40
In the given relaxation oscillator, the opamps and the zener diodes are ideal. The frequency (in $kHz$) of the square wave output $v_{\circ}$ is $\_\_\_\_\_\_$.

In the given relaxation oscillator, the opamps and the zener diodes are ideal. The frequency (in $kHz$) of the square wave output $v_{\circ}$ is $\_\_\_\_\_\_$.

asked Feb 20, 2018

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17

GATE2018IN: 39
Unit step response of a linear time invariant $(LTI)$ system is given by $y(t) = (1 – e^{-2t})u(t)$. Assuming zero initial condition, the transfer function of the system is $\frac{1}{s+1}$ $\frac{2}{(s+1)(s+2)}$ $\frac{1}{s+2}$ $\frac{2}{s+2}$

Unit step response of a linear time invariant $(LTI)$ system is given by $y(t) = (1 – e^{-2t})u(t)$. Assuming zero initial condition, the transfer function of the syste...

asked Feb 20, 2018

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18

GATE2018IN: 38
Consider a standard negative feedback configuration with G(s) = $\frac{1}{(s+1)(s+2)}$ and H(s) = $\frac{s+a}{s}$, For the closed loop system to have poles on the imaginary axis, the value of $\alpha$ should be equal to (up to one decimal place)$\_\_\_\_\_\_$.

Consider a standard negative feedback configuration with G(s) = $\frac{1}{(s+1)(s+2)}$ and H(s) = $\frac{s+a}{s}$, For the closed loop system to have poles on the imagina...

asked Feb 20, 2018

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19

GATE2018IN: 37
Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for this system is $x(t) = \begin{bmatrix}e^{-t} & te^{-2t} \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1 \\1\end{bmatrix}$ ... $\begin{bmatrix}1 \\1\end{bmatrix}$ $x(t) = \begin{bmatrix}e^{-t} & 0 \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1 \\1\end{bmatrix}$

Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for...

asked Feb 20, 2018

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20

GATE2018IN:36
Consider the standard negative feedback configuration with G(s) = $\frac{s^2+0.2s+100}{s^2 – 0.2s +100}$ and H(s) = $\frac{1}{2}$. The number of clockwise encirclements of (-1,0) in the Nyquist plot of the Loop transfer-function G(s)H(s) is $\_\_\_\_\_$

Consider the standard negative feedback configuration with G(s) = $\frac{s^2+0.2s+100}{s^2 – 0.2s +100}$ and H(s) = $\frac{1}{2}$. The number of clockwise encirclements...

asked Feb 20, 2018

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21

GATE2018IN: 35
For the sequence $x[n] = \{1, -1,1, -1\},$ with $n = 0,1,2,3,$ the DFT is computed as $X(k) = \displaystyle{}\Sigma^3_{n=0}x[n]e^{-j\frac {2\pi}{4}nk}$, for $k = 0,1,2,3.$ The value of k for which $X(k)$ is not zero is 0 1 2 3

For the sequence $x[n] = \{1, -1,1, -1\},$ with $n = 0,1,2,3,$ the DFT is computed as $X(k) = \displaystyle{}\Sigma^3_{n=0}x[n]e^{-j\frac {2\pi}{4}nk}$, for $k = 0,1,2,3....

asked Feb 20, 2018

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22

GATE2018IN: 34
Let y[n] = x[n] * h[n], where * denotes convolution and x[n] and h[n] are two discrete time sequences, Given that the z-transform of y[n] is y(z) = 2+ 3z$^{-1}$ + z$^{-2}$, the z- transform of p[n] = x[n] * h [n-2] is 2 + 3z + z$^{-2}$ 3z +z$^{-2}$ 2z$^2$ + 3z + 1 2z$^{-2}$ + 3z$^{-3}$ + z$^{-4}$

Let y[n] = x[n] * h[n], where * denotes convolution and x[n] and h[n] are two discrete time sequences, Given that the z-transform of y[n] is y(z) = 2+ 3z$^{-1}$ + z$^{-2}...

asked Feb 20, 2018

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23

GATE2018IN: 33
The Fourier transform of a signal x(t), denoted by X(j$\omega$), is shown in the figure Let y(t) = x(t) + e$^{jt}$x(t). The value of Fourier transform of y(t) evaluated at the angular frequency $\omega$ = 0.5 rad /s is 0.5 1 1.5 2.5

The Fourier transform of a signal x(t), denoted by X(j$\omega$), is shown in the figure Let y(t) = x(t) + e$^{jt}...

asked Feb 20, 2018

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24

GATE2018IN: 32
In the given circuit, the mesh currents $I{_1}$,$I{_2}$ and $I{_3}$ are $I{_1}$ = 1 A, $I{_2}$ =2 A and $I{_3}$ = 3A $I{_1}$ = 2 A, $I{_2}$ = 3 A and $I{_3}$ = 4A $I{_1}$ = 3 A, $I{_2}$ = 4 A and $I{_3}$ = 5A $I{_1}$ = 4 A, $I{_2}$ = 5 A and $I{_3}$ = 6A

In the given circuit, the mesh currents $I{_1}$,$I{_2}$ and $I{_3}$ are $I{_1}$ = 1 A, $I{_2}$ =2 A and $I{_3}$ ...

asked Feb 20, 2018

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25

GATE2018IN: 31
In the figure, an RLC load supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is $\_\_\_\_\_$.

In the figure, an RLC load supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is $\_\_\_\_\_$.

asked Feb 20, 2018

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26

GATE2018IN:30
In the given circuit, superposition is applied.When V$_2$ is set to 0 V, the current I$_2$ is -6 A. When V$_1$ is set to 0 v, the current I$_1$ is + 6A. Current I$_3$ (in A) when both sources are applied will be (up to two decimal places)$\_\_\_\_\_$.

In the given circuit, superposition is applied.When V$_2$ is set to 0 V, the current I$_2$ is -6 A. When V$_1$ is set to 0 v, the current I$_1$ is + 6A. Current I$_3$ (in...

asked Feb 20, 2018

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27

GATE2018IN: 29
Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy $\frac {\partial {V(x,y)}}{\partial y}$ = x$^2$ + qy$^2$ + 2xy where p and q are constant ,V(x,y) that satisfies the above equations is p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 2xy + 6 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 5 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$ + xy p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$

Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy ...

asked Feb 20, 2018

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28

GATE2018IN: 28
Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y =2 Here x and y are the unknows and k is real constant. The value of k for which there are infinite number of solutions is 3 1 -3 -6

Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y =2Here x and y are the unknows and k is real c...

asked Feb 20, 2018

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29

GATE2018IN: 27
Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red? 20% 25% 30% 40%

Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A...

asked Feb 20, 2018

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30

GATE2018IN: 26
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$\overrightarrow{k}$, the value of the linear integral $\int_c$\overrightarrow{F}$ . d$\overrightarrow{l}$ along the straight line c from (0,0,0) to (1,1,1) is 3/16 0 -5/12 -1

Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$$\overrightarrow{k}$, the value of the linear integral $\int_c$$\ove...

asked Feb 20, 2018

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31

GATE2018IN: 25
An optical pulse containing 6 x 10$^6$ photons is incident on a photodiode and 4.5 x 10$^6$ electron-hole pairs are created. The maximum possible quantum efficiency (in %) of the photodiode is $\_\_\_\_$.

An optical pulse containing 6 x 10$^6$ photons is incident on a photodiode and 4.5 x 10$^6$ electron-hole pairs are created. The maximum possible quantum efficiency (in %...

asked Feb 20, 2018

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32

GATE2018IN: 24
An amplitude modulated signal is shown in the figure. The modulation index is(up to one decimal place) $\_\_\_\_\_$

An amplitude modulated signal is shown in the figure. The modulation index is(up to one decimal place) $\_\_\_\_\_$

asked Feb 20, 2018

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33

GATE2018IN: 23
A piezoelectric pressure sensor has a bandpass characteristic with cut-off frequencies of 0.1 Hz and 1 MHz, and a sensitivity of 100 mV/kPa. The sensor is subjected to a static constant pressure of 100kpa. Its steady-state output will be 0 V 0.1 V 1 V 10 V

A piezoelectric pressure sensor has a bandpass characteristic with cut-off frequencies of 0.1 Hz and 1 MHz, and a sensitivity of 100 mV/kPa. The sensor is subjected to a ...

asked Feb 20, 2018

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34

GATE2018IN: 22
As shown in the figure, temperature $\theta$ is measured using a $K$ type thermocouple. It has a sensitivity of 40 $\mu V/^{\circ}C$. The gain $(G)$ of the ideal instrumentations amplifier is $25$. If the output $V_0$ is $96 \;mV,$ then the value of $\theta$(in $^{\circ}$C) is ______________.

As shown in the figure, temperature $\theta$ is measured using a $K$ type thermocouple. It has a sensitivity of 40 $\mu V/^{\circ}C$. The gain $(G)$ of the ideal instrume...

asked Feb 20, 2018

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35

GATE2018IN: 21
A 300 V, 5A, 0.2 pf low power factor wattmeter is used to measure the power consumed by a load. The wattmeter scale has 150 divisions and the pointer is on the 100$^{th}$ division. The power consumed by the load (in Watts) is $\_\_\_\_\_$

A 300 V, 5A, 0.2 pf low power factor wattmeter is used to measure the power consumed by a load. The wattmeter scale has 150 divisions and the pointer is on the 100$^{th}$...

asked Feb 20, 2018

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36

GATE2018IN: 20
A voltage of 6 cos(100$\pi$t) V is fed as y-input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively 1 V/div and 1 ms/div 1 V/div and 2 ms/div 2 V/div and 1 ms/div 2 V/div and 2 ms/div

A voltage of 6 cos(100$\pi$t) V is fed as y-input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are r...

asked Feb 20, 2018

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37

GATE2018IN:19
The number of comparators required for implementing an 8-bit flash analog-to-digital converter is 8 128 255 256

The number of comparators required for implementing an 8-bit flash analog-to-digital converter is8128255256

asked Feb 20, 2018

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38

GATE2018IN: 18
The representation of the decimal number (27.625)$_{10}$ in base -2 number system is 11011.110 11101.101 11011.101 10111.110

The representation of the decimal number (27.625)$_{10}$ in base -2 number system is11011.11011101.10111011.10110111.110

asked Feb 20, 2018

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39

GATE2018IN: 17
For the 3-bit binary counter shown in the figure, the output increments at every positive transition in the clock(CLK). Assume ideal diodes and the starting state of the counter as 000. If output high is 1 V and output low is 0 V, the current I(in mA) flowing through the 50 $\Omega$ resistor during the 5$^{th}$ clock cycle is(up to one decimal place) $\_\_\_\_\_\_$

For the 3-bit binary counter shown in the figure, the output increments at every positive transition in the clock(CLK). Assume ideal diodes and the starting state of the ...

asked Feb 20, 2018

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40

GATE2018IN: 16
The diodes given in the circuit are ideal. At t = 60ms, V$_{pq}$(in Volts) is $\_\_\_\_\_\_\_$

The diodes given in the circuit are ideal. At t = 60ms, V$_{pq}$(in Volts) is $\_\_\_\_\_\_\_$

asked Feb 20, 2018