Mock GATE Exam - 2019 - Electrical Engineering

The determinant of a 2x2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is  ________

The product of two complex numbers 1 + i and 2 - 5i is

• 7 - 3i

• 3 - 4i

• - 3 - 4i

• 7 + 3i

Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is

• 1/72

• 1/55

• 1/36

• 1/27

In the figure, the value of resistor R is (25 + I/2) ohms, where I is the current in amperes. The current I is ________

The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is __________. ________

Suppose the maximum frequency in a band-limited signal x(t)xt is 5 kHz. Then, the maximum frequency in x(t)cos(2000πt) , in kHz, is  ________

A separately excited DC motor runs at 1000 rpm on no load when its armature terminals are connected to a 200V DC source and the rated voltage is applied to the field winding. The armature resistance of this motor is 1Ω. The no-load armature current is negligible. With the motor developing its full load torque, the armature voltage is set so that the rotor speed is 500 rpm. When the load torque is reduced to 50% of the full load value under the same armature voltage conditions, the speed rises to 520 rpm. Neglecting the rotational losses, the full load armature current (in Ampere) is ________

The Maxwell's bridge shown in the figure is at balance. The parameters of the inductive coil are

• R =R₂R₃ / R₄, L = C₄R₂R₃

• L =R₂R₃ / R₄, R = C₄R₂R₃

• R =R₄ / R₂R₃, L = 1/(C₄R₂R₃)

• L =R₄ / R₂R₃, R = 1/(C₄R₂R₃)

A 0-1 Ampere moving iron ammeter has an internal resistance of 50mΩ  and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in mΩ of the shunt coil respectively are

• 1,2

• 5.55,2

• 2, 5.55

• 2,1

For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions Q_AQ_BQ_C=Q’_AQ’_BQ’_C=100. The minimum number of clock cycles after which the output Z would again become zero is  ________

The Octal equivalent of HEX and number AB.CD is

• 253.314

• 253.632

• 526.314

• 526.632

The inverse Laplace transform of 1/(s^2+s)  is 

• 1+e^t

• 1+e^-t

• 1-e^-t

• None

What is the adverb for the given word below? Misogynous

• Misogyousness

• Misogynity

• Misogynously

• Misogynous

The function y = |2 - 3x|

• Is continuous ∀x ∈ R and differentiable ∀x ∈ R

• Is continuous ∀x ∈ R and differentiable ∀x ∈ R except at x = 3/2

• Is continuous ∀x ∈ R and differentiable ∀x ∈ R except at x = 2/3

• Is continuous ∀x ∈ R except at x=3 and differentiable∀x ∈ R

In the 4×1 multiplexer, the output F is given by F=A⊕B . Find the required input ' I₃ I₂ I₁ I₀'.

• 1010

• 0110

• 1000

• 1110

Choose the most appropriate alternative from the options given below to complete the following sentence: Despite several ___________ the mission succeeded in its attempt to resolve the conflict.

• Attempts

• Setbacks

• Meetings

• Delegations

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

• 210 and 140

• 162.5 and 187.5

• 245 and 130

• 175 and 200

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is

• 5

• 12

• 15

• 20

Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson’s rule is Angle (degree) 0 60 120 180 240 300 360 Torque (Nm) 0 1066 -323 0 323 -355 0

• 542

• 993

• 986

• None

The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?

• 4

• 5

• 6

• 7

If V_A-V_B=6V, then V_C-V_D is

• –5V

• 2V

• 3V

• 6V

The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?

•  It corresponds to a frequency greater than K

• It corresponds to a frequency less than K

• It corresponds to a frequency K

• Root locus of modified system never transits to unstable region

For the network shown in the figure below, the frequency (in rad/s) at which the maximum phase lag occurs is, ___________. 

• 0.3

• 0.4

• 0.5

• 0.6

Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged

• P, Q

• Q, R

• P, R

• R, S

For the circuit given above, the Thevenin’s voltage across the terminals A and B is

• 1.25 V

• 0.25 V

• 1 V

• 0.5 V

A 4 point starter is used to start and control the speed of a

• Dc shunt motor with armature resistance control

• Dc shunt motor with field weakening control

• Dc series motor

• Dc compound motor

A cascade of 3 Linear Time Invariant systems is causal and unstable. From this, we conclude that

• Each system in the cascade is individually causal and unstable

• At least one system is unstable and at least one system is causal

• At least one system is causal and all systems are unstable

• The majority are unstable and the majority are causal

The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time t₁ by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle δδ shows the transient correctly?

The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is

• 0.029

• 0.034

• 0.039

• 0.044

A single-phase, 22 kVA, 2200 V/ 220 V, 50 Hz, distribution transformer is to be connected as an auto-transformer to get an output voltage of 2420 V. Its maximum kVA rating as an autotransformer is

• 24

• 42

• 242

• 2442

Nyquist plot of two functions  G1(s) and  G2(s) are shown in figure. Nyquist plot of the product of G1 (s) and G2(s)  is

The phase cross-over frequency of the transfer function G(S)=100/(S+1)^3  in rad/s is

• √3

• 1/√3

• 3

• 3√3

Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below is NOT logically possible, based on the given fact?

• If (iii), then (iv)

• If (i), then (iii).

• If (i), then (ii).

• If (ii), then (iv).

After the discussion, Tom said to me, 'Please revert!'. He expects me to _________.

• Retract

• Get back to him

• Move in reverse

• Retreat

The integral ∮_C(ydx−xdy)  is evaluated  along the circle  x^2+y^2=1/4 traversed in counter clockwise direction.The integral is equal to

• 0

• π/4

• −π/2

• None

The area of a triangle formed by the tips of vectors a¯, b¯and c¯ is

• 0.5(a¯−b¯)⋅(a¯−c¯)

• 0.5  * ∣ (a¯−b¯)×(a¯−c¯)  ∣

• 0.5 * (a¯×b¯)⋅c¯

• None

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are release but are constrained to move along the same straight line. Which of these will collide first?

• The particles will never collide

• All will collide together

• Proton and neutron

• Electron and neutron

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

• 155

• 156

• 157

• 158

A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, start connected through a star-delta transformer as shown in the figure. The line-to-line voltage rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected and Is¯=100∠0° A, then what is the value of  Ip¯ in Ampere?

• 200∠30∘

• 50∠30∘

• Zero

• None

In the following sequential circuit, the initial state (before the first clock pulse ) of the circuit is  Q1Q0= 00. The state (Q1Q0), immediately after the 333rd clock pulse is

• 00

• 01

• 10

• 11

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

• 25

• 50

• 100

• 200

A distribution feeder of 1 km length having resistance, but negligible reactance, is fed from both the ends by 400V, 50 Hz balanced sources. Both voltage sources S₁ and S₂ are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure. The contributions of S₁ and S₂ in 100 A current supplied at location P respectively, are

• 75 A and 25 A

•  0 A and 100 A

• 50 A and 50 A

• 25 A and 75 A

A single-phase thyristor-bridge rectifier is fed from a 230 V, 50 Hz, single-phase AC mains. If it is delivering a constant DC current of 10 A, at firing angle of 30^o, then value of the power factor at AC mains is  

• 0.87

• 0.9

• 0.78

• Zero

Let x(t) be a periodic signal with time period T,Let y(t)=x(t-t₀)+x(t+t₀) for some t₀.The Fourier Series coefficients of y(t) are denoted by b_k. if b_k=0 for all odd k,then t₀ can be equal to

• T/8

• T/4

• T/2

• 2T

The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are

• 2 and 3

• 5 and 2

• 3 and 4

• 4 and 3

Given digits 2, 2, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

• 50

• 51

• 52

• 53

A zero mean random signal is uniformly distributed between limits −a and +a and its mean square value is equal to its variance. Then the r.m.s value of the signal is

• A/√3

• A/√2

• A√3

• None