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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

View Question 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

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

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

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

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

View Question 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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

View Question 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

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

View Question 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

View Question