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QUESTION: 1

A system is described by the following differential equation:

Where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is

Solution:

We know for inverse system

So the transfer function of inverse system is H_{1} =

It is given that

+ zy (t) = + x (t)

⇒ SY (S) + 2Y (S) = SX (S) + X (S)

⇒ Y (S + 2) = X (S) (S +1)

⇒ =

*Answer can only contain numeric values

QUESTION: 2

If v is a non-zero vector of dimension then the matrix A=vv^{T} has a rank = _______

Solution:

*Answer can only contain numeric values

QUESTION: 3

A periodic signal x(t) is shown in the figure. The fundamental frequency of the signal x (t) in Hz is________.

Solution:

Fince fundamental time period T_{0}=1 so the fundamental frequency f_{0}=1/T_{0}=1Hz

QUESTION: 4

The silicon diode, shown in the figure, has a barrier potential of 0.7 V. There will be no forward current flow through the diode, if V_{dc}, in volt, is greater than

Solution:

QUESTION: 5

For a first order low pass filter with unity d.c. gain and -3 dB corner frequency of 2000π rad/s, the transfer function is

Solution:

A first order LPF that satisfy unity D.C. Gain should of forms

QUESTION: 6

A and B are the logical inputs and X is the logical output shown in the figure. The output X is related to A and B by

Solution:

QUESTION: 7

The most suitable pressure gauge to measure pressure in the range of 10-4 to10-3 torr is

Solution:

Pirani Gauge is best suitable for the above range 10^{-4} to 10^{-3} torr Application is to measure ‘‘Vacuum Pressure

QUESTION: 8

The standard for long distance analog signal transmission in process control industry is

Solution:

In process industries, the control signal used is

Current → 4-20 mA

Pressure→ 3-15 psi

QUESTION: 9

If a continuous-time signal x (t) = cos (2πt) is sampled at 4 Hz, the value of the discrete-time sequence x(n) at n = 5 is

Solution:

x (t) = cos (2πt)

If the sampling interval is T_{s} then the sampled signal

QUESTION: 10

The term hysteresis is associated with

Solution:

Hyeres’s is need to be introduce in on off control to reduce the oscillation.

QUESTION: 11

A current waveform, i(t), shown in the figure, is passed through a Permanent Magnet Moving coil (PMMC) type ammeter. The reading of the ammeter up to two decimal places is

Solution:

Consider the PMMC as zero centered meter

Average value of the above signal is

QUESTION: 12

The connection of two 2-port networks is shown in the figure. The ABCD parameters of N1 and N2 networks are given as

The ABCD parameters of the combined 2-port network are

Solution:

QUESTION: 13

The figure shows a shape ABC and its mirror image A_{1}B_{1}C_{1 }across the horizontal axis (X - axis). The coordinate transformation matrix that maps ABC to A_{1}B_{1}C_{1} is

Solution:

B (x_{2 } y_{2}) → (x_{2 }- y_{2})

*Answer can only contain numeric values

QUESTION: 14

The differential amplifier, shown in the figure, has a differential gain of A_{d} = 100 and common mode gain of A_{c} = 0.1. If V_{1} = 5.01 V and V_{2} = 5.00V, then V_{0}, in volt (up to one decimal place) is ___________.

Solution:

Given

A_{c} = 0.1; V_{1} = 5.01V; V_{2} = 5.00V; A_{d} = 100

V_{0} = A_{d} V_{d} + A_{c} V_{c}

*Answer can only contain numeric values

QUESTION: 15

A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at Node-1 is – 1 V, then the voltage at Node-2 is _________V.

Solution:

I_{2} = 1 - (-1) = 2A

QUESTION: 16

The eigen values of the matrix

Solution:

*Answer can only contain numeric values

QUESTION: 17

The figure shows a phase locked loop. The output frequency is locked at f_{0} = 5kHz. The value of fi in kHz is __________.

Solution:

f_{0} = nf_{i}

f_{i} = 5/5 = 1kHz

QUESTION: 18

Identify the instrument that does not exist:

Solution:

To Measure power we require to coils (C.C & P.C)

→ Dynamo meter will consist two coils. So it can measure power.

→ Dynamo meter can also measure current and voltage, if we connect C.C & P.C in series.

→ Moving Iron meter will have only one coil, so it can measure current and voltage But not power.

Note: Moving Iron wattmeter doesn’t exist.

QUESTION: 19

The output V_{o} shown in the figure, in volt, is close to

Solution:

*Multiple options can be correct

QUESTION: 20

An 8-bit microcontroller with 16 address lines has 3 fixed interrupts i.e., Int1, Int2 and Int3 with corresponding interrupt vector addresses as 0008H. 0010H and 0018H. To execute a 32-byte long Interrupt Service Subroutine for Int1 starting at the address ISSI, The location 0008H onwards should ideally contain

Solution:

*Answer can only contain numeric values

QUESTION: 21

A series R-L-C circuit is excited with a 50V, 50 Hz sinusoidal source. The voltage across the resistance and the capacitance are shown in the figure. The voltage across the inductor (V_{L}) is __________V

Solution:

bc3 V_{R} = V = 50V ⇒ The circuit is at resonance

at resonance V_{L} = V_{c} ⇒ V_{L} = 50V

QUESTION: 22

The condition for oscillation in a feedback oscillator circuit is that at the frequency of oscillation, initially the loop gain is greater than unity while the total phase shift around the loop in degree is

Solution:

QUESTION: 23

Solution:

QUESTION: 24

The region of Convergence (ROC) of the Z-transform of a causal unit step discrete-time sequence is

Solution:

The Z-transform of unit step sequence is

QUESTION: 25

The pressure drop across an orifice plate for a particular flow rate is 5 kg/m^{2}. If the flow rate is doubled (within the operating range of the orifice), the corresponding pressure drop in kg/m^{3} is

Solution:

In case of an orifice plate

*Answer can only contain numeric values

QUESTION: 26

The two-input voltage multiplier, shown in the figure, has a scaling factor of 1 and produces voltage output. If V_{1 }=+15V and V_{2} =+3V, the value of V_{0} in volt is _________.

Solution:

Given V_{1} = 15V; V_{2}= 3V

U sin g nodal analysis

*Answer can only contain numeric values

QUESTION: 27

For the circuit, shown in the figure, the total real power delivered by the source to the loads is _________kW

Solution:

*Answer can only contain numeric values

QUESTION: 28

The magnetic flux density of an electromagnetic flow meter is 100 mWb/m^{2}. The electrodes are wall-mounted inside the pipe having a diameter of 0.25m. A voltage of 1V is generated when a conducting fluid is passed through the flow meter. The volumetric flow rate of the fluid in m^{3}/s is ____________.

Solution:

*Answer can only contain numeric values

QUESTION: 29

In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by I_{D} = 1/2 (V_{GS} -1)^{2} mA, where V_{GS} is in V. If V_{s} = +5V, then the value of R_{S} in kΩ is _________.

Solution:

Given

*Answer can only contain numeric values

QUESTION: 30

The hot junction of a bare thermocouple, initially at room temperature (30^{°}C), is suddenly dipped in molten metal at t = 0s. The cold junction is kept at room temperature. The thermocouple can be modeled as a first-order instrument with a time constant of 1.0s and a static sensitivity of 10 μV/^{°}C. If the voltage, measured across the thermocouple indicates 10.0 mV at t = 1.0s, then the temperature of the molten metal in ^{°}C is __________.

Solution:

*Answer can only contain numeric values

QUESTION: 31

A series R-L-C circuit is excited with an a.c. voltage source. The quality factor (Q) of the circuit is given as Q = 30. The amplitude of current in ampere at upper half-power frequency will be __________.

Solution:

*Answer can only contain numeric values

QUESTION: 32

An angle modulated signal with carrier frequency is given by The maximum deviation of the frequency in the angle modulated signal from that of the carrier is _________ kHz.

Solution:

QUESTION: 33

Three DFT coefficients, out of five DFT coefficients of a five-point real sequence are given as as: X (0) = 4, X (1) = 1 - j1 and X (3) = 2+ j2. The zero-th value of the sequence x(n), x(0), is

Solution:

We know for N point DFT (for real sequence)

It is given that

x (0) = 4

x (1) = 1 - j1

x (3) = 2 + j2

u sin g equation (1)

x (2) = x * (5 - 2) = x * (3) = (2 +j2)* = 2 - j2

x (4) = x * (5 - 4) = x * (1) = (1 - j1) * = 1 + j1

u sin g equation (2)

QUESTION: 34

A closed-loop system is shown in the figure. The system parameter a is not known. The condition for asymptotic stability of the closed loop system is

Solution:

The characteristic equation of the unity feedback system is 1 + G(S) = 0

By R-H criterian if the equation is of form as^{3} + bs^{2} + cs + d = 0 then the condition for stability is bc > ad,

Using this

(2a) (α + 1) > (α + 1).1 ⇒ 2α > 1 ⇒ α > 0.5

*Answer can only contain numeric values

QUESTION: 35

The power delivered to a single phase inductive load is measured with a dynamometer type wattmeter using a potential transformer (PT) of turns ratio 200:1 and the current transformer (CT) of turns ratio 1:5. Assume both the transformers to be ideal. The power factor of the load is 0.8. If the wattmeter reading is 200W, then the apparent power of the load in kVA is _________.

Solution:

QUESTION: 36

The overall closed loop transfer function C(s) / R(s), represented in the figure, will be

Solution:

The Parallel connection of G_{1},G_{2} can be replaced by G_{1}+ G_{2}.

(G_{1}+G_{2}) forms a feedback loop with H_{1}, it can be replaced by

Final considering G3 and the unity feedback

*Answer can only contain numeric values

QUESTION: 37

When the voltage across a battery is measured using a d.c. potentiometer, the reading shows 1.08V. But when the same voltage is measured using a Permanent Magnet Moving Coil (PMMC) voltmeter, the voltmeter reading shows 0.99V. If the resistance of the voltmeter is 1100Ω, the internal resistance of the battery, in Ω, is _________.

Solution:

We use potentiometer to measure unknown voltages (very low) it is a Null type instrument

→ The Galvanometer reads zero when the voltage drop across slide wire and unknown Battery voltages are equal.

→ Given that potentiometer reading as 1.08V i.e., The Battery voltage will be 1.08 volts.

PMMC reads,

v_{m} = 0.99V.

V = 1.08 - 0.99

V = 0.09 Volts.

QUESTION: 38

The probability that a communication system will have high fidelity is 0.81. The probability that the system will have both high fidelity and high selectivity is 0.18. The probability that a given system with high fidelity will have high selectivity is

Solution:

Let A, B be the events respectively that the communication system will have high fidelity, high selectivity then

*Answer can only contain numeric values

QUESTION: 39

The current response of a series R-L circuit to a unit step voltage is given in the table. The value of L is ___________H.

Solution:

We know i(t) = 0.5-0.5

*Answer can only contain numeric values

QUESTION: 40

A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If V_{o} = +2.0V, then the value of x is __________.

Solution:

At the inverting terminal of the op-amp

i.e., at V_{(-)}

By virtual ground V_{(t) }= V_{(-)}= 0

*Answer can only contain numeric values

QUESTION: 41

The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between ±7 V. The width of the hysteresis band is _________V.

Solution:

When zener diode combination maintains output of ±7V

Width of hysteresis band = V_{UTP} - V_{LTP} = 0.333 - (- 0.333) = 0.666V

*Answer can only contain numeric values

QUESTION: 42

The loop transfer function of a closed-loop system is given by G (s) H (s) = . The

breakaway point of the root-loci will be ____________.

Solution:

To obtain the Break point first of all we have to arrange K intevms of GH, then the roots of dk/ds= 0 gives break point

To decide which among the two root is Breakaway draw the pole zero plot & mark real axis branch.

*Answer can only contain numeric values

QUESTION: 43

The unbalanced voltage of the Wheatstone bridge, shown in the figure, is measured using digital voltmeter having infinite input impedance and a resolution of 0.1mV. If R = 1000Ω, then the minimum value of ΔR in Ω to create a detectable unbalanced voltage is _________.

Solution:

*Answer can only contain numeric values

QUESTION: 44

In the circuit diagram, shown in the figure, S_{1} was closed and S_{2 }was open for a very long time. At t = 0, S_{1} is opened and S_{2} is closed. The voltage across the capacitor, in volt, at t = 5 ms is ___________.

Solution:

*Answer can only contain numeric values

QUESTION: 45

The block diagram of a closed-loop control system is shown in the figure. The values of k and kp are such that the system has a damping ratio of 0.8 and an undamped natural frequency of 4 rad/s respectively. The value of kp will be ___________.

Solution:

1+GH=0 represent the characteristic equation of the close loop –ve feed back system

*Answer can only contain numeric values

QUESTION: 46

Assuming the op-amp shown in the figure to be ideal, the frequency at which the magnitude of V_{o} will be 95% of the magnitude of V_{in} is ____________kHz.

Solution:

QUESTION: 47

The following table lists an n^{th} order polynomial f (x) = a_{n} x^{n} + a_{n -1}x^{n -1} + - - - + a_{1}x + a_{0} and the forward differences evaluated at equally spaced values of x. The order of the polynomial is

Solution:

Clearly the entries in the fourth forward difference (i.e.Δ^{4}f ) are all same which is 0.0072

The order of the polynomial is 4.

QUESTION: 48

Consider two discrete-time signals:

x_{1 }(n) = {1,1} and x_{2} (n) {1,2}, for n = 0.1.

The Z-transform of the convoluted sequence x (n) = x_{1} (n) * x_{2} (n) is

Solution:

*Answer can only contain numeric values

QUESTION: 49

In the a.c. bridge, shown in the figure, R = 10^{3} Ω and C = 10^{-7} F. If the bridge is balanced at a frequency , the value of in rad/s is __________.

Solution:

According to bridge balancing condition

*Answer can only contain numeric values

QUESTION: 50

The junction semiconductor temperature sensor shown in the figure is used to measure the temperature of hot air. The output voltage V_{o} is 2.1V. The current output of the sensor is given by I = TμA where T is the temperature in K. Assuming the opamp to be ideal, the temperature of the hot air in ^{o}C is approximately ___________.

Solution:

*Answer can only contain numeric values

QUESTION: 51

In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by , where is the carrier frequency and is the modulation frequency. The power carried by the sidebands in % of total power is __________%

Solution:

Given amplitude modulated signal

Power carried by the side bands in % of total power = 625/5625 = 11.11%

*Answer can only contain numeric values

QUESTION: 52

The angle between two vectors in radian is

_________.

Solution:

*Answer can only contain numeric values

QUESTION: 53

Quantum efficiency of a photodiode (ratio between the number of liberated electrons and the number of incident photons) is 0.75 at 830 nm. Given Plank’s constant h , the charge of an electron and the velocity of light in the photodiode . For an incident optical power of 100 mW at 830 nm, the photocurrent in μA is ___________.

Solution:

QUESTION: 54

The two inputs A and B are connected to an R-S latch via two AND gates as shown in the figure. If A = 1 and B = 0, the output is

Solution:

It is similar to JKFF A = J, B = K

*Answer can only contain numeric values

QUESTION: 55

The Laplace transform of a causal signal y (t) is y (s) = . The value of the signal y(t) at t = 0.1 s is __________ unit.

Solution:

QUESTION: 56

The event would have been successful if you ______ able to come.

Solution:

QUESTION: 57

Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red and blue.Proposition: If a card has an even value on one side, then its opposite face is red.

The cards which MUST be turned over to verify the above proposition are

Solution:

To check even ⇒ red, we must confirm that back of 2 is red and back of blue is an odd number.

QUESTION: 58

What is the value of x when

Solution:

QUESTION: 59

There was no doubt that their work was** " thorough."**

Which of the words below is closest in meaning to the underlined word above?

Solution:

QUESTION: 60

Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

Solution:

QUESTION: 61

Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

Solution:

People coming out in the same order in which they enter indicates that the centre operates on a first-come-first-serve basis.

QUESTION: 62

The points in the graph below represent the halts of a lift for durations of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

(i) The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

(ii) The elevator stays on the fourth floor for the longest duration over the one hour period

Solution:

(i) is incorrect as it moves directly

(ii) is incorrect as it stayed for maximum duration on ground floor.

QUESTION: 63

A map show the elevations of Darjeeling, Gangtok, Kalimpong, Pelling, and Siliguri, Kalimpong is at a lowest elevation than Gangtok. Pelling is at a lower elevation than Gangtok.Pelling is at a higher elevation than Siliguri. Darjeeling is at a higher elevation than Gangtok.

Which of the following statements can be inferred from the paragraph above?

(i) Pelling is at a higher elevation than Kalimpong

(ii) Kalimpong is at a lower elevation than Darjeeling

(iii) Kalimpong is at a higher elevation than Siliguri

(iv) Siliguri is at a lower elevation than Gangtok

Solution:

The given information is K<G, P<G, S<P and G<D

From these it can be inferred

S<P<G<D and also K<G

So K<D as well but no comparison between K and S (or) K and P is given.

QUESTION: 64

P, Q, R, S, T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true?

Solution:

Following two possibilities can be drawn

Given in question P and U interchange then new diagram can be drawn.

now only option (C) verifies.

QUESTION: 65

Budhan covers a distance of 19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

Solution:

Let cycling speed = c and walking speed = w

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