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2681
GATE ECE 2014 Set 3 | Question: 50
A real band-limited random process $X(t)$ ... -pass filter of unity gain with centre frequency of $8$ $kHz$ and band-width of $2$ kHz. The output power (in Watts) is ___________.
A real band-limited random process $X(t)$ has two-sided power spectral density$$S_{X}(f)= \begin{cases} 10^{-6} (3000-\mid f \mid) \text{Watts/Hz} & \text{for } \mid f \...
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2684
GATE ECE 2014 Set 3 | Question: 53
Given the vector $\textbf{A}= ( \cos x ) ( \sin y )\hat{a_{x}}+( \sin x )( \cos y )\hat{a_{y}},$ where $\hat{a_{x}},$ $\hat{a_{y}}$ denote unit vectors along $x$, $y$ directions, respectively. The magnitude of curl of $\textbf{A}$ is __________
Given the vector $\textbf{A}= ( \cos x ) ( \sin y )\hat{a_{x}}+( \sin x )( \cos y )\hat{a_{y}},$ where $\hat{a_{x}},$ $\hat{a_{y}}$ denote unit vectors along $x$, $y$ di...
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2688
GATE ECE 2014 Set 2 | GA Question: 5
Fill in the missing number in the series. $2$ $3$ $6$ $15$ __________ $157.5$ $630$
Fill in the missing number in the series.$2$ $3$ $6$ $15$ __________ $157.5$ $630$
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2689
GATE ECE 2014 Set 2 | GA Question: 6
Find the odd one in the following group $Q,W,Z,B \qquad B,H,K,M \qquad W,C,G,J \qquad M,S,V,X$ $Q, W, Z, B$ $B,H,K,M$ $W,C,G,J$ $M,S,V,X$
Find the odd one in the following group$Q,W,Z,B \qquad B,H,K,M \qquad W,C,G,J \qquad M,S,V,X$$Q, W, Z, B$$B,H,K,M$$W,C,G,J$$M,S,V,X$
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2691
GATE ECE 2014 Set 2 | GA Question: 8
The sum of eight consecutive odd numbers is $656$. The average of four consecutive even numbers is $87$. What is the sum of the smallest odd number and second largest even number?
The sum of eight consecutive odd numbers is $656$. The average of four consecutive even numbers is $87$. What is the sum of the smallest odd number and second largest eve...
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2694
GATE ECE 2014 Set 2 | Question: 1
The determinant of matrix $A$ is $5$ and the determinant of matrix B is $40$. The determinant of matrix $AB$ is ________
The determinant of matrix $A$ is $5$ and the determinant of matrix B is $40$. The determinant of matrix $AB$ is ________
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2695
GATE ECE 2014 Set 2 | Question: 2
Let $X$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $100$. The expectation, $E[X]$, is ________.
Let $X$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $100$. The expectation, $E[X]$, is ________.
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2696
GATE ECE 2014 Set 2 | Question: 3
For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at $t= log_{e}4$ $t= log_{e}2$ $t= 0$ $t= log_{e}8$
For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at$t= log_{e}4$$t= log_{e}2$$t= 0$$t= log_{e}8$
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2697
GATE ECE 2014 Set 2 | Question: 4
The value of $\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x}$ is $\text{ln }2$ $1.0$ $e$ $\infty$
The value of $$\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x}$$ is$\text{ln }2$$1.0$$e$$\infty$
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2698
GATE ECE 2014 Set 2 | Question: 5
If the characteristic equation of the differential equation $\frac{\mathrm{d}^2 y}{\mathrm{dx}^2}+2\alpha \frac{\mathrm{d}y}{\mathrm{d} x}+y= 0$ has two equal roots, then the value of $\alpha$ are $\pm 1$ $0,0$ $\pm j$ $\pm 1/2$
If the characteristic equation of the differential equation $$\frac{\mathrm{d}^2 y}{\mathrm{dx}^2}+2\alpha \frac{\mathrm{d}y}{\mathrm{d} x}+y= 0$$ has two equal roots, th...
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2700
GATE ECE 2014 Set 2 | Question: 7
In the figure shown, the ideal switch has been open for a long time. If it is closed at t = 0, then the magnitude of the current (in mA) through the $4k \Omega$ resistor at $t= 0^{+}$ is ________.
In the figure shown, the ideal switch has been open for a long time. If it is closed at t = 0, then the magnitude of the current (in mA) through the $4k \Omega$ resistor ...
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2702
GATE ECE 2014 Set 2 | Question: 9
An increase in the base recombination of a BJT will increase the common emitter dc current gain $\beta$ the breakdown voltage $BV_{CEO}$ the unity-gain cut-off frequency $f_{T}$ the transconductance $g_{m}$
An increase in the base recombination of a BJT will increasethe common emitter dc current gain $\beta$the breakdown voltage $BV_{CEO}$the unity-gain cut-off frequency $f_...
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2703
GATE ECE 2014 Set 2 | Question: 10
In CMOS technology, shallow P-well or N-well regions can be formed using low pressure chemical vapour deposition low energy sputtering low temperature dry oxidation low energy ion-implantation
In CMOS technology, shallow P-well or N-well regions can be formed usinglow pressure chemical vapour deposition low energy sputteringlow temperature dry oxidationlow ener...
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2706
GATE ECE 2014 Set 2 | Question: 13
A cascade connection of two voltage amplifier $A1$ and $A2$ is shown in the figure. The open-loop gain $A_{V0}$, input resistance $R_{in}$, and output resistance $R_{o}$ ... $V_{out}/V_{in}$ is __________.
A cascade connection of two voltage amplifier $A1$ and $A2$ is shown in the figure. The open-loop gain $A_{V0}$, input resistance $R_{in}$, and output resistance $R_{o}$ ...
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2708
GATE ECE 2014 Set 2 | Question: 17
As FIR system is described by the system function $ H(z) = 1 + \frac{7}{2} z^{-1} + \frac{3}{2}z^{-2}$. The system is maximum phase minimum phase mixed phase zero phase
As FIR system is described by the system function $$ H(z) = 1 + \frac{7}{2} z^{-1} + \frac{3}{2}z^{-2}$$. The system ismaximum phaseminimum phasemixed phasezero phase
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2709
GATE ECE 2014 Set 2 | Question: 18
Let $x[n] = x[-n]$. Let $X(z)$ be the $z$-transform of $x[n]$. If $0.5 + j 0.25$ is a zero of $X(z)$, which one of the following must also be a zero of $x(z)$ $0.5 – j 0.25$ $1/(0.5 + j 0.25)$ $1/(0.5 – j 0.25)$ $2+j 4$
Let $x[n] = x[-n]$. Let $X(z)$ be the $z$-transform of $x[n]$. If $0.5 + j 0.25$ is a zero of $X(z)$, which one of the following must also be a zero of $x(z)$$0.5 – j 0...
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2711
GATE ECE 2014 Set 2 | Question: 20
The natural frequency of an undamped second-order system is $40$ rad/s. If the system is damped with a damping ratio $0.3$, the damped natural frequency in $rad/s$ is ___________.
The natural frequency of an undamped second-order system is $40$ rad/s. If the system is damped with a damping ratio $0.3$, the damped natural frequency in $rad/s$ is ___...
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2712
GATE ECE 2014 Set 2 | Question: 21
For the following system, when $X_{1} (s) = 0$, the transfer function $\frac{Y(s)}{X_{2}(s)}$ is $\frac{s+1}{s^{2}}\\ $ $\frac{1}{s+1} \\$ $\frac{s+2}{s(s+1)} \\$ $\frac{s+1}{s(s+2)}$
For the following system, when $X_{1} (s) = 0$, the transfer function $\frac{Y(s)}{X_{2}(s)}$ is$\frac{s+1}{s^{2}}\\ $$\frac{1}{s+1} \\$$\frac{s+2}{s(s+1...
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2715
GATE ECE 2014 Set 2 | Question: 25
Which one of the following field patterns represents a TEM wave travelling in the position $x$ direction? $E= +8\hat{y,} \: H = -4\hat{z}$ $E= -2\hat{y,} H = -3\hat{z}$ $E= +2\hat{y,} H = +2\hat{y}$ $E= -3\hat{y,} H = +4\hat{z}$
Which one of the following field patterns represents a TEM wave travelling in the position $x$ direction?$E= +8\hat{y,} \: H = -4\hat{z}$$E= -2\hat{y,} H = -3\hat{z}$$E= ...
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2717
GATE ECE 2014 Set 2 | Question: 27
The real part of an analytic function $f(z)$ where $z = x + jy$ is given by $e^{-y} \cos(x)$. The imaginary part of $f(z)$ is $e^{y} \cos( x )$ $e^{-y} \sin( x )$ $-e^{y} \sin ( x )$ $-e^{-y} \sin (x )$
The real part of an analytic function $f(z)$ where $z = x + jy$ is given by $e^{-y} \cos(x)$. The imaginary part of $f(z)$ is$e^{y} \cos( x )$$e^{-y} \sin( x )$$-e^{y} \s...
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2718
GATE ECE 2014 Set 2 | Question: 28
The maximum value of the determinant among all $2 \times 2$ real symmetric matrices with trace $14$ is __________.
The maximum value of the determinant among all $2 \times 2$ real symmetric matrices with trace $14$ is __________.
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2719
GATE ECE 2014 Set 2 | Question: 29
If $\overrightarrow {r}= x\hat{a_{x}}+y\hat{a_{y}}+z\hat{a_{z}}$ and $\mid \overrightarrow{r} \mid= r$ , then $\text{div} ( r^{2} \nabla ( \text{ln }r ) )$ = _______ .
If $\overrightarrow {r}= x\hat{a_{x}}+y\hat{a_{y}}+z\hat{a_{z}}$ and $\mid \overrightarrow{r} \mid= r$ , then $\text{div} ( r^{2} \nabla ( \text{ln }r ) )$ = _______ .
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