Practice Test: Gate Electrical Engineering GATE 2017 Paper - Electrical Engineering (EE) MCQ

There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

A test has twenty questions worth 100 marks in total.  There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

Directions:

Q. No. 6 – 10 Carry Two Marks Each

Q.

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot

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If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

“We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”The author‟s belief that ideology is not as important as literature is revealed by the word:

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X³ will have

The number of roots of e^x + 0.5x² - 2 = 0 in the range [ -5, 5] is

Directions:

Q. No. 11 – 35 Carry One Mark Each

Q.

In the circuit shown, the diodes are ideal, the inductance is small, and Io ≠ 0. Which one of the following statements is true?

For a 3-input logic circuit shown below, the output Z can be expressed as

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

When a unit ramp input is applied to the unity feedback system having closed loop transfer 
function  the steady state error will be

A three-phase voltage source inverter with ideal devices operating in 180^o conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is V_dc. The peak of the fundamental component of the phase voltage is

The figures show diagrammatic representations of vector fields  respectively. 
Which one of the following choices is true?

Assume that in a traffic junction, the cycle of traffic signal lights is 2 minutes of green(vehicle does not stop) and 3 minutes of red (vehicle stops). Consider the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time in minutes for the vehicle at the junction is _________

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.

The transfer function C (s ) of a compensator is given below.

The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is

The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α is a complex number with non-zero real and imaginary parts.

For the given circuit, Y_bus and Z_bus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 x 2. Which one of the following statements is true?

A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is

Let x and y be integers satisfying the following equations 

2x² + y² = 34

x + 2y = 11

The value of ( x +y ) is ________.

Consider a function f ( x, y, z ) given by

f(x,y,z) = (x² + y² -2z²) (x² + y² )

The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is

For the given 2-port network, the value of transfer impedance Z₂₁ in ohms is_______

The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ______. (Give the answer up to one decimal place.)

The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T₁ and T₂ are 90^o and 270^o , respectively.

The RMS value of the current through diode D₃ in amperes is _____

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 x 100. If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.

A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to

Two resistors with nominal resistance values R₁ and R₂ have additive uncertainties
ΔR₁ and ΔR₂ , respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

The nominal- π circuit of a transmission line is shown in the figure.

Impedance  and reactance X = 3300Ω . The magnitude of the characteristic impedance of the transmission line, in Ω , is _______________. (Give the answer up to one decimal place.)