GATE EE 2015 Set 1

## GATE EE

In the given circuit, the silicon transistor has $$\beta $$ $$=75$$ and a collector voltage $${V_C} = 9\,V.$$ Then the r

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Consider the circuit shown in the figure. In this circuit $$R = 1\,\,k\Omega ,$$ and $$C = 1\,\,\mu F.$$ The input volta

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Of the four characteristics given below, which are the major requirements for an instrumentation amplifier?
P. $$\,\,\,\

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The op-amp shown in the figure has a finite gain $$A = 1000$$ and an infinite input resistance. A step voltage $${V_i}

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

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Find the transfer function $${{Y\left( s \right)} \over {X\left( s \right)}}$$ of the system given below:

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

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The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $$\l

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In the signal flow diagram given in the figure, $${u_1}$$ and $${u_2}$$ are possible inputs whereas $${y_1}$$ and $${y_2

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$$f\left( {A,\,B,\,C,\,D} \right) = \Pi M\left( {0,1,3,4,5,7,9,11,12,13,14,15} \right)$$ is a Maxterm representation of

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In the $$4 \times 1$$ multiplexer, the output $$F$$ is given by $$F = A \oplus B.$$ Find the required input $${{\rm I}_3

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The figure shows a digital circuit constructed using negative edge triggered $$J-K$$ flip flops. Assume a starting state

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An $$8$$-bit, unipolar Successive Approximation Register type $$ADC$$ is used to convert $$3.5$$ $$V$$ to digital equiva

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The voltages developed across the 3Ω and 2Ω resistors shown in the figure are 6V and
2V respectively, with the polarity

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In the given circuit, the parameter k is
positive, and the power dissipated in the
2 Ω resistor is 12.5 W. The value of

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For the given circuit the Thevenin equivalent is to be determined. The Thevenin voltage,
VTh (in volt), seen from termin

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An inductor is connected in parallel with a capacitor as shown in the figure.
As the frequency of current i is increase

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The circuit shown in the figure has two sources connected in
series. The instantaneous voltage of the AC source (in volt

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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-cir

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A ($$0-50$$ $$A$$) moving coil ammeter has a voltage drop of $$0.1$$ $$V$$ across its terminals at full scale deflection

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When the Wheatstone bridge shown in the figure is used to find the value of resistor $${R_x},$$ the galvanometer $$G$$ i

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An unbalanced $$DC$$ Wheatstone bridge is shown in the figure. At what value of $$p$$ will the magnitude of $${V_0}$$ be

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A separately excited DC generator has an armature resistance of 0.1 $$\Omega$$ and negligible armature inductance. At ra

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A separately excited DC motor runs at 1000 rpm on no load when its armature terminals are connected to a 200 V DC source

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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 c

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The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800
mH, and that of the secondary wi

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Two single-phase transformers T1 and T2 each rated at 500 kVA are operated in parallel. Percentage impedances of T1 and

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A 200/400 V, 50 Hz, two-winding transformer is rated at 20 kVA. Its windings are connected as an auto-transformer of rat

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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 5t

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Consider a function $$\overrightarrow f=\frac1{r^2}\widehat r$$ where r is the distance from the origin and $$\widehat r

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A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric stre

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A steady current I is flowing in the −x direction through each of two infinitely long wires at $$y=\pm\frac L2$$ as show

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Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the

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If the sum of the diagonal elements of a $$2 \times 2$$ matrix is $$-6$$, then the maximum possible value of determinant

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The maximum value of $$'a'$$ such that the matrix $$\left[ {\matrix{
{ - 3} & 0 & { - 2} \cr
1 & { -

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Two players, $$A$$ and $$B,$$ alternately keep rolling a fair dice. The person to get a six first wins the game. Given t

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A random variable $$X$$ has probability density function $$f(x)$$ as given below:
$$$\,\,f\left( x \right) = \left\{ {\

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Given Set $$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$ and Set $$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$

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The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c$$ respectively. Of th

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A solution of the ordinary differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y = 0\,\,$$ is

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If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of t

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In the following chopper, the duty ratio of switch $$S$$ is $$0.4.$$ If the inductor and capacitor are sufficiently larg

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A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch $$S$$ i

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A self commutating switch $$SW,$$ operated at duty cycle $$\delta $$ is used to control the load voltage as shown in the

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The circuit shown is meant to supply a resistive load $${R_L}$$ from two separate $$DC$$ voltage sources. The switches $

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The single-phase full-bridge voltage source inverter $$(VSI),$$ shown in figure, has an output frequency of $$50$$ $$Hz$

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A 50 Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous sp

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A sustained three phase fault occurs in the power system shown in the figure. The current and voltage phasors during the

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Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in $$Rs/MWh$$ along

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

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Determine the correctness or otherwise of the following Assertion (a) and the Reason (R).
Assertion (A): Fast decoupled

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Consider a $$HVDC$$ link which uses thyristor based line commutated converters as shown in the figure. For a power flow

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A moving average function is given by $$y\left(t\right)=\frac1T\int_{t-T}^tu\left(\tau\right)d\tau$$. If the input u is

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

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The signum function is given by
$$$\mathrm{sgn}\left(\mathrm x\right)=\left\{\begin{array}{l}\frac{\mathrm x}{\left|\mat

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Consider a discrete time signal given by
x[n]=(-0.25)nu[n]+(0.5)nu[-n-1]
The region of convergence of its Z-transform wo

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