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2442
GATE ECE 2016 Set 1 | Question: 33
An AC voltage source $V = 10 \sin(t)$ volts is applied to the following network. Assume that $R_1 = 3 k\Omega$, $R_2 = 6 k\Omega$ and $R_3 = 9k\Omega$, and that the diode is ideal. RMS current $I_{rms}$(in mA) through the diode is _______
An AC voltage source $V = 10 \sin(t)$ volts is applied to the following network. Assume that $R_1 = 3 k\Omega$, $R_2 = 6 k\Omega$ and $R_3 = 9k\Omega$, and that the diode...
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2445
GATE ECE 2015 Set 3 | Question: 27
A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The expected value of $X$ is _______.
A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The...
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2446
GATE ECE 2015 Set 3 | Question: 11
In the circuit shown in the figure, the BJT has a current gain $(\beta)$ of $50.$ For an emitter-base voltage ܸ $V_{EB} = 600\: mV,$ the emitter-collector voltage $V_{EC}$ (in Volts) is _______.
In the circuit shown in the figure, the BJT has a current gain $(\beta)$ of $50.$ For an emitter-base voltage ܸ $V_{EB} = 600\: mV,$ the emitter-collector voltage $V_{EC...
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2447
GATE ECE 2015 Set 2 | Question: 52
Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to $pq+(1-p)(1-q)$ $pq$ $p(1-q)$ $1-pq$
Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to$pq+(1-p)(1-q)$$pq$$p(1-q)$...
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2449
GATE ECE 2015 Set 2 | Question: 31
In the circuit shown, the Norton equivalent resistance $(\text{in}\: \Omega)$ across terminals $a-b$ is _______.
In the circuit shown, the Norton equivalent resistance $(\text{in}\: \Omega)$ across terminals $a-b$ is _______.
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2450
GATE ECE 2016 Set 2 | GA Question: 2
The students ___________ the teacher on the teachers’ day for twenty years of dedicated teaching. facilitated felicitated fantasized facillitated
The students ___________ the teacher on the teachers’ day for twenty years of dedicated teaching.facilitatedfelicitatedfantasizedfacillitated
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2451
GATE ECE 2015 Set 2 | Question: 55
The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression ... The type of the polarization is Right Hand Circular Left Hand Elliptical Right Hand Elliptical Linear
The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression $$\text{E}(z,t) = \textbf{a}_{x} 5 \cos(2\pi \times ...
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2456
GATE ECE 2015 Set 2 | Question: 3
Let $f(z)=\dfrac{az+b}{cz+d}.$ If $f(z_{1})=f(z_{2})$ for all $z_{1}\neq z_{2},a=2,b=4$ and $c=5,$ then $d$ should be equal to ________.
Let $f(z)=\dfrac{az+b}{cz+d}.$ If $f(z_{1})=f(z_{2})$ for all $z_{1}\neq z_{2},a=2,b=4$ and $c=5,$ then $d$ should be equal to ________.
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2457
GATE ECE 2015 Set 1 | GA Question: 4
Operators $\square,$ $\Diamond$ and $\rightarrow$ are defined by: $a\,\square\,b=\frac{a+b}{a-b};\, a\,\Diamond, b=\frac{a+b}{a-b};$ $a\,\rightarrow\, b=ab.$ Find the value of $(66\,\square\, 6)\rightarrow(66\,\Diamond, 6).$ $-2$ $-1$ $1$ $2$
Operators $\square,$ $\Diamond$ and $\rightarrow$ are defined by: $a\,\square\,b=\frac{a+b}{a-b};\, a\,\Diamond, b=\frac{a+b}{a-b};$ $a\,\rightarrow\, b=ab.$Find the valu...
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2459
GATE ECE 2015 Set 1 | Question: 13
In the circuit shown, the switch SW is thrown from position $A$ to position $B$ at time $t=0$. The energy (in $\mu J$) taken from the $3$ V source to charge the $0.1 \: \mu F$ capacitor from $0$ V t $3$ V is $0.3$ $0.45$ $0.9$ $3$
In the circuit shown, the switch SW is thrown from position $A$ to position $B$ at time $t=0$. The energy (in $\mu J$) taken from the $3$ V source to charge the $0.1 \: \...
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2461
GATE ECE 2014 Set 3 | Question: 20
Consider the following block diagram in the figure. The transfer function $\frac{C(s)}{R(s)}$ is $\frac{G_{1}G_{2}}{1+G_{1}G_{2}}$ $G_{1}G_{2}+G_{1}+1$ $G_{1}G_{2}+G_{2}+1$ $\frac{G_{1}}{1+G_{1}G_{2}}$
Consider the following block diagram in the figure. The transfer function $\frac{C(s)}{R(s)}$ is$\frac{G_{1}G_{2}}{1+G_{1}G_{2}}$$G_{1}G_{2}+G_{1}+1$$G_{1...
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2466
GATE ECE 2015 Set 3 | Question: 5
The value of $\displaystyle{}\sum_{n=0}^{\infty} n \left(\dfrac{1}{2}\right)^{n}$ is ________.
The value of $\displaystyle{}\sum_{n=0}^{\infty} n \left(\dfrac{1}{2}\right)^{n}$ is ________.
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2467
GATE ECE 2015 Set 1 | Question: 7
In the network shown in the figure, all resistors are identical with $R = 300 \Omega$. The resistance $R_{ab}$ (in $\Omega$) of the network is __________.
In the network shown in the figure, all resistors are identical with $R = 300 \Omega$. The resistance $R_{ab}$ (in $\Omega$) of the network is __________.
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2468
GATE ECE 2014 Set 3 | Question: 46
The steady state error of the system shown in the figure for a unit step input is _________.
The steady state error of the system shown in the figure for a unit step input is _________.
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2471
GATE ECE 2016 Set 3 | Question: 6
Consider the signal $x(t) = \cos(6\pi t) + \sin (8\pi t)$, where $t$ is in seconds. The Nyquist sampling rate (in samples/second) for the signal $y(t) = x(2t + 5)$ is $8$ $12$ $16$ $32$
Consider the signal $x(t) = \cos(6\pi t) + \sin (8\pi t)$, where $t$ is in seconds. The Nyquist sampling rate (in samples/second) for the signal $y(t) = x(2t + 5)$ is$8$$...
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2472
GATE ECE 2015 Set 3 | Question: 26
The Newton-Raphson method is used to solve the equation $f(x) = x^{3} – 5x^{2} + 6x – 8 = 0.$ Taking the initial guess as $x = 5,$ the solution obtained at the end of the first iteration is __________.
The Newton-Raphson method is used to solve the equation $f(x) = x^{3} – 5x^{2} + 6x – 8 = 0.$ Taking the initial guess as $x = 5,$ the solution obtained at the end of...
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2476
GATE ECE 2015 Set 2 | Question: 29
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _______.
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _...
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2478
GATE ECE 2015 Set 1 | Question: 29
The maximum area (in square units) of a rectangle whose vertices lie on the eclipse $x^2+4y^2=1$ is __________.
The maximum area (in square units) of a rectangle whose vertices lie on the eclipse $x^2+4y^2=1$ is __________.
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2479
GATE ECE 2015 Set 1 | GA Question: 9
A cube of side $3$ units is formed using a set of smaller cubes of side $1$ unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible. $1:4$ $1:3$ $1:2$ $2:3$
A cube of side $3$ units is formed using a set of smaller cubes of side $1$ unit. Find the proportion of the number of faces of the smaller cubes visible to those which a...
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2480
GATE ECE 2015 Set 1 | Question: 44
For the discrete-time system shown in the figure, the poles of the system transfer function are located at $2,3 \\$ $\frac{1}{2},3 \\$ $\frac{1}{2}, \frac{1}{3} \\$ $2, \frac{1}{3}$
For the discrete-time system shown in the figure, the poles of the system transfer function are located at$2,3 \\$$\frac{1}{2},3 \\$$\frac{1}{2}, \frac{1}{3} \\$$2, \frac...
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