Electrical Engineering - GATE 2018 Paper Solution

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“Since you have gone off the ________, the _________ sand is likely to damage the car.”

The words that best fill the blanks in the above sentence are

“A common misconception among writers is that sentence structure mirrors thought; the more _________ the structure, the more complicated the ideas.”

The word that best fills the blank in the above sentence is

The three roots of the equation $ f(x)=0 $ are x = {-2, 0, 3}. What are the three values of $ x $ for which $ f\;(x-3)=0\;? $

For what values of $ k $ given below is $ \textstyle\frac{(k+2)^2}{k-3} $ an integer?

Functions $ F(a,b) $ and $ G(a,b) $ are defined as follows:

$ F(a,b)=(a,b)^2 $ and $ G(a,b)=\left|a-b\right| $ , where $ \left|x\right| $ represents the absolute value of $ x $ What would be the value of $ \style{font-family:'Times New Roman'}{G(F(1,3),G(1,3))?} $ 

An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%. Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design?

Blue Black Red Yellow
40% 25% 20% 15%

P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.

(i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.

(ii) P is unable to row when someone else is in the boat.

(iii) Q is unable to row with anyone else except R.

(iv) Each person rowed for at least one trip. (v) Only one person can row during a trip.

Who rowed twice?

A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is

In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is

A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current?

 

Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are)

 

Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is

Consider a lossy transmission line with $ V_1 $ and $ V_2 $ as the sending and receiving end voltages, respectively $ Z $ and $ X $. are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be

The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

In the figure, the voltages are $ v_1(t)=100\cos\left(wt\right),\;v_2(t)=100\cos\left(wt+\mathrm\pi18\right)\;\; $ and $ v_3(t)=100\cos\left(wt+\mathrm\pi36\right) $. The circuit is in sinusoidal steady state, and $ R<<wL.P_1,P_2\; $ and $ P_3 $ are the average power outputs. Which one of the following statements is true?

 

Match the transfer functions of the second-order systems with the nature of the systems given below. 

Transfer functions 
Nature of system 
$ \style{font-family:'Times New Roman'}{P:\;\frac{15}{s^2+5s+15}} $   I:  Overdamped  
$ \style{font-family:'Times New Roman'}{Q:\;\frac{25}{s^2+10s+25}} $ II: Critically damped
$ \style{font-family:'Times New Roman'}{R:\;\frac{35}{s^2+18s+35}} $  III: Underdamped

 

A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take $ \in_0=8.85\times10^{-12} $ F/m. The $ Z $ component of the E field at (0, 0, 0.1) is closest to

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