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QUESTION: 1

**Q.1-5 Carry One Mark Each**

Choose the most appropriate word from the options given below to complete the following sentence.

A person suffering from Alzheimer?s disease _________ short-term memory loss.

Solution:

QUESTION: 2

Choose the most appropriate word from the options given below to complete the following sentence.

_________ is the key to their happiness; they are satisfied with what they have.

Solution:

QUESTION: 3

Which of the following options is the closest in meaning to the sentence below?

“As a woman, I have no country.”

Solution:

*Answer can only contain numeric values

QUESTION: 4

In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 5

The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate?

Solution:

QUESTION: 6

**Q. 6 – 10 Carry Two Marks Each.**

In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group?

**Statements: **

1. Shiv is younger to Riaz.

2. Shiv is elder to Som.

Solution:

QUESTION: 7

Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis.

From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier

The main point of the paragraph is:

Solution:

QUESTION: 8

The total exports and revenues from the exports of a country are given in the two pie charts below.

The pie chart for exports shows the quantity of each item as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram?

Solution:

QUESTION: 9

X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km?

Solution:

*Answer can only contain numeric values

QUESTION: 10

10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _________.

Solution:

Let total population = 100

HIV + patients = 10

For the patient to be +Ve, should be either +VE and test is showing the or the patient

should be – Ve but rest is showing +Ve

QUESTION: 11

**Q.11 – 35 Carry One Mark Each.**

**Given**

The x-y plot will be

Solution:

*Answer can only contain numeric values

QUESTION: 12

Given that x is a random variable in the range [0, ∞] with a probability density

the value of the constant K is ___________.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 13

The figure shows the plot of y as a function of x

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is:

Solution:

*Answer can only contain numeric values

QUESTION: 14

A vector is defined as are unit vectors in Cartesian (x, y, z) coordinate system.

The surface integral ? ??. ??s over the closed surface S of a cube with vertices having the following coordinates: (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1) is ___________ .

(**Important** - Enter only the numerical value in the answer)

Solution:

From Gauss divergence theorem, we have

*Answer can only contain numeric values

QUESTION: 15

The figure shows the schematic of a production process with machines A, B and C. An input job needs to be pre-processed either by A or by B before it is fed to C, from which the final finished product comes out. The probabilities of failure of the machines are given as:

P_{A}=0.15, P_{B}=0.05, P_{C}=0.1

Assuming independence of failures of the machines, the probability that a given job is successfully processed (up to the third decimal place) is ___________.

Solution:

Let X, Y, Z be respectively that machines A, B, C success (works) then

P(x) = 0.85, P(y) = 0.95, P(z) = 0.9

P[Job to be completed successful] = P [(machines A or machine B success) and

(machine C success)]

*Answer can only contain numeric values

QUESTION: 16

The circuit shown in figure was at steady state for t < 0 with the switch at position 'A'. The switch is thrown to position 'B' at time t = 0. The voltage V(volts) across the 10Ω resistor at time t = 0^{+} is ___________.

(**Important** - Enter only the numerical value in the answer)

Solution:

At t < 0, switch is at position “A” and it was at steady state.

*Answer can only contain numeric values

QUESTION: 17

The average real power in watts delivered to a load impedance Z_{L }= (4 - j2) by an ideal current

source i(t) = 4sin(ωt + 20^{o}) A is __________ .

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 18

Time domain expressions for the voltage v_{1}(t) and v_{2}(t) are given as

Which one of the following statements is TRUE?

Solution:

*Answer can only contain numeric values

QUESTION: 19

A pHelectrode obeys Nernst equation and is being operated at 25^{o}C. The change in the open circuit voltage in millivolts across the electrode for a pH change from 6 to 8 is ___________.

(**Important** - Enter only the numerical value in the answer)

Solution:

The potential (E) of the PH electrode may be written by means of Nernst equation as

QUESTION: 20

The pressure and velocity at the throat of a Venturi tube, measuring the flow of a liquid, are related to the upstream pressure and velocity, respectively, as follows:

Solution:

The convergent entrance of venture-tube is called as “upstream”. As pipe becomes narrow towards throat, a gradual decrease in cross-sectional area of the conduct causes higher fluid velocity according to continuity equation). Due to this, pressure drops.

QUESTION: 21

Semiconductor strain gages typically have much higher gage factors than those of metallic strain gages, primarily due to:

Solution:

The resistance of the semiconductors changes with change in applied strain, due to change in resistivity. While the resistance of metallic gauges changes with change in dimensions. Hence semiconductor strain gauge depend on piezoresistive effect for their action.

Piezoresistive coefficient is a measure of change in the value of resistance by straining the gauge.

QUESTION: 22

For a rotameter, which one of the following statements is TRUE?

Solution:

Rotameters or variable area flow meters, operate on the principle that the variation in area, of flow stream required to produce a constant pressure differential, is proportional to flow rate.

The flowing fluid enters the bottom of the meter, passes upward through a tapered metering tube, and around a float, exiting at the top. The float is forced upward until the force is balanced by gravitational force and drag force on float acting downwards.

QUESTION: 23

For the op-amp shown in the figure, the bias currents are I_{b1 }= 450 nA and I_{b2 }= 350 nA. The values of the input bias current (I_{B}) and the input offset current (I_{f}) are:

Solution:

QUESTION: 24

The amplifier in the figure has gain of −10 and input resistance of 50 kΩ. The values of Ri and

Solution:

*Answer can only contain numeric values

QUESTION: 25

For the circuit shown in the figure assume ideal diodes with zero forward resistance and zero forward voltage drop. The current through the diode D_{2} in mA is_________.

(**Important **- Enter only the numerical value in the answer)

Solution:

QUESTION: 26

The system function of an LTI system is given by

The above system can have stable inverse if the region of convergence of H(z) is defined as

Solution:

If poles lie inside the unit circle then it will be stable only if R_{oc} include unit circle or R_{oc} is

extension of circle whose radius is given by outer most pole.

QUESTION: 27

The figure is a logic circuit with inputs A and B and output Y.V_{ss} = + 5 V. The circuit is of type

Solution:

Given circuit is cmos implementation of digital function. Cmos containing two type of transistant network, generally upper network containing pmos and lower network containing Nmos.

Irrespective of detail operation of any individual network or transistors, by inspection we can find out

the output expression.

If the Nmos transistors are connected in series, then take the products of their inputs with overall complement, OR if the pmos transistor are connected in parallel, then take the products of their inputs with overall complement

QUESTION: 28

The impulses response of an LTI system is given as:

It represents an ideal

Solution:

It is non-causal, since h[n] = 0 for h < 0.

It is an low-pass filter

QUESTION: 29

A discrete-time signal x[n] is obtained by sampling an analog signal at 10 kHz. The signal x[n] is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutoff frequency of the filter is:

Solution:

QUESTION: 30

A full duplex binary FSK transmission is made through a channel of bandwidth 10 kHz. In each direction of transmission the two carriers used for the two states are separated by 2 kHz. The maximum baud rate for this transmission is:

Solution:

Because the transmission is full duplex,only 5000(5KHz) allocated for each direction.

B.W=Baud rate + f_{2} - f_{1}

given f_{2} – f_{1} =2K=2000

Baud rate = B.W- (f_{2} –f_{1} ) = 5000- 2000

Baud rate=3000 bps

*Answer can only contain numeric values

QUESTION: 31

A loop transfer function is given by:

The point of intersection of the asymptotes of G(s)H(s) on the real axis in the s-plane is at __________.

Solution:

The point of intersection of the asymptotes is nothing but a centroid.

QUESTION: 32

The resistance and inductance of an inductive coil are measured using an AC bridge as shown in the figure. The bridge is to be balanced by varying the impedance Z_{2}.

For obtaining balance, Z_{2} should consist of element(s):

Solution:

QUESTION: 33

A plant has an open-loop transfer function,

The approximate model obtained by retaining only one of the above poles, which is closest to the frequency response of the original transfer function at low frequency is

Solution:

QUESTION: 34

In order to remove respiration related motion artifacts from an ECG signal, the following filter should be used:

Solution:

The useful bandwidth of an ECG signal range from 0.5 Hz to 50 Hz. A standard ECG

application has a bandwidth of 0.05Hz to 100Hz. Respiration related motion artifacts are often denoted as low-frequency noise in the skin-electrode interface. So, it can be removed by a HPF with f_{c} = 0.5 Hz.

QUESTION: 35

In a time-of-flight mass spectrometer if q is the charge and m is the mass of the ionized species, then the time of flight is proportional to

Solution:

QUESTION: 36

**Q. 26 – 55 Carry Two Marks Each**

A scalar valued function is defined as f(x) = x^{T}Ax + b^{T}x + c,where A is a symmetric positive definite matrix with dimension n× n; b and x are vectors of dimension n×1. The minimum value of f(x) will occur when x equals

Solution:

QUESTION: 37

The iteration step in order to solve for the cube roots of a given number N using the Newton - Raphson?s method is

Solution:

QUESTION: 38

For the matrix A satisfying the equation given below, the eigen values are

Solution:

*Answer can only contain numeric values

QUESTION: 39

In the circuit shown in the figure, initially the capacitor is uncharged. The switch 'S' is closed at t = 0 . Two milliseconds after the switch is closed, the current through the capacitor (in mA) is _____________.

(**Important** - Enter only the numerical value in the answer)

Solution:

When switch 'S' is closed,

At t=0 :

*Answer can only contain numeric values

QUESTION: 40

A capacitor „C? is to be connected across the terminals 'A' and 'B' as shown in the figure so that the power factor of the parallel combination becomes unity. The value of the capacitance required in μF is __________.

(**Important** - Enter only the numerical value in the answer)

Solution:

Power factor of the parallel combination is unity.

i.e., in total impedance equate the imaginary term to zero, which gives the capacitance required.

*Answer can only contain numeric values

QUESTION: 41

The resistance of a wire is given by the expression

, where, ρ is the resistivity (Ω-meter), L is the length (meter) and D (meter) is the diameter of the wire. The error in measurement of each of the parameters ρ, L, and D is ±1.0%. Assuming that the errors are independent random variables, the percent error in measurement of R is _________.

Solution:

*Answer can only contain numeric values

QUESTION: 42

The circuit shown in the figure contains a dependent current source between A and B terminals.

The Thevenin?s equivalent resistance in kΩ between the terminals C and D is ___________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 43

A thermistor has a resistance of 1 kΩ at temperature 298 K and 465 Ω 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 _________.

Solution:

*Answer can only contain numeric values

QUESTION: 44

A barium titanate piezoelectric crystal with d_{33}=150 pC/N, C_{crystal} = 25 pF and R_{crystal} = 1010 Ω is used to measure the amplitude of a step force. The voltage output is measured using a digital voltmeter with input impedance 1013 Ω connected across the crystal. All other capacitances and resistances may be neglected. A step force of 2 N is applied from direction “3” on the crystal. The time in milliseconds within which the voltmeter should sample the crystal output voltage so that the drop from the peak value is no more than 0.12V is ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 45

A thermopile is constructed using 10 junctions of Chromel-Constantan (sensitivity 60μ V/^{o}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 ^{o}C is

Solution:

*Answer can only contain numeric values

QUESTION: 46

A transit time ultrasonic flowmeter uses a pair of ultrasonic transducers placed at 45^{o} 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 sound in the static fluid, which is 1500 m/s and the size 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 _________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 47

Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance v_{0 }/i in M? of the current to voltage converter shown in the figure is _______.

**(Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 48

For the circuit shown in the figure, the transistor has β = 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 _________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 49

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 0.7V. The value of V_{1} - V_{2} in V is _________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 50

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

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 51

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:

Solution:

QUESTION: 52

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 external interrupt (Ext INT1) is received will be :

Solution:

When a single external interrupt (Exp INT1) is raised then it is sensed by programmable interrupt controller and as per their priority it is serviced first and now INT signal is raised by interrupt controller and it is sensed by microprocessor, then microprocessor first completes their current machine cycle and raised the INTA (interrupt acknowledge) signal back to PI controller. This is vectored interrupt so, their address is fixed and ISR (interrupt service Routine) execution will takes place from that address. So, this sequences is mactching with option (B) only

QUESTION: 53

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 and enabling the output buffer by asserting EOC. Assuming all components to be ideal, V_{ref} , DAC output and input to be positive, the maximum error in conversion of the analog sample value is:

Solution:

Shoulder

shoulder

So, the maximum error is directly proportional to V_{ref} of R-2R ladder type D_{AC}

QUESTION: 54

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

Solution:

QUESTION: 55

The transfer function of a digital system is given by:

; where a_{2} is real.

The transfer function is BIBO stable if the value of a_{2} is:

Solution:

Transfer function of the digital system is,

The stability of a two-pole system can be investigated by a stability criterion method called “schr−cohn” stability test”.

In this approach the reflection coefficients K_{1 }and K_{2} are to be calculated from the denominator pdynomial. This method states that a second order system is stable if its reflection coefficients |k_{1}| <1 and |k2| <1. It is also given that,

These two conditions are satisfied by 0.5

Note: An alternative approach to solve this problem is trial and error method. Each option is substituted for 'a_{2}'in the system function and poles are to be calculated. The value 'a_{2}' which gives both the poles inside the unit-circle is the suitable „a2?. Here a2 = 0.5 satisfies the

condition.

*Answer can only contain numeric values

QUESTION: 56

The transfer function of a system is given by

The input to the system is x(t ) = sin100πt . In periodic steady state the output of the system is found to be y(t ) = Asin(100πt - φ) . The phase angle (φ) in degree is ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 57

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 V_{L} to V_{H} through R_{x} in T_{x} seconds.

If T_{x} = kT_{ref} then

Solution:

QUESTION: 58

Frequency of an analog periodic signal in the range of 5 kHz – 10 kHz is to be measured with a resolution of 100 Hz 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:

Solution:

*Answer can only contain numeric values

QUESTION: 59

The loop transfer function of a feedback control system is given by

Its phase crossover frequency (in rad/s), approximated to two decimal places, is _________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 60

Consider a transport lag process with a transfer function

The process is controlled by a purely integral controller with transfer function in a unity feedback configuration. The value of i K for which the closed loop plant has a pole at s = −1, is __________.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 61

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:

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 62

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 _________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 63

Monochromatic light from a step index (n_{1} = 1.500; n_{2} = 1.485), multimode optical fiber of core diameter 100 μm 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 perpendicular to the axis of the fiber. The detector array is oriented parallel to the exit plane of the tip. The array consists of photo-detector elements each of 5 μm 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 ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 64

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. muscles) show up as high exposure regions(mapped near B).

If the exposure time is increased 10 times, while keeping the voltages and currents in the Xray machine constant, in the image,

Solution:

If the exposure is increased beyond the toe of the curve, the density begins to increase in direct proportion to log E. If the exposure is increase further, the density saturates after an intermediate region called the “shoulder”. In the saturated region, there is no further increase in the density of the developed grains as the exposure increases.

Optical density, D = −log_{10}E

Where E is the exposure given by integral of the intensity per unit area over the exposure time Δt intensity per unit area over the exposure time Δt

If exposure time is increased 10 times then optical density will be also increased.

For human eye, increase in optical density means decrease in brightness.

Hence, contrast decreases since B moves into the shoulder region.

*Answer can only contain numeric values

QUESTION: 65

For the given low-pass circuit shown in the figure, the cutoff frequency in Hz will be ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

### Instrumentation (IN) 2014 GATE Paper with solution

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