Recent questions tagged gate2017-ee-2

There are $3$ red socks, $4$ green socks and $3$ blue socks. You choose $2$ socks. The probability that they are of the same colour is$1/5$$7/30$$1/4$$4/15$

The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5, 5]$ is$0$$1$$2$$3$

$X$ is a $30$ digit number starting with the digit $4$ followed by the digit $7$. Then the number $X^{3}$ will have$90$ digits$91$ digits$92$ digits$93$ digits

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If...

A test has twenty questions worth $100$ marks in total. There are two types of questions. Multiple choice questions are worth $3$ marks each and essay questions are worth...

There are five buildings called $V, W, X, Y$ and $Z$ in a row (not necessarily in that order). $V$ is to the West of $W . Z$ is to the East of $X$ and the West of $V$. $W...

Saturn is _______ to be seen on a clear night with the naked eye.Enough brightBright enoughAs enough brightBright as enough

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Con...

If the primary line voltage rating is $3.3$kV (Y side) of a $25$kVA, $Y-\Delta$ transformer (the per phase turns ratio is $5:1$), then the line current rating of the seco...

In the circuit shown in the figure, the diode used is ideal. The input power factor is ________. (Give the answer up to two decimal places).

A thin soap bubble of radius $R=1$ cm, and thickness $a=3.3 \mu m (a << R)$, is at a potential of $1$ V with respect to a reference point at infinity. The bubble bursts a...

A $3$-phase, $2$-pole, $50$Hz, synchronous generator has a rating of $250$ MVA, $0.8$ pf lagging. The kinetic energy of the machine at synchronous speed is $1000$MJ. The ...

Two generating units rated $300$MW and $400$MW have governor speed regulation of $6 \%$ and $4 \%$ respectively from no load to full load. Both the generating units are o...

A $3$-phase, $50$Hz generator supplies power of $3$MW at $17.32$kV to a balanced $3$-phase inductive load through an overhead line. The per phase line resistance and reac...

Consider an overhead transmission line with $3$-phase, $50$ Hz balanced system with conductors located at the vertices of an equilateral triangle of length $D_{ab}=D_{bc}...

In the circuit shown all elements are ideal and the switch $S$ is operated at $10$kHz and $60 \%$ duty ratio. The capacitor is large enough so that the ripple across it i...

A $10 \frac{1}{2}$ digit timer counter possesses a base clock of frequency $100$ MHz. When measuring a particular input, the reading obtained is the same in:Frequency mod...

Consider the system described by the following state space representation$\begin{bmatrix}\dot{x}_{1}(t)\\\dot{x}_{2}(t)\end{bmatrix}=\begin{bmatrix}0 &1 \\0 & -2\end{bmat...

A $25$ kVA, $400$ V, $\Delta$-connected, $3$-phase, cylindrical rotor synchronous generator requires a field current of $5$ A to maintain the rated armature current under...

For the synchronous sequential circuit shown below, the output $Z$ is zero for the initial conditions $Q_{A}, Q_{B}, Q_{C}= Q'_{A}, Q'_{B}, Q'_{C}=100$The minimum number ...

For the network given in the figure below, the Thevenin's voltage $V_{ab}$ is$-1.5$V$-0.5$V$0.5$V$1.5$V

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $3$ tosses. Let the random variable $Y$ denote the number of heads. The value o...

For the circuit shown below, assume that the $OPAMP$ is ideal.Which one of the following is TRUE?$v_{0}=v_{s}$$v_{0}=1.5 v_{s}$$v_{0}=2.5 v_{s}$$v_{0}=5 v_{s}$

For the circuit shown in the figure below, it is given that $V_{CE}=\frac{V_{CC}}{2}$. The transistor has $\beta=29$ and $V_{BE}=0.7 V$ when the $B-E$ junction is forward...

The range of $K$ for which all the roots of the equation $s^{3}+3s^{2}+2s+K=0$ are in the left half of the complex $s$-plane is$0 < K < 6$$0 < K < 16$$6 < K < 36$$6 < K <...

A cascade system having the impulse responses $h_{1}(n)= \{ \underset{\uparrow}{1}-1 \}$ and $h_{2}(n)= \{ \underset{\uparrow}{1}-1, 1 \}$ is shown in the figure below, ...

The root locus of the feedback control system having the characteristic equation $s^{2}+6Ks+2s+5=0$ where $K>0$, enters into the real axis at.$s=-1$$s=-\sqrt{5}$$s=-5$$s=...

A star-connected, $12.5$kW, $208$ V (line), $3$-phase, $60$Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: ...