Practice Test: Gate Electrical Engineering GATE 2014 Paper

What is the average of all multiples of 10 from 2 to 198?

The value of  

Q.No. 6 – 10 Carry Two Marks Each

The old city of Koenigsberg, which had a German majority population before World War 2, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east respectively. Which of the statements below can be inferred from this passage?

The number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in north India is twice the number diagnosed last year. Municipal authorities have concluded that measures to control the mosquito population have failed in this region.
Which one of the following statements, if true, does not contradict this conclusion?

If x is real and    then possible values of  include

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009?

At what time between 6 a.m. and 7 a.m will the minute hand and hour hand of a clock make an angle closest to 60°?

Q.No. 11 – 35 Carry One Mark Each

Which one of the following statements is true for all real symmetric matrices?

Consider a dice with the property that the probability of a face with n dots showing up is proportional to n. The probability of the face with three dots showing up is_________.

Maximum of the real valued function f(x)= (x −1)^2/3 occurs at x equal to

All the values of the multi-valued complex function 1ⁱ, where i= √1 , are

Consider the differential equation  Which of the following is a solution to this differential equation for x > 0?

Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are 380μH and 240μH . Their mutual inductance in μH is ________

The switch SW shown in the circuit is kept at position ‘1’ for a long duration. At t = 0+, the switch is moved to position ‘2’ Assuming |V₀₂| > |V₀₁| , the voltage V_c (t) across capacitor is

A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is place symmetrically with respect to the plates.

If the potential difference between one of the plates and the nearest surface of dielectric interface is 2Volts, then the ratio is

Consider an LTI system with transfer function If the input to the system is cos(3t) and the steady state output is Asin(3t + α), then the value of A is

Consider an LTI system with impulse response h(t) = e^-5t u (t). If the output of the system is  then the input, x(t), is given by

Assuming an ideal transformer,. The Thevenin’s equivalent voltage and impedance as seen from the terminals x and y for the circuit in figure are

A single phase, 50kVA, 1000V/100V two winding transformer is connected as an autotransformer as shown in the figure. The kVA rating of the autotransformer is

A three-phase, 4pole, self excited induction generator is feeding power to a load at a frequency f₁. If the load is partially removed, the frequency becomes f₂. If the speed of the generator is maintained at 1500 rpm in both the cases, then

A single phase induction motor draws 12 mW power at 0.6 lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to 0.8 lagging. Assuming that the real and reactive power drawn by the motor remains same as before, the reactive power delivered by the capacitor in MVAR is ____________.

A three phase star-connected load is drawing power at a voltage of 0.9 pu and 0.8 power factor lagging. The three phase base power and base current are 100MVA and 437.38A respectively. The line-to line load voltage in kV is ___________.

Shunt reactors are sometimes used in high voltage transmission system to

The closed-loop transfer function of a system is  The steady state error due to unit step input is ________.

The state transition matrix for the system

The saw-tooth voltage wave form shown in the figure is fed to a moving iron voltmeter. Its reading would be close to ______________

While measuring power of a three-phase balanced load by the two-wattmeter method, the readings are 100W and 250 W. The power factor of the load is ______________.

Which of the following is an invalid state in an 8-4-2-1. Binary Coded Decimal counter

The transistor in the given circuit should always be in active region. Take V_CE(sat) = 0.2V. V_EE = 0.7V. The maximum value of RC in  which can be used is __________.

A sinusoidal ac source in the figure has an rms value of   Considering all possible values of RL, the minimum value of RS in W to avoid burnout of the Zener diode is ________.

A step-up chopper is used to feed a load at 400 V dc from a 250 V dc source. The inductor current is continuous. If the ‘off’ time of the switch is 20μs, the switching frequency of the chopper is kHz is __________.

In a constant V/f control of induction motor, the ratio V/f is maintained constant from 0 to base frequency, where V is the voltage applied to the motor at fundamental frequency f. Which of the following statements relating to low frequency operation of the motor is TRUE?

Q.No. 36 – 65 Carry Two Marks Each

To evaluate the double integral  we make the substitution    and v = y/2 . The integral will reduce to

Let X be a random variable with probability density function

The probability P(0.5<x<5) is

The minimum value of the function  in the interval [-3. 3] is

Assuming the diodes to be ideal in the figure, for the output to be clipped, the input voltage v_i must be outside the range

The voltage across the capacitor, as sown in the figure, is expressed as 

The value of A₁ and A₂ respectively, are

The total power dissipated in the circuit, show in the figure, is 1kW.

The voltmeter, across the load, reads 200 V. The value of X_L is _________.

The magnitude of magnetic flux density  at a point having normal distance d meters from an infinitely extended wire carrying current of l A is μ₀I/2nd (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2A current in the +ve y direction μ₀ is permeability of free space Assume  to be unit vectors along x, y and z axes respectively.

Assuming right handed coordinate system, magnetic field intensity,  at coordinate (2,1,0) will be

A discrete system is represented by the difference equation

It has initial condition  The pole location of the system for a = 1, are

An input signal x(t) = 2 + 5sin(100πt) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by

where, N represents the number of samples per cycle. The output y(n) of the system under steady state is

A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is

A 250 V dc shunt machine has armature circuit resistance of 0.6 and field circuit resistance of125 . The machine is connected to 250 V supply mains. The motor is operated as a generator and then as a motor separately. The line current of the machine in both the cases is 50 A. The ratio of the speed as a generator to the speed as a motor is ____________.

A three-phase slip-ring induction motor, provided with a commutator winding, is shown in the figure. The motor rotates in clockwise direction when the rotor windings are closed.

If the rotor winding is open circuited and the system is made to run at rotational speed f_r with the help of prime-mover in anti-clockwise direction, then the frequency of voltage across slip rings is f₁ and frequency of voltage across commutator brushes is f₂. The values of f₁ and f₂ respectively are

A 20-pole alternator is having 180 identical stator slots with 6 conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize single-phase winding, the generated voltage is V₁. If the coils are reconnected to realize three-phase star-connected winding, the generated phase voltage is V₂. Assuming full pitch, single-layer winding, the ratio V₁/V₂ is

For a single phase, two winding transformer, the supply frequency and voltage are both increased by 10%. The percentage changes in the hysteresis loss and eddy current loss, respectively, are

A synchronous generator is connected to an infinite bus with excitation voltage Ef = 1.3 pu. The generator has a synchronous reactance of 1.1 pu and is delivering real power (P) of 0.6 pu to the bus. Assume the infinite bus voltage to be 1.0 pu. Neglect stator resistance. The reactive power (Q) in pu supplied by the generator to the bus under this condition is _________.

There are two generators in a power system. No-load frequencies of the generators are 51.5 Hz and 51Hz, respectively, and both are having droop constant of 1 Hz/MW. Total load in the system is 2.5 MW. Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in Hz in the steady state is __________.

The horizontally placed conductors of a single phase line operating at 50 Hz are havingoutside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854×10⁻¹² . The capacitance to ground per kilometer of each line is

A three phase, 100 MVA, 25 kV generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are 0.2 pu, 0.2 pu, and 0.05 pu, respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is _________.

A system with the open loop transfer function:  is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of K is ______

For the transfer function 

The values of the constant gain term and the highest corner frequency of the Bode plot respectively are

The second order dynamic system has the matrices P, Q and R as follows:

The system has the following controllability and observability properties:

Suppose that resistors R₁ and R₂ are connected in parallel to give an equivalent resistor R. If resistors R₁ and R₂ have tolerance of 1% each., the equivalent resistor R for resistors R₁ = 300 and R₂ = 200 will have tolerance of

Two ammeters X and Y have resistances of 1.2 and 1.5 respectively and they give full scale deflection with 150 mA and 250 mA respectively. The ranges have been extended by connecting shunts so as to give full scale deflection with 15 A. The ammeters along with shunts are connected in parallel and then placed in a circuit in which the total current flowing is 15A. The current in amperes indicated in ammeter X is __________.

An oscillator circuit using ideal op-amp and diodes is shown in the figure

 The time duration for +ve part of the cycle is Δt₁ and for-ve part is Δt₂ .The value of  will be___________.

The SOP (sum of products) form of a Boolean function is  , where inputs are A,B,C,D (A is MSB, and D is LSB). The equivalent minimized expression of the function is

A JK flip flop can be implemented by T flip-flops. Identify the correct implementation.

In an 8085 microprocessor, the following program is executed

At the end of program, register A contains

A fully controlled converter bridge feeds a highly inductive load with ripple free load current. The input supply (v_s) to the bridge is a sinusoidal source. Triggering angle of the bridge converter is α = 30°. The input power factor of the bridge is_________.

A single-phase SCR based ac regulator is feeding power to a load consisting of 5 resistance and 16 mH inductance. The input supply is 230 V, 50 Hz ac. The maximum firing angle at which the voltage across the device becomes zero all throughout and the rms value of current through SCR, under this operating condition, are

The SCR in the circuit shown has a latching current of 40 mA. A gate pulse of 50 μs is applied to the SCR. The maximum value of R in  to ensure successful firing of the SCR is _________.