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Recent questions tagged numerical-answers

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GATE ECE 2018 | Question: 43
In the circuit shown below, the $(W/L)$ value for $M_{2}$ is twice that for $M_{1}$. The two $\text{nMOS}$ transistors are otherwise identical. The threshold voltage $V_{T}$ for both transistors is $1.0\:V$. Note that $V_{GS}$ for $M_{2}$ ... $V_{x}$ is ________.
In the circuit shown below, the $(W/L)$ value for $M_{2}$ is twice that for $M_{1}$. The two $\text{nMOS}$ transistors are otherwise identical. The threshold voltage $V_{...
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411
GATE ECE 2018 | Question: 36
For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) $0.5$ second after closing the switch is _______.
For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) $0.5$ second after closing the switch is _______.
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412
GATE ECE 2018 | Question: 23
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the four is ________.
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the fou...
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413
GATE ECE 2018 | Question: 24
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $$f\left ( x \right )={a}_{0}+a_{1}x+a_{2}...
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414
GATE ECE 2018 | Question: 22
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value of $k$ for which the equation $Ax=0$ has infinitely many solutions is _________.
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value o...
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418
GATE ECE 2018 | Question: 21
A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation constant (in $\text{Np/m}$, correct to three decimal places) of the line is ________.
A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation ...
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420
GATE ECE 2018 | Question: 16
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at least $2$. The maximum number of codewords such a code can contain is __________.
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at le...
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422
GATE ECE 2018 | Question: 18
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to $0.6\:\mu m$ is __________.
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two...
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425
GATE ECE 2017 Set 2 | Question: 51
A modulating signal given by $x(t)=5\sin (4\pi 10^3t -10\pi \cos 2\pi 10^3t)V$ is fed to a phase modulator with phase deviation constant $k_p=5$ rad/V. If the carrier frequency is $20$ kHz, the instantaneous frequency(in kHz) at $t=0.5$ ms is ____________
A modulating signal given by $x(t)=5\sin (4\pi 10^3t -10\pi \cos 2\pi 10^3t)V$ is fed to a phase modulator with phase deviation constant $k_p=5$ rad/V. If the carrier f...
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429
GATE ECE 2017 Set 2 | Question: 46
A unity feedback control system is characterized by the open-loop transfer function $G(s)=\frac{2(s+1)}{s^3+ks^2+2s+1}$ The value of $k$ for which the system oscillates at $2$ rad/s is ___________
A unity feedback control system is characterized by the open-loop transfer function $$G(s)=\frac{2(s+1)}{s^3+ks^2+2s+1}$$ The value of $k$ for which the system oscillates...
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433
GATE ECE 2017 Set 2 | Question: 32
Consider the circuit shown in the figure. The Thevenin equivalent resistance (in Ω) across P-Q is _____________
Consider the circuit shown in the figure. The Thevenin equivalent resistance (in Ω) across P-Q is _____________
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434
GATE ECE 2017 Set 2 | Question: 34
The transfer function of a causal LTI system is $H(s)=1/s$. If the input to the system is $x(t)=[\sin(t)/\pi t] u(t)$, where $u(t)$ is a unit step function, the system output $y(t)$ as $t\to \infty$ is ____________
The transfer function of a causal LTI system is $H(s)=1/s$. If the input to the system is $x(t)=[\sin(t)/\pi t] u(t)$, where $u(t)$ is a unit step function, the system ou...
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GATE ECE 2017 Set 2 | Question: 30
The minimum value of the function $f(x)=\frac{1}{3} x(x^2-3)$ in the interval $-100≤x≤100$ occurs at $x =$ ________.
The minimum value of the function $f(x)=\frac{1}{3} x(x^2-3)$ in the interval $-100≤x≤100$ occurs at $x =$ ________.
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