Recent questions tagged gate2012-ec

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1

GATE2012-65
$A$ and $B$ are friends. They decide to meet between $1:00$pm and $2:00$ pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is $1/4$ $1/16$ $7/16$ $9/16$

asked Mar 25, 2018 in Numerical Ability by Milicevic3306 (15.7k points)

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2

GATE2012-64
The data given in the following table summarizes the monthly budget of an average household. ... $10\%$ $14\%$ $81\%$ $86\%$

asked Mar 25, 2018 in Numerical Ability by Milicevic3306 (15.7k points)

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3

GATE2012-63
There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is $2$ $3$ $4$ $8$

asked Mar 25, 2018 in Numerical Ability by Milicevic3306 (15.7k points)

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4

GATE2012-62
Raju has $14$ currency notes in his pocket consisting of only Rs. $20$ notes and Rs. $10$ notes. The total money value of the notes is Rs. $230$. The number of Rs. $10$ notes that Raju has is $5$ $6$ $9$ $10$

asked Mar 25, 2018 in Numerical Ability by Milicevic3306 (15.7k points)

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5

GATE2012-61
One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them. Which one ... their seniors. The harsh discipline to which the legions were subjected to led to the odds and conditions being against them.

asked Mar 25, 2018 in Verbal Ability by Milicevic3306 (15.7k points)

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6

GATE2012-60
One of the parts $(A, B, C, D)$ in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow. requested that should be given the driving test instead of tomorrow

asked Mar 25, 2018 in Verbal Ability by Milicevic3306 (15.7k points)

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7

GATE2012-59
Which one of the following options is the closest in meaning to the word given below? Latitude Eligibility Freedom Coercion Meticulousness

asked Mar 25, 2018 in Verbal Ability by Milicevic3306 (15.7k points)

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8

GATE2012-58
Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness of the situation that he had to face, his ___ was impressive. beggary nomenclature jealousy nonchalance

asked Mar 25, 2018 in Verbal Ability by Milicevic3306 (15.7k points)

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9

GATE2012-57
Choose the most appropriate alternative from the options given below to complete the following sentence: If the tired soldier wanted to lie down, he _______ the mattress out on the balcony. should take shall take should have taken will have taken

asked Mar 25, 2018 in Verbal Ability by Milicevic3306 (15.7k points)

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10

GATE2012-56
If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=?$ $2.23$ $4.33$ $11.37$ $27.64$

asked Mar 25, 2018 in Numerical Ability by Milicevic3306 (15.7k points)

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11

GATE2012-55
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}$ rad/s $\sqrt{3}$ rad/s $\sqrt{6}$ rad/s $\frac{1}{\sqrt{3}}$ rad/s

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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12

GATE2012-54
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1,b=2$ $a=3,b=2$ $a=-3,b=-1$ $a=3,b=1$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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13

GATE2012-53
An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. A hole of radius $b$ (b < a) ia now drilled along the length of the wire at a distance $d$ from the center of the wire as shown below. The ... hole is uniform and depends only on $d$ uniform and depends only on $b$ uniform and depends only on both $b$ and $d$ non uniform

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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14

GATE2012-52
An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. The magnetic field at a distance $r$ from the center of the wire is proportional to $r$ for $r\lt a$ and $\frac{1}{r^2}$ for $r\gt a$ $0$ for $r\lt a$ and $\frac{1}{r}$ ... $r\lt a$ and $\frac{1}{r}$ for $r\gt a$ $0$ for $r\lt a$ and $\frac{1}{r^2}$ for $r\gt a$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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15

GATE2012-51
In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta=20\:nm$. The transistor is of width $1\: \mu m$. The depletion width formed at every p-n junction is $10\:nm$. The relative permittivities of $Si$ and $SiO_2$, respectively, are $11.7$ ... $2\:fF$ $7\:fF$ $2\:pF$ $7\:pF$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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16

GATE2012-50
In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta=20\:nm$. The transistor is of width $1\: \mu m$. The depletion width formed at every p-n junction is $10\:nm$. The relative permittivities of $Si$ and $SiO_2$, respectively, are $11.7$ and ... $0.7\:fF$ $0.7\:pF$ $0.35\:fF$ $0.24\:pF$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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17

GATE2012-49
With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ For the same network, with $6\: V$ dc ... . If $8\:V$ dc is connected to port A, the open circuit voltage at port B is $6\:V$ $7\:V$ $8\:V$ $9\:V$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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18

GATE2012-48
With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ With $10\: V$ dc connected at port A, the ... $\frac{3}{7}\: A$ $\frac{5}{7}\: A$ $1\: A$ $\frac{9}{7}\: A$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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19

GATE2012-47
Given that $A=\begin{bmatrix} -5 &-3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is $15\:A+12\:I$ $19\:A+30\:I$ $17\:A+15\:I$ $17\:A+21\:I$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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20

GATE2012-46
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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21

GATE2012-45
If $V_A-V_B=6\:V$, then $V_C-V_D$ is $-5\:V$ $2\:V$ $3\:V$ $6\:V$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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22

GATE2012-44
The voltage gain $A_v$ of the circuit shown below is $\mid A_v \mid\approx 200$ $\mid A_v\mid \approx 100$ $ \mid A_v \mid \approx 20$ $\mid A_v \mid \approx 10$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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23

GATE2012-43
The state transition diagram for the logic circuit shown is

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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24

GATE2012-42
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(\frac{1}{2})^nu[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y[1]=\frac{1}{2}$, then $g[1]$ equals $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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25

GATE2012-41
The circuit shown is a low pass filter with $f_{3\:dB}=\frac{1}{(R_1+R_2)C}\: rad/s$ high pass filter with $f_{3\:dB}=\frac{1}{R_1C}\: rad/s$ low pass filter with $f_{3\:dB}=\frac{1}{R_1C}\: rad/s$ high pass filter with $f_{3\:dB}=\frac{1}{(R_1+R_2)C}\: rad/s$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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26

GATE2012-40
The magnetic field along the propagation direction inside a rectangular waveguide with the cross-section shown in the figure is $H_Z=3\:\cos(2.094\times10^2x)\:\cos(2.618\times10^2y)\:\cos(6.283\times10^{10}t-\beta z)$ The phase velocity $v_p$ of the wave inside the waveguide satisfies $v_p\gt c$ $v_p=c$ $0\lt v_p\lt c$ $v_p=0$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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27

GATE2012-39
The signal $m(t)$ as shown is applied both to a phase modulator (with $k_p$ as the phase constant) and a frequency modulator (with $k_f$ as the frequency constant) having the same carrier frequency. The ratio $\frac{k_p}{k_f}$ (in $rad/Hz$) for the same maximum phase deviation is $8\pi$ $4\pi$ $2\pi$ $\pi$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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28

GATE2012-38
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probability of error for an optimum receiver will be $\frac{7}{80}$ $\frac{63}{80}$ $\frac{9}{10}$ $\frac{1}{10}$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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29

GATE2012-37
In the CMOS circuit shown, electron and hole mobilities are equal, and $M1$ and $M2$ are equally sized. The device $M1$ is in the linear region if $V_{in}\lt 1.875\:V$ $1.875\:V\lt V_{in}\lt 3.125\:V$ $V_{in}\gt 3.125\:V$ $0\lt V_{in}\lt 5\:V$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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30

GATE2012-36
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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31

GATE2012-35
The direction of vector $A$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\triangledown.A=0$ is $-2$ $2$ $1$ $0$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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32

GATE2012-34
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)\big|_{t=0^-}=-2$ and $\frac{dy}{dt}\big|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}\big|_{t=0^+}$ is $-2$ $-1$ $0$ $1$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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33

GATE2012-33
Assuming both the voltage sources are in phase, the value of $R$ for which maximum power is transferred from circuit $A$ to circuit $B$ is $0.8\:\Omega$ $1.4\:\Omega$ $2\:\Omega$ $2.8\:\Omega$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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34

GATE2012-32
The state variable description of an LTI system is given by ... for $a_1\neq 0,a_2=0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3=0$ $a_1\neq 0,a_2\neq0,a_3=0$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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35

GATE2012-31
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega$. The value of $h(0)$ is $\frac{1}{4}$ $\frac{1}{2}$ $1$ $2$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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36

GATE2012-30
The feedback system shown below oscillates at $2\:rad/s$ when $K=2$ and $a=0.75$ $K=3$ and $a=0.75$ $K=4$ and $a=0.5$ $K=2$ and $a=0.5$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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37

GATE2012-29
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\underset{-\infty}{\int}x(\tau)\cos(3\tau)d\tau$. The system is time-invariant and stable stable and not time-invariant time-invariant and not stable not time-invariant and not stable

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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38

GATE2012-28
A trasmission line with a characteristic impedance of $100\:\Omega$ is used to match a $50\:\Omega$ section to a $200\:\Omega$ section. If the matching is to be done both at $429\:MHz$ and $1\:GHz$, the length of the transmission line can be approximately $82.5\:cm$ $1.05\:m$ $1.58\:m$ $1.75\:m$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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39

GATE2012-27
A BPSK scheme operating over an AWGN channel with noise power spectral density of $\frac{N_o}{2}$, uses equiprobable signals $s_1(t)=\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ and $s_2(t)=-\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ over the symbol interval $(0,T)$. If the local oscillator in a ... $Q(\sqrt{\frac{E}{N_o}})$ $Q(\sqrt{\frac{E}{2N_o}})$ $Q(\sqrt{\frac{E}{4N_o}})$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)

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40

GATE2012-26
The source of a silicon ($n_i=10^{10}\:per\:cm^3$) n-channel MOS transistor has an area of $1\:sq\:\mu m$ and a depth of $1\:\mu m$. If the dopant density in the source is $10^{19}/cm^3$, the number of holes in the source region with the above volume is approximately $10^7$ $100$ $10$ $0$

asked Mar 25, 2018 in Others by Milicevic3306 (15.7k points)