GATE EE 2015 PYQ

Consider the circuit shown in the figure. In this circuit R=1k , and C=1 F. The input voltage is sinusoidal with a frequency of 50 Hz, represented as a phasor with magnitude and phase angle 0 radian a

In the given circuit, the silicon transistor has =75 and a collector voltage =9 V. Then the ratio of and is ________.

Of the four characteristics given below, which are the major requirements for an instrumentation amplifier? P. High common mode rejection ratio Q. High input impedance R. High linearity S. High output

The op-amp shown in the figure has a finite gain A = 1000 and an infinite input resistance. A step-voltage is applied at the input at time t=0 as shown. Assuming that the operational amplifier is not

The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is . The amplitude of the output voltage (in Volt) is _______.

In the following circuit, the transistor is in active mode and =2 V. To get =4 V, we replace with . Then the ratio is ______.

The saturation voltage of the ideal op-amp shown below is 10 V. The output voltage of the following circuit in the steady-state is

The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown in Figure (c). The cut-off frequencies of F1 and F2 are respectively. If , the resultant circuit exh

When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector-base (CB) and the base-emitter (BE) junctions?

Nyquist plots of two functions are shown in figure. Nyquist plot of the product of is

In the signal flow diagram given in the figure, are possible inputs whereas are possible outputs. When would the SISO system derived from this diagram be controllable and observable?

The unit step response of a system with the transfer function is given by which one of the following waveforms?

Find the transfer function of the system given below.

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 suppo

A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

For the system governed by the set of equations: the transfer function Y(s)/U(s) is given by

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at (2-j3). List all the poles and zeroes.

An open loop control system results in a response of for a unit impulse input. The DC gain of the control system is ______.

An open loop transfer function G(s) of a system is For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function ?

An 8-bit, unipolar Successive Approximation Register type ADC is used to convert 3.5 V to digital equivalent output. The reference voltage is +5 V. The output of the ADC, at the end of 3rd clock pulse

Consider the following Sum of Products expression, F. The equivalent Product of Sums expression is

f(A,B,C,D)= M(0,1,3,4,5,7,9,11,12,13,14,15) is a maxterm representation of a Boolean function f(A,B,C,D) where A is the MSB and D is the LSB. The equivalent minimized representation of this function i

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

In the 4 x 1 multiplexer, the output F is given by . Find the required input ' '.

The figure shows a digital circuit constructed using negative edge triggered J-K flip flops. Assume a starting state of . This state will repeat after _______ number of cycles of the clock CLK

A Boolean function f(A,B,C,D)= (1,5,12,15) is to be implemented using an 8x1 multiplexer (A is MSB). The inputs ABC are connected to the select inputs of the multiplexer respectively. Which one of the

An inductor is connected in parallel with a capacitor as shown in the figure. As the frequency of current i is increased, the impedance (Z) of the network varies as

The circuit s hown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in Volt) is given by . If the circuit is in steady state, then the rms value of the cu

For the given circuit, the Thevenin equivalent is to be determined. The Thevenin voltage, (in Volt), seen from terminal AB is __________.

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5 V is applied to Port 1, a current of 1.25 A flows through a 1 res

In the given network V, V, V. The phasor current i (in Ampere) is

Find the transformer ratios a and b such that the impedance ( ) is resistive and equals 2.5 when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of L is obtained by interconnecting these two coils, the minimum value of is ____.

A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, the value of is

A symmetrical square wave of 50% duty cycle has amplitude of 15 V and time period of 0.4 ms. This square wave is applied across a series RLC circuit with R=5 , L=10 mH, and C=4 F. The amplitude of the

An unbalanced DC Wheatstone bridge is shown in the figure. At what value of p will the magnitude of be maximum?

A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to extend its range to (0-500 A) is ______

A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The power consumed by the load is 5 kW. The power is measured by the two-wattmeter method. The readings of

When the Wheatstone bridge shown in the figure is used to find the value of resistor , the galvanometer G indicates zero current when and . If is known with % tolerance on its nominal value of 100 , w

Match the following.

A capacitive voltage divider is used to measure the bus voltage in a high-voltage 50 Hz AC system as shown in the figure. The measurement capacitors have tolerances of 10% on their nominal capacitance

The coils of a wattmeter have resistances 0.01 and 1000 ; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 25

A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is connected to an 11 kV, 50 Hz source. Its synchronous reactance is 50 per phase, and its stator resistance is

A 3-phase 50 Hz square wave (6-step) VSI feeds a 3-phase, 4 pole induction motor. The VSI line voltage has a dominant harmonic component. If the operating slip of the motor with respect to fundamental

Two three-phase transformers are realized using single-phase transformers as shown in the figure. The phase difference (in degree) between voltages is _______.

A 200/400 V, 50 Hz, two-winding transformer is rated at 20 kVA. Its windings are connected as an auto-transformer of rating 200/600 V. A resistive load of 12 is connected to the high voltage (600 V) s

A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum t

A separately excited DC generator has an armature resistance of 0.1 and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is 200 V. When this gener

The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The

With an armature voltage of 100 V and rated field winding voltage, the speed of a separately excited DC motor driving a fan is 1000 rpm, and its armature current is 10 A. The armature resistance is 1

A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a lap win

A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as follows: =100, =50, =50. If the magnetizing current is neglected, and the currents i

A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. The line-to-line voltage rating is

The primary mmf is least affected by the secondary terminal conditions in a

Two single-phase transformers T1 and T2 each rated at 500 kVA are operated in parallel. Percentage impedances of T1 and T2 are (1 + j6) and (0.8 + j4.8), respectively. To share a load of 1000 kVA at 0

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 o

The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The "air-gap" voltage, across the magnetizing inductance, is 210 V rms, and the slip, s,

A DC motor has the following specifications: 10 hp, 37.5 A, 230 V; flux/pole = 0.01 Wb, number of poles = 4, number of conductors = 666, number of parallel paths = 2. Armature resistance = 0.267 . The

A steady current I is flowing in the -x direction through each of two infinitely long wires at as shown in the figure. The permeability of the medium is . The -field at (0,L,0) is

Consider a function , where r is the distance from the origin and is the unit vector in the radial direction. The divergence of this function over a sphere of radius R, which includes the origin, is

Two semi-infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y 0) and region 2 (y 0) are 2 and 5, respectively. Region 1 has uniform electric

Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4 , a

A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The value of is in SI unit. If a uniform magnetic field intensity is applied, then t

A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum vol

Match the following.

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is

For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switchin

The single-phase full-bridge voltage source inverter (VSI), shown in figure, has an output frequency of 50 Hz. It uses unipolar pulse width modulation with switching frequency of 50 kHz and modulation

Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and the current,

The circuit shown is meant to supply a resistive load from two separate DC voltage sources. The switches S1 and S2 are controlled so that only one of them is ON at any instant. S1 is turned on for 0.2

A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to directly

A self commutating switch SW, operated at duty cycle is used to control the load voltage as shown in the figure Under steady state operating conditions, the average voltage across the inductor and the

In the following circuit, the input voltage is 100sin(100 t). For 100 RC=50, the average voltage across R (in Volts) under steady-state is nearest to

A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage is 36 V. Assume that all the

In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the charging

In the given rectifier, the delay angle of the thyristor measured from the positive going zero crossing of is 30 . If the input voltage is 100sin(100 t) V, the average voltage across R (in Volt) under

A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is If the shunt capacitance of all transmission lines is 50% compensated, the imagi

A 50 Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous speed, and producing 1 pu of real power. The initial value of the rotor angle is 5

A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents , if th

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below: ; ; The incremental c

The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers in MW, and are given by where . For a certain load demand, have been chosen such that =

A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR . The value of

Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]. Assertion: Fast decoupled load flow method gives approximate load flow solution because it uses several assump

Base load power plants are P: wind farms. Q: run-of-river plants. R: nuclear power plants. S: diesel power plants.

A sustained three-phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are

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 t

Consider a signal defined by Its Fourier Transform is

For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE?

The signum function is given by The Fourier series expansion of sgn(cos(t)) has

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables x and y. The integration time

The Laplace transform of is . The Laplace transform of is

A moving average function is given by . If the input u is a sinusoidal signal of frequency Hz, then in steady state, the output y will lag u (in degree) by ______ .

Consider a discrete time signal given by The region of convergence of its Z-transform would be

The z-Transform of a sequence x[n] is given as . If y[n] is the first difference of x[n], then Y(z) is given by

The impulse response g(t) of a system, G , is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of G as shown in Figure (b)?