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QUESTION: 1

**Q.1 – Q.5 Carry One Mark Each**

Q. An apple costs Rs.10. An onion costs Rs. 8.

Select the most suitable sentence with respect to grammar and usage.

Solution:

Based on the given sentences option ‘C’ is the correct sentence which is in the comparative degree.

Option ‘A’ and ‘B’ convey the wrong comparison and ‘D’ has double comparative and so they are wrong

QUESTION: 2

The Buddha said, “Holding on to anger is like "__ grasping"__ a hot coal with the intent of throwing it at

Someone else; you are the one who gets burnt.”

Select the word below which is closest in meaning to the word underlined above.

Solution:

The underlined word ‘__ grasping__’ means clutching or holding something tightly.

QUESTION: 3

**M** has a son **Q** and a daughter **R**. He has no other children.** E** is the mother of **P** and daughter-in-law of **M**. How is **P** related to **M**?

Solution:

Q and R is the son and Daughter’s of M, E is the mother of P and daughter-in-law of M means Q and E are married couples in the family

P is the grandchild of M

QUESTION: 4

The number that least fits this set: (324, 441, 97 and 64) is __________.

Solution:

In the given set of numbers, all are perfect squares but 97 is not

324 is square of 18 ⇒ (18)^{2} = 324

441 is square of 21 ⇒ (21)^{2} = 441

64 is square of 8 ⇒ (8)^{2} = 64

97 is not the square of any number

The number that least fits in given set is 97.

QUESTION: 5

It takes 10 s and 15 s, respectively, for two trains traveling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ______.

Solution:

QUESTION: 6

**Q.6 – Q.10 Carry Two Marks Each**

**Q.** The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the 7 seconds, how much will the odometer reading increase by (in m) ?

Solution:

The odometer reading increases from starting point to end point

Area of the given diagram = Odometer reading

Area of the velocity and time graph per second

QUESTION: 7

The overwhelming number of people infected with rabies in India has been flagged by the World Health Organization as a source of concern. It is estimated that inoculating 70% of pets and stray dogs against rabies can lead to a significant reduction in the number of people infected with rabies.

Which of the following can be logically inferred from the above sentences?

Solution:

Only option ‘A’ can be logically inferred from the information provided in the argument.

QUESTION: 8

A flat is shared by four first year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat?

Solution:

Manu age = sravan age + 2 months

Manu age = Trideep age – 3 months

Pavan age = Sravan’s age + 1 month

From this Trideep age > Manu > Pavan > Sravan

Trideep can occupy the extra space in the flat

QUESTION: 9

Find the area bounded by the lines 3x + 2y = 14, 2x –3y = 5 in the first quadrant.

Solution:

QUESTION: 10

A straight line is fit to a data set (ln x,y). This line intercepts the abscissa at In x = 0.1 and has a

slope of –0.02. What is the value of y at x = 5 from the fit?

Solution:

*Answer can only contain numeric values

QUESTION: 11

**Q.11 – Q.35 Carry One Mark Each**

Q. A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The value of m is __________.

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

Solution:

y = mx + c ------- (1)

Equation (1) passes through (0,0) we get C = 0

Equation (1) passes through (2,6), we get 6 = 2 m

m = 3

*Answer can only contain numeric values

QUESTION: 12

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

Solution:

*Answer can only contain numeric values

QUESTION: 13

A voltage V_{1} is measured 100 times and its average and standard deviation are 100 V and 1.5 V respectively. A second voltage V_{2}, which is independent of V_{1}, is measured 200 times and its average and standard deviation are 150 V and 2 V respectively. V_{3} is computed as: V_{3} = V_{1} + V_{2}.

Then the standard deviation of V_{3} in volt is ___________.

Solution:

QUESTION: 14

The vector that is NOT perpendicular to the vectors (i + j + k) and (I + 2j + 3k) is________.

Solution:

QUESTION: 15

In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1 + (1 - z) + (1 - z)^{2} + ………………

Then f(z) is

Solution:

f (z) = 1 + (1–z) + (1–z) 2 + …..

= 1 – (z – 1) + (z – 1)^{2} – (z – 1)^{3} + (z – 1)^{4}+ ….

*Answer can only contain numeric values

QUESTION: 16

Three currents i_{1}, i_{2} and i_{3} meet at a node as shown in the figure below, If i_{1} = 3 cos (ωt) ampere, i_{2} = 4 sin (ωt) ampere and i_{3} = I_{3} cos (ωt + θ) ampere, the value of I_{3} in ampere is ____________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 17

An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting skin effect) will be ___________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 18

A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial charge. The voltage across the capacitor for t > 2 s in volt is __________

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

Solution:

*Answer can only contain numeric values

QUESTION: 19

The signal x[n] shown in the figure below is convolved with itself to get y [n]. The value of y [-1] is _________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 20

In the circuit shown below (v_{1} + v_{2}) = [1 sin (2π 10000t) + 1 sin (2π 30000 t)] V. The RMS value of the current through the resistor R will be minimum if the value of the capacitor C in microfarad is _________.

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

Solution:

At parallel resonance impedance is maximum and current is minimum.

1^{st} circuit is under resonance at f = 10000 Hz and 2^{nd} circuit is under resonance at f = 30000 Hz

*Answer can only contain numeric values

QUESTION: 21

If X(s), the Laplace transform of signal x(t) is given by , then the value of x(t) as t → ∞ is ________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 22

The number of times the Nyquist plot of will encircle the origin clockwise is _______.

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

Solution:

Here nothing is said about feed back. Therefore G(s) must be treated as simple complex function not as open loop transfer function.

QUESTION: 23

The value of ao which will ensure that the polynomial s^{3} + 3s^{2} + 2s + a_{o} has roots on the left half of

the s-plane is

Solution:

C.E = s^{3} + 3s^{2} + 2s + a_{o}

*Answer can only contain numeric values

QUESTION: 24

The input i(t) = 2sin(3t + π) is applied to a system whose transfer function . The amplitude of the output of the system is__________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 25

The diode D used in the circuit below is ideal. The voltage drop V_{ab} across the 1 k? resistor in volt is _____.

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

Solution:

First diode is replaced by O.C.

*Answer can only contain numeric values

QUESTION: 26

In the circuit given below, the op amp is ideal. The output voltage V_{O} in volt is ______

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

Solution:

*Answer can only contain numeric values

QUESTION: 27

In the circuit given below, the diodes D_{1} and D_{2} have a forward voltage drop of 0.6 V. The opamp used is ideal. The magnitude of the negative peak value of the output V_{O} in volt is ________.

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

Solution:

QUESTION: 28

The Boolean expression XY + (X' + Y') Z is equivalent to

Solution:

QUESTION: 29

In the digital circuit given below, F is

Solution:

*Answer can only contain numeric values

QUESTION: 30

A 3 ½ digit DMM has an accuracy specification of __+__1% of full scale (accuracy class 1). A reading of 100.00 mA is obtained on its 200 mA full scale range. The worst case error in the reading in milliampere is __+__ _______

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

Solution:

*Answer can only contain numeric values

QUESTION: 31

A dc potentiometer, shown in figure below, is made by connecting fifteen 10? resistors and a 10? slide wire of length 1000 mm in series. The potentiometer is standardized with the current I_{P} = 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11 (11 numbers of the fixed 10? resistor are included) and the slide wire is on the 234^{th} mm position. The unknown voltage (up to four decimal places) in volt is ________.

Solution:

*Answer can only contain numeric values

QUESTION: 32

In the circuit given below, each input terminal of the op-amp draws a bias current of 10 nA. The effect due to these input bias currents on the output voltage VO will be zero, if the value of R chosen in **kilo-ohm** is _________.

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

Solution:

The value of ‘R’ chosen to make output voltage V_{o} due to input bias current to be zero is parallel combination of 30 K & 60 K

R=(30K//60K)

R = 20 k?

*Answer can only contain numeric values

QUESTION: 33

A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to 300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in millivolt is ________.

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

Solution:

For constant (DC) pressure peizo electric sensor will not respond so output is 0 Volt.

QUESTION: 34

The signal m(t) = cos(ω_{m}t) is SSB (single side-band) modulated with a carrier cos(ω_{c}t) to get s(t). The signal obtained by passing s(t) through an ideal envelope detector is

Solution:

QUESTION: 35

Let be a signal passed through an AWGN (additive white Gaussian noise) channel with noise power spectral density to get v(t). If v(t) is passed through a matched-filter that is matched to s(t), then output signal-to nose ratio (SNR) of the matched-filter is

Solution:

*Answer can only contain numeric values

QUESTION: 36

**36 – 65 Carry Two Marks Each**

Let f:[–1, 1] → R, where f(x) = 2x^{3} –x^{4 }–10. The minimum value of f(x) is _________.

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

Solution:

QUESTION: 37

An urn contains 5 red and 7 green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is

Solution:

*Answer can only contain numeric values

QUESTION: 38

Consider the matrix A whose eigen values are 1, –1 and 3. Then trace of (A^{3} – 3A^{2}) is ________.

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

Solution:

QUESTION: 39

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

X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K = 10

in appropriate units, the transfer function is

Solution:

*Answer can only contain numeric values

QUESTION: 40

The value of the integral where z is a complex number and C is a unit circle with

center at 1 + 0j in the complex plane is _________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 41

The current I_{x} in the circuit given below in milliampere is ________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 42

In the circuit shown below, The current Is is in phase with V_{s}. The magnitude of I_{s} in milliampere is __________.

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

Solution:

At resonance both I & V are in phase & Imaginary part is zero.

*Answer can only contain numeric values

QUESTION: 43

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 10 A and 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 watt is _________.

Solution:

*Answer can only contain numeric values

QUESTION: 44

In the strain gauge bridge circuit given below, R_{1} = R_{3} = R(1–x) and R_{2} = R_{4} = R(1+x) where R is 350?. The voltage sources v_{s} and ν_{n} represent the dc excitation and the undesired noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure that the output across a and b is low-pass filtered with cutoff frequency 150Hz is _______

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

Solution:

*Answer can only contain numeric values

QUESTION: 45

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

Solution:

QUESTION: 46

For the periodic signal x(t) shown below with period T = 8 s, the power in the 10^{th} harmonic is

Solution:

Given signal satisfies odd and half wave symmetry so it contains only odd harmonics. power in 10^{th} harmonic will be zero.

*Answer can only contain numeric values

QUESTION: 47

The fundamental period N_{0} of the discrete-time sinusoid is _______.

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

Solution:

QUESTION: 48

The transfer function G(s) of a system which has the asymptotic Bode plot shown below is

Solution:

It is a second order lead compensator at ω_{m }= 10 phase is maximum

QUESTION: 49

For the feedback system given below, the transfer function The system CAN NOT be stabilized with

Solution:

QUESTION: 50

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

Solution:

*Answer can only contain numeric values

QUESTION: 51

An ideal op-amp is used to realize a difference amplifier circuit given below having a gain of 10. If x = 0.025, the CMRR, the of the circuit in dB is ______.

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

Solution:

*Answer can only contain numeric values

QUESTION: 52

In the circuit given below, the op-amp is ideal. The input v_{x} is a sinusoid. To ensure v_{y} = v_{x}, the value of C_{N} in Pico-farad is ________.

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

Solution:

*Answer can only contain numeric values

QUESTION: 53

In the circuit given below, the op-amp is ideal. The value of current I_{L} in microampere is ______.

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

Solution:

QUESTION: 54

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

Solution:

QUESTION: 55

A synchronous counter using two J – K flip flops that goes through the sequence of states: Q_{1} Q_{2} =

00 → 10 → 01 → 11 → 00 …. Is required. To achieve this, the inputs to the flip flops are

Solution:

QUESTION: 56

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 of the memory module is connected to the y_{5} output of a 3 to 8 decoder with active low outputs. S_{0}, S_{1}, and S_{2} are the input lines to the decoder, with S_{2} as the MSB. The decoder has one active low and one active high EN_{2} enable lines a shown below. The address range(s) that gets mapped onto this memory module is (are)

Solution:

1 kB memory interfaced

*Answer can only contain numeric values

QUESTION: 57

A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a capacitance of 110 pF. When the frequency is doubled, the capacitance required for resonance is 20 pF. The distributed capacitance of the coil in pico farad is _______.

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

Solution:

*Answer can only contain numeric values

QUESTION: 58

The comparators (output = ‘1’, when input > 0 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 voltage of the exclusive-OR gate is 0V and 5V. The cutoff frequency of the low-pass filter is 0.1 Hz. For V_{1} = 1 sin (3000t + 36^{o}) V and V_{2} = 1 sin (3000t) V, the value of V_{O} in volt is _______.

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

Solution:

*Answer can only contain numeric values

QUESTION: 59

A 200 mV full scale dual-slope 3 ½ digit DMM has a reference voltage of 100 mV and a first integration time of 100 ms. For an input of [100 + 10 Cos (100πt)] mV, the conversion time (without taking the auto-zero phase time into consideration) in millisecond is ______.

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

Solution:

*Answer can only contain numeric values

QUESTION: 60

In the circuit below, the op-amp is ideal and the sensor is an RTD whose resistance R_{0} = 1000 (1+ 0.004 θ) ?, where θ is temperature in ^{o}C. The output sensitivity in mV/^{o}C is _____.

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

Solution:

*Answer can only contain numeric values

QUESTION: 61

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 μA. The i-to-v converter has a sensitivity of 100 mV/μA. For an input light intensity of 4 W/m^{2}, the output V_{O} in volt is _____.

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

Solution:

*Answer can only contain numeric values

QUESTION: 62

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 _______.

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

Solution:

*Answer can only contain numeric values

QUESTION: 63

The band gap 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 x10^{–15} eV s and speed of light c = 2.998 x 10^{8} m/s).

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

Solution:

*Answer can only contain numeric values

QUESTION: 64

The signal 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 kilohertz is ______.

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

Solution:

*Answer can only contain numeric values

QUESTION: 65

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 ______.

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

Solution:

### Instrumentation (IN) 2016 GATE Paper with solution

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