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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

View Question 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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

View Question 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\

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

View Question 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

View Question