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1
GATE2016 EC3: 3
The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _________
asked
Nov 21
in
Probability and Statistics
by
Kushagra गुप्ता
(
260
points)
gate2016ec
probability
0
votes
0
answers
2
GATE2009 EC: 11
A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads. (A) $\left(\dfrac{1}{2}\right)^{2}$ (B) $^{10}C_2\left(\dfrac{1}{2}\right)^{2}$ (C) $\left(\dfrac{1}{2}\right)^{10}$ (D) $^{10}C_2\left(\dfrac{1}{2}\right)^{10}$
asked
Nov 21
in
Probability and Statistics
by
Kushagra गुप्ता
(
260
points)
gate2009ec
probability
0
votes
0
answers
3
GATE2019 EC: GA7
The bar graph in panel (a) shows the proportion of male and female illiterates in $2001$ and $2011.$ The proportions of males and females in $2001$ and $2011$ are given in Panel (b) and (c), respectively. The total population did not change during this period. The percentage increase in the total number of literates from $2001$ to $2011$ is ______. $30.43$ $33.43$ $34.43$ $35.43$
asked
Feb 12
in
Numerical Ability
by
Arjun
(
1.4k
points)
gate2019ec
generalaptitude
numericalability
datainterpretation
0
votes
0
answers
4
GATE2019 EC: GA8
"Indian history was written by British historiansextremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subservient to the glory of the Union Jack. Latterday Indian scholars ... biased was well documented and researched but was sometimes biased was not well documented and researched and was sometimes biased
asked
Feb 12
in
Verbal Ability
by
Arjun
(
1.4k
points)
gate2019ec
generalaptitude
verbalability
passagereading
0
votes
0
answers
5
GATE2019 EC: GA9
Two design consultants, $P$ and $Q,$ started working from $8$ AM for a client. The client budgeted a total of USD $3000$ for the consultants. $P$ stopped working when the hour hand moved by $210$ degrees on the clock. $Q$ stopped working when the hour ... . After paying the consultants, the client shall have USD _______ remaining in the budget. $000.00$ $166.67$ $300.00$ $433.33$
asked
Feb 12
in
Numerical Ability
by
Arjun
(
1.4k
points)
gate2019ec
generalaptitude
numericalability
clock
worktime
+2
votes
0
answers
6
GATE2019 EC: 1
Which of the following functions is analytic over the entire complex plane? $\ln(z)$ $e^{1/z}$ $\frac{1}{1z}$ $cos(z)$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
7
GATE2019 EC: 2
The families of curves represented by the solution of the equation $\frac{dy}{dx}= – (\frac{x}{y})^n$ for $n=1$ and $n= +1,$ respectively, are Parabolas and Circles Circles and Hyperbolas Hyperbolas and Circles Hyperbolas and Parabolas
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
8
GATE2019 EC: 3
Let $H(z)$ be the $z$ transform of a realvalued discretetime signal $h[n].$ If $P(z) = H(z) H(\frac{1}{z})$ has a zero at $z= \frac{1}{2}+\frac{1}{2}j,$ and $P(z)$ has a total of four zeros, which one of the following plots represents all the zeros correctly?
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
9
GATE2019 EC: 4
Consider the twoport resistive network shown in the figure. When an excitation of $5$V is applied across Port $1$, and Port $2$ is shorted, the current through the short circuit at Port $2$ is measured to be $1$ A (see (a) in the figure). Now, if an excitation of $5$ V is ... the current through the short circuit at Port $1$? $\text{0.5 A}$ $\text{1 A}$ $\text{2 A}$ $\text{2.5 A}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
10
GATE2019 EC: 5
Let $Y(s)$ be the unitstep response of a causal system having a transfer function $G(s)= \frac{3s}{(s+1)(s+3)}$ that is ,$Y(s)=\frac{G(s)}{s}.$ The forced response of the system is $u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)$ $u(t)$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
11
GATE2019 EC: 6
For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles $N_{p}$ and the number of system zeros $N_{z}$ in the frequency range $1 Hz \leq f\leq 10^{7} Hz$ is $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
12
GATE2019 EC: 7
A linear Hamming code is used to map $4bit$ message to $7bit$ codewords. The encoder mapping is linear. If the message $0001$ is mapped to the codeword $0000111$, and the message $0011$ is mapped to the codeword $1100110$, then the message $0010$ is mapped to $0010011$ $1100001$ $1111000$ $1111111$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
13
GATE2019 EC: 8
Which one of the following options describes correctly the equilibrium band diagram at $T=300$K of a Silicon $pnn^{+}$ $p^{++}$ configuration shown in the figure?
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
14
GATE2019 EC: 9
The correct circuit representation of the structure shown in the figure is
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
15
GATE2019 EC: 10
The figure shows the highfrequency CV curve of a MOS capacitor (at $T=300$K) with $Φ_{ms}=0 V$ and no oxide charges. The flatband, inversion, and accumulation conditions are represented, respectively, by the points $P,Q,R$ $Q,R,P$ $R,P,Q$ $Q,P,R$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
16
GATE2019 EC: 11
What is the electric flux $(\int \vec{E}.d \hat{a})$ through a quartercylinder of height $H$(as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of $Q$ ? $\frac{HQ}{\varepsilon_{0}}$ $\frac{HQ}{4\varepsilon_{0}}$ $\frac{H\varepsilon}{4Q}$ $\frac{4H}{Q\varepsilon_{0}}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
17
GATE2019 EC: 12
In the table shown, List I and List II, respectively, contain terms appearing on the lefthand side and the righthand side of Maxwell's equations (in their standard form). Match the lefthand side with the corresponding righthand side. ... $\text{1Q,2S,3P,4R}$ $\text{1R,2Q,3S,4P}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
18
GATE2019 EC: 13
A standard CMOS inverter is designed with equal rise and fall times $(\beta_{n}=\beta_{p}).$ If the width of the pMOS transistor in the inverter is increased what would be the effect on the LOW noise margin $NM_{L}$ and the HIGH noise margin $NM_{H}$ ... decreases. $NM_{L}$ decreases and $NM_{H}$ increases. Both $NM_{L}$ and $NH_{H}$ increases. No change in the noise margins.
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
19
GATE2019 EC: 14
In the circuit shown, what are the values of $F$ for $EN=0$ and $EN=1$, respectively? $\text{0 and D}$ $\text{HiZ and D}$ $\text{0 and 1}$ $\text{HiZ and}$ $ \overline{D}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
20
GATE2019 EC: 15
In the circuit shown, $A$ and $B$ are the inputs and $F$ is the output. What is the functionality of the circuit? Latch XNOR SRAM Cell XOR
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
21
GATE2019 EC: 16
The value of the contour integral $\frac{1}{2\pi j} \oint(z+\frac{1}{z})^{2}dz$ evaluated over the unit circle $z=1$ is_______.
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
22
GATE2019 EC: 18
If $X$ and $Y$ are random variable such that $E[2X+Y]=0$ and $E[X+2Y]=33$, then $E[X]+E[Y]=$__________________.
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
23
GATE2019 EC: 19
The value of the integral $\int_{0}^{\pi} \int_{y}^{\pi}\frac{sinx}{x}dx dy ,$ is equal to _____________.
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
24
GATE2019 EC: 20
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$is given by $F_{z}(x)=$\begin{Bmatrix} 1e^{x}& if x\geq 0 \\ 0& if x< 0 \end{Bmatrix}$ Then Pr$(z>2z>1)$, rounded off to two decimal places, is equal to ___________.
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
25
GATE2019 EC: 21
Consider the signal $f(t)=1+2 cos(\pi t)+3 sin (\frac{2\pi}{3}t)+4 cos (\frac{\pi}{2}t+\frac{\pi}{4})$, where $t$ is in seconds. Its fundamental time period, in seconds, is _____________________.
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
26
GATE2019 EC: 22
The baseband signal $m(t)$ shown in the figure is phasemodulated to generate the $PM$ signal $\varphi(t)=cos(2\pi f_{c}t+ k m(t)).$ The time $t$ on the $x$ axis in the figure is in milliseconds. If the carrier ... ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is ___________________ (rounded off to $2$ decimal places).
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
27
GATE2019 EC: 23
Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change in the radiation resistance, rounded off to two decimal places, is ______________ $\%.$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
28
GATE2019 EC: 24
In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8 V$ and $10 V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50 \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place.)
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
29
GATE2019 EC: 25
In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is $12kHz$. The frequency of the signal at $Q_{2}$ is _____________ kHz.
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
0
votes
0
answers
30
GATE2019 EC: 26
Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(1)=0$ and $f’(x) \leq2.$ Given these conditions, which one of the following inequalities is necessarily true for all $x \in[2,2]?$ $f(x)\leq \frac{1}{2}x+1$ $f(x)\leq 2x+1$ $f(x)\leq \frac{1}{2}x$ $f(x)\leq 2x$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
31
GATE2019 EC: 27
Consider the line integral $\int_{c} (xdyydx)$ the integral being taken in a counterclockwise direction over the closed curve $C$ that forms the boundary of the region $R$ shown in the figure below. The region $R$ is the area enclosed by the union of a $2 \times 3$ rectangle and ... circle of radius $1$. The line integral evaluates to $6+ \frac{\pi}{2}$ $8+\pi$ $12+\pi$ $16+2\pi$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
32
GATE2019 EC: 28
Consider a sixpoint decimationintime Fast Fourier Transform (FFT) algorithm, for which the signalflow graph corresponding to $X[1]$ is shown in the figure. Let $W_{6}=exp(\frac{j2\pi}{6}).$ In the figure, what should be the values of the coefficients $a_{1},a_{2},a_{3}$ in terms of $W_{6}$ so ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
33
GATE2019 EC: 29
It is desired to find a threetap casual filter which gives zero signal as an output to an input of the form $x[n]= c_{1}exp(\frac{j\pi n}{2})+c_{2}(\frac{j\pi n}{2}),$ where $c_{1}$ and $c_{2}$ ... $y[n]=0$ for all $n$, when $x[n]$ is as given above ? $a=1,b=1$ $a=0,b=1$ $a=1,b=1$ $a=0,b=1$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
34
GATE2019 EC: 30
In the circuit shown, if $v(t)=2 sin(1000 t)$ volts, $R=1k\Omega$ and $C=1\mu F,$ then the steadystate current $i(t)$, milliamperes(mA). is $\text{sin(1000 t)+ cos(1000 t)}$ $\text{2 sin(1000 t) +2 cos(1000t)}$ $\text{3 sin(1000 t) + cos(1000t)}$ $\text{sin(1000 t) +3 cos(1000t)}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
35
GATE2019 EC: 31
Consider a casual secondorder system with the transfer function $G(s)=\frac{1}{1+2s+2s^{2}}$ with a unitstep $R(s)=\frac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its steadystate value $\lim_{t\rightarrow \infty}c(t)$, rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
36
GATE2019 EC: 32
The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\frac{Y(s)}{X(s)}$ is $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
37
GATE2019 EC: 33
Let the statespace representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the system, and $y(t)$ is its output. Let $B=[0\quad0\quad1]^{T}$ ... $A=\begin{bmatrix} 0&1&0\\ 0&0&1\\3&2&1 \\\end{bmatrix} \text{and} \quad C=\begin{bmatrix} 0&0&1 \end{bmatrix}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
38
GATE2019 EC: 34
A single bit, equally likely to be $0$ and $1$, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density $N_{0}/2.$ Binary signaling with $0 \mapsto p(t),$ and $1 \mapsto q(t),$ is used for the transmission, along with an optimal ... $E$ would we obtain the same biterror probability $P_{b}$? $0$ $1$ $2$ $3$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
39
GATE2019 EC: 35
The quantum efficiency $\eta$ and responsivity $R$ at wavelength $\lambda$ (in $\mu$m) in a pin photodetector are related by $R= \frac{\eta \times \lambda}{1.24}$ $R= \frac{\lambda}{\eta \times 1.24}$ $R= \frac{1.24 \times\lambda}{\eta}$ $R= \frac{1.24}{\eta \times \lambda}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
0
votes
0
answers
40
GATE2019 EC: 36
Two identical copper wires $W1$ and $W2$ placed in parallel as shown in the figure, carry currents $I$ and $2I$, respectively, in opposite directions. If the two wires are separated by a distance of $4r$, then the magnitude of the magnetic field $\overrightarrow{B}$ between the wires at a distance $r$ ... $\frac{5\mu_{0}I}{6\pi r}$ $\frac{\mu_{0}^{2}I^{2}}{2\pi r^{2}}$
asked
Feb 12
in
Others
by
Arjun
(
1.4k
points)
gate2019ec
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