GATE EE 2016 Set 1

## GATE EE

A transistor circuit is given below. The Zener diode breakdown voltage is $$5.3$$ $$V$$ as shown. Take base to emitter v

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Given the following polynomial equation $${s^3} + 5.5{s^2} + 8.5s + 3 = 0$$ the number of roots of the polynomial which

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The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady

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The phase cross-over frequency of the transfer function $$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}

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Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$ is in $$rad/s$$)
Which one of the following

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Loop transfer function of a feedback system is $$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3

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Consider the following state - space representation of a linear time-invariant system.
$$\mathop x\limits^ \bullet \lef

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Consider the following circuit which uses a $$2$$-to-$$1$$ multiplexer as shown in the figure below. The Boolean express

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The current state $${Q_A}{Q_B}$$ of a two $$JK$$ flip-flop system is $$00.$$ Assume that the clock rise-time is much sma

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A $$2$$-bit flash Analog to Digital Converter $$(ADC)$$ is given below. The input is $$0 \le {V_N} \le 3$$ Volts. The ex

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In the portion of a circuit shown, if the heat generated in 5 Ω resistance is 10 calories per second
then heat generated

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RA and RB are the input resistances of circuits as shown below. The circuits extend infinitely in
the direction shown. W

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In the circuit shown below, the node voltage VA is _________ V.

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In the given circuit, the current supplied by the battery, in ampere, is ________.

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In the circuit shown, switch S2 has been closed for a long time. A time t = 0 switch S1 is closed. At
t=0+ , the rate of

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The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the
admittance of the circuit becom

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In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady
state current through

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A dc voltage with ripple is given by $$v\left( t \right)\,\,\,\, = \,\,\,\,\left[ {100 + 10\sin \left( {\omega t} \right

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A 4-pole, lap-connected, separately excited dc motor is drawing a steady current of 40 A while
running at 600 rpm. A goo

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A DC shunt generator delivers 45 A at a terminal voltage of 220 V. The armature and the shunt
field resistance are 0.01

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If an ideal transformer has an inductive load element at port 2 as shown in the figure below, the
equivalent inductance

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A single-phase, 22 kVA, 2200 V/220 V, 50 Hz, distribution transformer is to be connected as an autotransformer
to get an

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If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then

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A single-phase 400 V, 50 Hz transformer has an iron loss of 5000 W at the condition. When
operated at 200 V, 25 Hz, the

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In a constant V/f induction motor drive, the slip at the maximum torque

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A three-phase, $$50$$ $$Hz$$ salient-pole synchronous motor has a per-phase direct-axis reactance $$\left( {{X_d}} \righ

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Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the
zero equipotential cu

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In cylindrical coordinate system, the potential produced by a uniform ring charge is given $$\phi=f\left(r,\;z\right)$$,

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Consider $$3 \times 3$$ matrix with every element being equal to $$1.$$ Its only non-zero eigenvalue is __________.

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Let $$A$$ be a $$4 \times 3$$ real matrix which rank$$2.$$ Which one of the following statement is TRUE?

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Let the eigenvalues of a $$2 \times 2$$ matrix $$A$$ be $$1,-2$$ with eigenvectors $${x_1}$$ and $${x_2}$$ respectively.

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The maximum value attained by the function $$f(x)=x(x-1) (x-2)$$ in the interval $$\left[ {1,2} \right]$$ is _________.

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Let $$\,\,S = \sum\limits_{n = 0}^\infty {n{\alpha ^n}} \,\,$$ where $$\,\,\left| \alpha \right| < 1.\,\,$$ The val

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Candidates were asked to come to an interview with $$3$$ pens each. Black, blue, green and red were the permitted pen co

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A function $$y(t),$$ such that $$y(0)=1$$ and $$\,y\left( 1 \right) = 3{e^{ - 1}},\,\,$$ is a solution of the differenti

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The value of the integral $$\oint\limits_c {{{2z + 5} \over {\left( {z - {1 \over 2}} \right)\left( {{z^2} - 4z + 5} \ri

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A steady dc current of 100 A is flowing through a power module (S, D) as shown in Figure (a). The V-I characteristics of

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A buck converter, as shown in Figure $$(a)$$ below, is working in steady state. The output voltage and the inductor curr

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The switches $$T1$$ and $$T2$$ in Figure are switched in a complementary fashion with sinusoidal pulse width modulation

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A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance

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A three-phase cable is supplying $$800$$ kW and $$600$$ kVAr to an inductive load. It is intended to supply an additiona

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A 30 MVA, 3-phase, 50Hz, 13.8 kV, star-connected synchronous generator has positive, negative and zero sequence reactanc

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The magnitude of three-phase fault currents at buses A and B of a power system are 10 pu and 8 pu, respectively. Neglect

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In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in

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The value of $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dira

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Consider a continuous-time system with input x(t) and output y(t) given by
$$y\left(t\right)=x\left(t\right)\cos\left(t\

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Suppose x1(t) and x2(t) have the Fourier transforms as shown below.
Which one of the following statements is TRUE?

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The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x(t) is
the input signal. A si

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