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683
GATE ECE 2013 | Question: 33
The impulse response of a continuous time system is given by $h(t) = \delta(t-1) + \delta(t-3).$ The value of the step response at $t = 2$ is $0$ $1$ $2$ $3$
The impulse response of a continuous time system is given by $h(t) = \delta(t-1) + \delta(t-3).$ The value of the step response at $t = 2$ is $0$$1$$2$$3$
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690
GATE ECE 2013 | Question: 26
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is$4/9$...
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691
GATE ECE 2013 | Question: 25
Let $g(t) = e^{-\pi t^{2}},$ and $h(t)$ is a filter matched to $g(t).$ If $g(t)$ is applied as input to $h(t),$ then the Fourier transformation of the output is $ e^{-\pi f^{2}}$ $ e^{-\pi f^{2}/ 2}$ $ e^{-\pi \mid f \mid }$ $ e^{-2\pi f^{2}}$
Let $g(t) = e^{-\pi t^{2}},$ and $h(t)$ is a filter matched to $g(t).$ If $g(t)$ is applied as input to $h(t),$ then the Fourier transformation of the output is$ e^{-\pi ...
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692
GATE ECE 2013 | Question: 24
The return loss of a device is found to be $20\:dB.$ The voltage standing wave ratio (VSWR) and magnitude of reflection coefficient are respectively $1.22$ and $0.1$ $0.81$ and $0.1$ $-1.22$ and $0.1$ $2.44$ and $0.2$
The return loss of a device is found to be $20\:dB.$ The voltage standing wave ratio (VSWR) and magnitude of reflection coefficient are respectively $1.22$ and $0.1$$0.81...
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693
GATE ECE 2013 | Question: 23
A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$ should be $3$ $4$ $5$ $7$
A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum powe...
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694
GATE ECE 2013 | Question: 22
The transfer function $\dfrac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is $\frac{0.5s+1}{s+1} \\ $ $\frac{3s+6}{s+2} \\ $ $\frac{s+2}{s+1} \\ $ $\frac{s+1}{s+2}$
The transfer function $\dfrac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is$\frac{0.5s+1}{s+1} \\ $$\frac{3s+6}{s+2} \\ $$\frac{s+2}{s+1} \\ $$\frac{s+1}{s+2}$
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695
GATE ECE 2013 | Question: 21
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is $u(t)$ $tu(t)$ $\frac{t^{2}}{2}u(t)$ $e^{-t}u(t)$
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is$u(t)$$tu(t)$$\frac{t^{2}}{2}u(t)$$e^{-t}u(t)$
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696
GATE ECE 2013 | Question: 20
A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive has no real roots no negative real root odd number of real roots at least one positive and one negative real root
A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive hasno real rootsno negative real rootodd number of real roots a...
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697
GATE ECE 2013 | Question: 19
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
The minimum eigenvalue of the following matrix is$$\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$$$0$$1$$2$$3$
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699
GATE ECE 2013 | Question: 17
In a MOSFET operating in the saturation region, the channel length modulation effect causes an increase in the gate-source capacitance a decrease in the transconductance a decrease in the unity-gain cutoff frequency a decrease in the output resistance
In a MOSFET operating in the saturation region, the channel length modulation effect causes an increase in the gate-source capacitancea decrease in the transconductance a...
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700
GATE ECE 2013 | Question: 16
A band-limited signal with a maximum frequency of $5\: kHz$ is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is $5\: kHz $ $12\: kHz$ $15\: kHz$ $20\: kHz$
A band-limited signal with a maximum frequency of $5\: kHz$ is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is$5\: kHz $$12...
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702
GATE ECE 2013 | Question: 14
For a periodic signal $v(t) = 30\sin100\:t + 10\cos300\:t + 6\sin(500\:t+\pi/4),$ the fundamental frequency in $rad/s$ is $100$ $300$ $500$ $1500$
For a periodic signal $v(t) = 30\sin100\:t + 10\cos300\:t + 6\sin(500\:t+\pi/4),$ the fundamental frequency in $rad/s$ is$100$$300$$500$$1500$
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703
GATE ECE 2013 | Question: 13
The bit rate of a digital communication system is $R$ kbits/s. The modulation used is $32$-QAM. The minimum bandwidth required for ISI free transmission is $R/10\: Hz$ $R/10\: kHz$ $R/5\: Hz$ $R/5\: kHz$
The bit rate of a digital communication system is $R$ kbits/s. The modulation used is $32$-QAM. The minimum bandwidth required for ISI free transmission is $R/10\: Hz$$R/...
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706
GATE ECE 2013 | Question: 10
In the circuit shown below what is the output voltage $(V_{\text{out}})$ if a silicon transistor $Q$ and an ideal op-amp are used? $-15\: V$ $-0.7\: V$ $+0.7\: V$ $+15\: V$
In the circuit shown below what is the output voltage $(V_{\text{out}})$ if a silicon transistor $Q$ and an ideal op-amp are used?$-15\: V$$-0.7\: V$$+0.7\: V$$+15\: V$
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708
GATE ECE 2013 | Question: 8
The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is $\frac{t^{2}}{2}u(t)$ $\frac{t(t-1)}{2}u(t-1)$ $\frac{(t-1)^{2}}{2}u(t-1)$ $\frac{t^{2}-1}{2}u(t-1)$
The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is$\frac{t^{2}}{2}u(t)$$\frac{t(t-1)}{2}u(t-1)$$\frac{(t-1)^{2}}{2}u(t-1)$$\frac...
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709
GATE ECE 2013 | Question: 7
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$ $1/3$ $1$ $3$
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$$1/3$ $1$ $3$
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710
GATE ECE 2013 | Question: 6
The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta $ holds to within $10\%$ error is $10^{\circ}$ $18^{\circ}$ $50^{\circ}$ $90^{\circ}$
The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta $ holds to within $10\%$ error is$10^{\circ}$$18^{\circ}$$50^{\circ}$$90^{\circ}$
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717
GATE ECE 2012 | Question: 64
The data given in the following table summarizes the monthly budget of an average household. ... $10\%$ $14\%$ $81\%$ $86\%$
The data given in the following table summarizes the monthly budget of an average household.$$\begin{array}{|l|c|c|} \hline \textbf{Category} & \textbf{Amount(Rs.)} \\\hl...
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718
GATE ECE 2012 | Question: 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 $2$ $3$ $4$ $8$
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 balanc...
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719
GATE ECE 2012 | Question: 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 $5$ $6$ $9$ $10$
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. $10$ n...
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