List of top Questions asked in GATE EE

Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch. When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to 50 MW and 80 MW respectively. At an overall incremental cost of 10,600 Rs./MWh, the power output of the units are 80 MW and 92 MW, respectively. The total plant MW-output (without overloading any unit) at an overall incremental cost of 11,800 Rs./MWh is ___________ (round off to the nearest integer).

A controller \( D(s) \) of the form \( (1 + K_D s) \) is to be designed for the plant \[ G(s) = \frac{1000\sqrt{2}}{s(s+10)^2} \] as shown in the figure. The value of \( K_D \) that yields a phase margin of \(45^\circ\) at the gain cross-over frequency of 10 rad/sec is __________ (round off to one decimal place). 

Consider a distribution feeder, with \( R/X \) ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is: \[ \text{(round off to three decimal places).} \]
The bus impedance matrix of a 3-bus system (in pu) is: \[ Z_{{bus}} = \begin{bmatrix} j0.059 & j0.061 & j0.038
j0.061 & j0.093 & j0.066
j0.038 & j0.066 & j0.110 \end{bmatrix} \] A symmetrical fault (through a fault impedance of \( j0.007 \) pu) occurs at bus 2. Neglecting pre-fault loading conditions, the voltage at bus 1 during the fault is: \[ {(round off to three decimal places).} \]

A single-phase half-controlled bridge converter supplies an inductive load with ripple-free load current. The triggering angle of the converter is \( 60^\circ \). The ratio of the rms value of the fundamental component of the input current to the rms value of the total input current of the bridge is (rounded off to 3 decimal places).

In the DC–DC converter shown in the figure, the current through the inductor is continuous. The switching frequency is \(500\,\text{Hz}\). 

The output voltage \(V_o\) across the load is assumed to be constant and ripple-free. 

The peak value of the inductor current (in amperes) is __________ (rounded off to the nearest integer). 


 

A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications: 

  • Rated armature voltage = 210 V
  • Rated armature current = 10 A
  • Rated speed = 1200 rpm
  • Armature resistance = 1 Ω
  • Input to the converter bridge = 240 V at 50 Hz

Assume that the motor is running at 600 rpm and the armature terminals are suitably reversed for regenerative braking.

If the armature current of the motor is to be maintained at the rated value, the triggering angle of the converter bridge (in degrees) should be ____________ (rounded off to two decimal places).

Motor and converter parameters: 

ParameterValue
Rated armature voltage210 V
Rated armature current10 A
Rated speed1200 rpm
Armature resistance1 Ω
Input to converter bridge240 V at 50 Hz

The armature of the DC motor is fed from the full-controlled bridge, and the field current is maintained constant.

A single-phase full bridge voltage source inverter (VSI) feeds a purely inductive load. The inverter output voltage is a square wave in \( 180^\circ \) conduction mode. The fundamental frequency of the output voltage is \( 50 \, \text{Hz} \). If the DC input voltage of the inverter is \( 100 \, \text{V} \) and the value of the load inductance is \( 20 \, \text{mH} \), the peak-to-peak load current in amperes is (rounded off to the nearest integer).

A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in dB) of the difference amplifier is (rounded off to 2 decimal places).
 

In the given circuit, the diodes are ideal. The current \( I \) through the diode \( D_1 \) in milliamperes is (rounded off to two decimal places).
 

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of \( G(s) \) are given in the table below. The value of the gain \( K_I \; (>0) \) required for a 50° phase margin is __________ (rounded off to two decimal places). 

Frequency response data of \( G(s) \): 

\(\omega\) (rad/s)Magnitude (dB)Phase (degrees)
0.5-7-40
1.0-10-80
2.0-18-130
10.0-40-200

System diagram:

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of \( G(s) \) has a constant slope of \( -20 \, \text{dB/decade} \) at least till \( 100 \, \text{rad/sec} \) with the gain crossover frequency being \( 10 \, \text{rad/sec} \). The asymptotic Bode phase plot remains constant at \( -90^\circ \) at least till \( \omega = 10 \, \text{rad/sec} \). The steady-state error of the closed-loop system for a unit ramp input is (rounded off to 2 decimal places).

 

Consider the closed-loop system shown in the figure with \[ G(s) = \frac{K(s^2 - 2s + 2)}{s^2 + 2s + 5}. \] The root locus for the closed-loop system is to be drawn for \( 0 \leq KLt;\infty \). The angle of departure (between \( 0^\circ \) and \( 360^\circ \)) of the root locus branch drawn from the pole \( (-1 + j2) \), in degrees, is (rounded off to the nearest integer).

The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being \( P_{max} \sin \delta \), where \( \delta \) is the load angle and the mechanical power input is \( 0.5 P_{max} \). A fault occurs on line 2 such that the power output of the generator is less than \( 0.5 P_{max} \) during the fault. After the fault is cleared by opening line 2, the power output of the generator is \( \frac{P_{max}}{\sqrt{2}} \sin \delta \). If the critical fault clearing angle is \( \pi/2 \) radians, the accelerating area on the power angle curve is _________________ times \( P_{max} \) (rounded off to 2 decimal places).

 

If ‘→’ denotes increasing order of intensity, then the meaning of the words [talk → shout → scream] is analogous to [please → \_\_\_\_\_ → pander]. Which one of the given options is appropriate to fill the blank?
\(P\) and \(Q\) have been allotted a hostel room with two beds, a study table, and an almirah. \(P\) is an avid birdwatcher and wants to sit at the table and watch birds outside the window. \(Q\) prefers a bed close to the ceiling fan. Which one of the following arrangements suits them the most?
The decimal number system uses the characters \(0, 1, 2, ..., 8, 9,\) and the octal number system uses the characters \(0, 1, 2, ..., 6, 7.\) For example, the decimal number \(12 (= 1 \times 10^1 + 2 \times 10^0)\) is expressed as \(14 (= 1 \times 8^1 + 4 \times 8^0)\) in the octal number system. The decimal number 108 in the octal number system is:
A shopkeeper buys shirts from a producer and sells them at 20\% profit. A customer has to pays Rs. 3186 including 18\% taxes per shirt. At what price did the shopkeeper buy each shirt?
If, for non-zero real variables \(x, y\) and a real parameter \(a>1\), \(x : y = (a+1) : (a-1)\). Then, the ratio \((x^2 - y^2) : (x^2 + y^2)\) is:
In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. Following a row \_\_ (i) \_\_ the shopkeeper \_\_ (ii) \_\_ the price of a frying pan, the cook stood \_\_ (iii) \_\_ a row to withdraw cash \_\_ (iv) \_\_ the ATM booth.
In the following figure, CD = 5 cm, BE = 10 cm, AE = 12 cm, \(\angle DAB = \angle DCB\), and \(\angle DAE = \angle DBC = 90^\circ\). Points AFCD create a rhombus. The length of BF (in cm) is:
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The chart below shows the data of the number of cars bought by Millennials and Gen X people in a country from the year 2010 to 2020 as well as the yearly fuel consumption of the country (in Million liters). Considering the data presented in the chart, which one of the following options is true?
\includegraphics[width=0.5\linewidth]{8.png}
The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate clockwise or anti-clockwise staying at its own center. Racks can translate towards the left (\(\leftarrow\)) or the right (\(\rightarrow\)) direction. If the object \(A\) (Rack) is translating towards the right (\(\rightarrow\)) direction, the correct statement among the following is:
\includegraphics[width=0.5\linewidth]{9.png}
A surveyor has to measure the horizontal distance from her position to a distant reference point \(C\). Using her position as the center, a 200 m horizontal line segment is drawn with the two endpoints \(A\) and \(B\). Points \(A\), \(B\), and \(C\) are not collinear. Each of the angles \(\angle CAB\) and \(\angle CBA\) are measured as \(87.8^\circ\). The distance (in m) of the reference point \(C\) from her position is nearest to:
Which one of the following matrices has an inverse?