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GATE2018GA8
A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys? $0 \\ $ $\frac{325}{864} \\ $ $\frac{525}{864} \\ $ $\frac{5}{12}$
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Feb 19, 2018
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Numerical Ability
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Arjun
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generalaptitude
numericalability
probability
0
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1
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2
GATE2018GA9
A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by $25 \%$. Therefore, the ... $35.75$ $40.25$ $43.75$ $46.25$
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Feb 19, 2018
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Numerical Ability
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generalaptitude
numericalability
percentage
0
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1
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3
GATE2018GA10
$P, Q, R,$ and $S$ crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available. The boat held two persons on each of the three forward trips across the lake and one person on each of the two ... $P$ $Q$ $R$ $S$
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Feb 19, 2018
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Verbal Ability
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5.4k
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generalaptitude
verbalability
verbalreasoning
0
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1
answer
4
GATE2018GA1
“Since you have gone off the ________, the _________ sand is likely to damage the car.” The words that best fill the blanks in the above sentence are course, coarse course, course coarse, course coarse, coarse
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Feb 19, 2018
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Verbal Ability
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generalaptitude
verbalability
mostappropriateword
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0
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5
GATE201854
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S$ is the slip. At noload, the motor speed can be approximated to the synchronous speed. The noload lagging power factor of the motor is __________ (up to $3$ decimal places).
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Feb 19, 2018
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gate2018ee
numericalanswers
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6
GATE201855
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100 \text{ radian/s}$. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance $Z$ (in $\Omega$) seen between the terminals $a$ and $b$ is __________ (up to $2$ decimal places)
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Feb 19, 2018
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gate2018ee
numericalanswers
0
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0
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7
GATE201846
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ___________ (up to $2$ decimal places).
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Feb 19, 2018
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Arjun
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5.4k
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gate2018ee
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0
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0
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8
GATE201847
A threephase load is connected to a threephase balanced supply as shown in the figure. If $V_{\text{an}} = 100 \angle 0^{\circ} \: V$, $V_{\text{bn}}=100 \angle  120 ^{\circ} \: V$ ... positive in the anticlockwise direction), the value of $R$ for zero current in the neutral wire is __________ $\Omega$ (up to $2$ decimal places).
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Feb 19, 2018
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gate2018ee
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0
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9
GATE201848
The voltage across the circuit in the figure, and the current through it, are given by the following expressions: $v(t)=510 \cos (\omega t+ 60^{\circ}) \: V$ $i(t)=5 + X \cos (\omega t) \: A$ where $\omega =100 \: \pi \text{ radian}/s$. If the average power delivered to the circuit is zero, then the value of $X$ (in Ampere) is _______ (up to $2$ decimal places)
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Feb 19, 2018
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Arjun
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5.4k
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gate2018ee
numericalanswers
0
votes
0
answers
10
GATE201849
A phase controlled single phase rectifier, supplied by an AC source, feeds power to an $RLE$ load as shown in the figure. The rectifier output voltage has an average value given by $V_{\text{o}}= \frac{V_m}{2 \pi} (3+\cos \alpha)$ ... firing angle. If the power delivered to the lossless battery is $1600$ W, $\alpha$ in degree is ___________ (up to $2$ decimal places).
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Feb 19, 2018
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gate2018ee
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11
GATE201850
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of identical value. The load resistance is $1 \: \Omega$. The capacitor voltage has negligible ripple. Both ... average value of $i_{s1}$, the current of switch $S1$ (in Ampere), is ____________ (up to $2$ decimal places).
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Feb 19, 2018
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gate2018ee
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0
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12
GATE201851
A $3$phase $900$ kVA, $3 \: kV/ \sqrt{3} kV$ ( $\Delta/$), $50$ Hz transformer has primary (high voltage side) resistance per phase of $0.3 \: \Omega$ and secondary (low voltage side) resistance per phase of $0.02 \: \Omega$. Iron loss of the transformer is $10 \: kW$. The full load $\%$ efficiency of the transformer operated at unity power factor is _______ (up to $2$ decimal places)
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Feb 19, 2018
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gate2018ee
numericalanswers
0
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1
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13
GATE201852
A $200$ V DC series motor, when operating from rated voltage while driving a certain load, draws $10$ A current and runs at $1000$ r.p.m. The total series resistance is $1 \: \Omega$. The magnetic circuit is assumed to be linear. At the same supply voltage, the load torque is increased by $44 \%$. The speed of the motor in r.p.m (rounded to the nearest integer) is _____________
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Feb 19, 2018
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0
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0
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14
GATE201853
A dc to dc converter shown in the figure is charging a battery bank, $B2$ whose voltage is constant at $150 \: V$. $B1$ is another battery bank whose voltage is constant at $50 \: V$. The value of the inductor, $L$ is $5$ ... state and assuming the diode D to be ideal, the power transferred from $B1$ to $B2$ (in Watt) is ___________ (up to $2$ decimal places)
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Feb 19, 2018
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gate2018ee
numericalanswers
0
votes
0
answers
15
GATE201839
The signal energy of he continuoustime signal $x(t)=[(t1)u(t1)][(t2)u(t2)][(t3)u(t3)]+[(t4)u(t4)]$ is $11/3$ $7/3$ $1/3$ $5/3$
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Feb 19, 2018
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0
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0
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16
GATE201840
The Fourier transform of a continuoustime signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{1}$ and $\omega$ denoes frequency. Then the value of $\mid \text{ln } x(t) \mid$ at $t=1$ is _________ (up to $1$ decimal place). ($\text{ln}$ denotes the logarithm base $e$)
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Feb 19, 2018
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Arjun
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gate2018ee
numericalanswers
0
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0
answers
17
GATE201841
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The baseemitter voltage drop is a constant, $V_{BE}=0.7 \: V$. The value of the Thevenin equivalent resistance $R_{Th}$ (in $\Omega$) as shown in the figure is _________ (up to $2$ decimal places)
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Feb 19, 2018
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0
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0
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18
GATE201842
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).
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Feb 19, 2018
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numericalanswers
0
votes
0
answers
19
GATE201843
Let $f(x) = 3x^37x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
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Feb 19, 2018
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numericalanswers
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0
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20
GATE201844
Let $A= \begin{bmatrix} 1 & 0 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ and $B=A^3A^24A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
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gate2018ee
numericalanswers
0
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0
answers
21
GATE201845
The capacitance of an airfilled parallelplate capacitor is $60$ pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes $86$ pF. Neglecting the fringing effects, the relative permittivity of the dielectric is ___________ (up to $2$ decimal places)
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Feb 19, 2018
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gate2018ee
numericalanswers
0
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0
answers
22
GATE201832
The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is $\text{j} 12 \: \Omega$ $\text{j} 12 \: \Omega$ $\text{j} 13 \: \Omega$ $13 \: \Omega$
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Feb 19, 2018
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5.4k
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gate2018ee
0
votes
0
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23
GATE201833
Consider a system governed by the following equations $ \frac{dx_1(t)}{dt} = x_2(t)x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)x_2(t)$ The initial conditions are such that $x_1(0)<x_2(0)< \infty$. Let $x_{1f}= \underset{t \to \infty}{\lim} x_1(t)$ ... is true? $x_{1f}<x_{2f}<\infty$ $x_{2f}<x_{1f}<\infty$ $x_{1f}<=_{2f}<\infty$ $x_{1f}=x_{2f}=\infty$
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Feb 19, 2018
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5.4k
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gate2018ee
0
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24
GATE201834
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is $3$ $4$ $5$ $6$
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Feb 19, 2018
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5.4k
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0
votes
0
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25
GATE201835
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^23z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is $1$ $0$ $1$ $2$
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Feb 19, 2018
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0
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0
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26
GATE201836
Which one of the following statements is true about the digital circuit shown in the figure It can be used for dividing input frequency by $3$ It can be used for dividing input frequency by $5$ It can be used for dividing input frequency by $7$ It cannot be reliably used as a frequency divider due to disjoint internal cycles
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Feb 19, 2018
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27
GATE201837
Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function $F=m_0+m_2+m_3+m_5+m_7$, where $m_i$ denotes the $i$ th minterm. In addition, $F$ has a don’t care for $m_1$. The simplified expression for $F$ is given by $\overline{A} \: \overline{C} + \overline{B} C + AC$ $\overline{A}+C$ $\overline{C}+A$ $\overline{A} C + BC + A \overline{C}$
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Feb 19, 2018
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28
GATE201838
Consider the two continuoustime signals defined below: ... is greater than the energy of $x_1[n]$ $x_1[n]$ and $x_2[n]$ have equal energies Neither $x_1[n]$ nor $x_2[n]$ is a finiteenergy signal
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29
GATE201824
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produces a torque of $500$ Nm at zero speed. Neglecting all mechanical losses, the noload speed of the motor (in $\text{radian /s}$) for an armature voltage of $150$ V is ____________ (up to $2$ decimal places).
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Feb 19, 2018
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Arjun
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5.4k
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gate2018ee
numericalanswers
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0
answers
30
GATE201825
Consider a unity feedback system with forward transfer function given by $G(s) = \frac{1}{(s+1)(s+2)}$ The steadystate error in the output of the system for a unitstep input is _______ (up to $2$ decimal places).
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Feb 19, 2018
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0
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31
GATE201826
A transformer with toroidal core of permeability $\mu$ is shown in the figure. Assuming uniform flux density across the circular core crosssection of radius $r < < R$, and neglecting any leakage flux, the best estimate for the mean radius $R$ is $\frac{\mu V r^2 N_P^2 \omega}{I} \\ $ ... $\frac{\mu V r^2 N_P^2 \omega}{2I} \\ $ $\frac{\mu I r^2 N_P^2 \omega}{2V} $
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Feb 19, 2018
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32
GATE201827
A $01$ Ampere moving iron ammeter has an internal resistance of $50 \: m \Omega$ and inductance of $0.1 \: mH$. A shunt coil is connected to extend its range to $010$ Ampere for all operating frequencies. The time constant in milliseconds and resistance in $m \Omega$ of the shunt coil respectively are $2, \: 5.55$ $2, \: 1$ $2.18, \: 0.55$ $11.1, \: 2$
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Feb 19, 2018
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33
GATE201828
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a linetoline fault with fault impedance $Z_f$, the fault current is $I_{f1}= kI_f$, where $I_f$ is the fault current with zero fault impedance. The relation between $Z_f$ ... $Z_f=\frac{(Z_1+Z_2)k}{1k} \\$ $Z_f=\frac{(Z_1+Z_2)k}{1+k}$
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34
GATE201829
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1}$, $Q_{G2}$ ... $6.34, \: 10.00, \: 1.34$ $6.34, \: 11.34, \: 2.68$ $5.00, \: 11.34, \: 1.34$
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35
GATE201830
The perunit power output of a salientpole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $\delta$ is the load angle. NewtonRaphson method is used to calculate the value of $\delta$ ... (in degree) at the end of the first iteration is $15^{\circ}$ $28.28^{\circ}$ $28.74^{\circ}$ $31.20^{\circ}$
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Feb 19, 2018
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36
GATE201831
A DC voltage source is connected to a series $LC$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the following circular loci represents the plot of $i(t)$ versus $v(t)$?
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37
GATE201816
A continuoustime input signal $x(t)$ is an eigenfunction of an LTI system, if the output is $k \: x(t)$, where $k$ is an eigenvalue $k \: e^{j \omega t} \: x(t)$, where $k$ is an eigenvalue and $e^{j \omega t}$ is a complex exponential signal ... $k \: H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system
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38
GATE201817
Consider a nonsingular $2 \times 2$ square matrix $\textbf{A}$. If $\textit{trace}(\textbf{A})=4$ and $\textit{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).
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39
GATE201818
Let $f$ be a realvalued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).
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40
GATE201819
In the twoport nework shown, the $h_{11}$ parameter $\bigg($ where, $h_{11} = \frac{V_1}{I_1}$, when $V_2=0 \bigg)$ in ohms is _________ (up to $2$ decimal places).
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