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2481
GATE ECE 2015 Set 1 | Question: 17
The result of the convolution $x(-t) * \delta (-t-t_0)$ is $x(t+t_0)$ $x(t-t_0)$ $x(-t+t_0)$ $x(-t – t_0)$
The result of the convolution $x(-t) * \delta (-t-t_0)$ is$x(t+t_0)$$x(t-t_0)$$x(-t+t_0)$$x(-t – t_0)$
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2482
GATE ECE 2015 Set 1 | Question: 18
The waveform of a periodic signal $x(t)$ is shown in the figure. A signal $g(t)$ is defined by $g(t) = x \big( \frac{t-1}{2} \big)$. The average power of $g(t)$ is ________
The waveform of a periodic signal $x(t)$ is shown in the figure.A signal $g(t)$ is defined by $g(t) = x \big( \frac{t-1}{2} \big)$. The average power of $g(t)$ is _______...
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2483
GATE ECE 2015 Set 1 | Question: 19
Negative feedback in a closed-loop control system $\textbf{ DOES NOT}$ reduce the overall gain reduce bandwidth improve disturbance rejection reduce sensitivity to parameter variation
Negative feedback in a closed-loop control system $\textbf{ DOES NOT}$reduce the overall gainreduce bandwidthimprove disturbance rejectionreduce sensitivity to parameter ...
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2484
GATE ECE 2015 Set 1 | Question: 20
A unity negative feedback system has the open-loop transfer function $G(s) = \frac{K}{s(s+1)(s+3)}$. The value of the gain $K (>0)$ at which the root locus crosses the imaginary axis is ________
A unity negative feedback system has the open-loop transfer function $G(s) = \frac{K}{s(s+1)(s+3)}$. The value of the gain $K (>0)$ at which the root locus crosses the im...
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2485
GATE ECE 2015 Set 1 | Question: 21
The polar plot of the transfer function $G(s) = \frac{10(s+1)}{s+10}$ for $0 \leq \omega < \infty$ will be in the first quadrant second quadrant third quadrant fourth quadrant
The polar plot of the transfer function $G(s) = \frac{10(s+1)}{s+10}$ for $0 \leq \omega < \infty$ will be in thefirst quadrantsecond quadrantthird quadrantfourth quadran...
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2490
GATE ECE 2015 Set 1 | Question: 25
The solution of the differential equation $\frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y=0$ with $y(0)=y’(0)=1$ is $(2-t)e^t$ $(1+2t)e^{-t}$ $(2+t)e^{-t}$ $(1-2t)e^t$
The solution of the differential equation $\frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y=0$ with $y(0)=y’(0)=1$ is$(2-t)e^t$$(1+2t)e^{-t}$$(2+t)e^{-t}$$(1-2t)e^t$
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2492
GATE ECE 2015 Set 1 | Question: 28
Which one of the following graphs describes the function $f(x)=e^{-x}(x^2+x+1)$?
Which one of the following graphs describes the function $f(x)=e^{-x}(x^2+x+1)$?
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2493
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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2494
GATE ECE 2015 Set 1 | Question: 30
The damping ratio of a series RLC circuit can be expressed as $\frac{R^2C}{2L} \\$ $\frac{2L}{R^2C} \\$ $\frac{R}{2} \sqrt{\frac{C}{L}} \\$ $\frac{2}{R} \sqrt{\frac{L}{C}}$
The damping ratio of a series RLC circuit can be expressed as$\frac{R^2C}{2L} \\$$\frac{2L}{R^2C} \\$$\frac{R}{2} \sqrt{\frac{C}{L}} \\$$\frac{2}{R} \sqrt{\frac{L}{C}}$
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2495
GATE ECE 2015 Set 1 | Question: 31
In the circuit shown, switch SW is closed at $t=0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t=1$ sec is _________.
In the circuit shown, switch SW is closed at $t=0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t=1$ sec is _________.
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2496
GATE ECE 2015 Set 1 | Question: 32
In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.
In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.
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2497
GATE ECE 2015 Set 1 | Question: 33
The built-in potential of an abrupt p-n junction is $0.75$ V. If its junction capacitance $(C_J)$ at a reverse bias $(V_R)$ of $1.25 \: V$ is $5$ pF, the value of $C_J$ (in pF) when $V_R = 7.25 \: V$ is ________.
The built-in potential of an abrupt p-n junction is $0.75$ V. If its junction capacitance $(C_J)$ at a reverse bias $(V_R)$ of $1.25 \: V$ is $5$ pF, the value of $C_J$ (...
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2498
GATE ECE 2015 Set 1 | Question: 34
A MOSFET in saturation has a drain current of $1$ mA for $V_{DS} =0.5 \: V$. If the channel length modulation coefficient is $0.05 \: V^{-1}$, the output resistance (in $k \Omega$) of the MOSFET is ___________.
A MOSFET in saturation has a drain current of $1$ mA for $V_{DS} =0.5 \: V$. If the channel length modulation coefficient is $0.05 \: V^{-1}$, the output resistance (in $...
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2500
GATE ECE 2015 Set 1 | Question: 36
The Boolean expression $F(X,Y,Z) = \overline{X} \: Y \: \overline{Z}+ X \: \overline{Y} \: \overline{Z}+ X \: Y \: \overline{Z} + X \: Y \: Z$ ... $(X+\overline{Y}+\overline{Z})(\overline{X}+Y+Z)(\overline{X}+\overline{Y}+Z)(X + Y + Z)$
The Boolean expression $F(X,Y,Z) = \overline{X} \: Y \: \overline{Z}+ X \: \overline{Y} \: \overline{Z}+ X \: Y \: \overline{Z} + X \: Y \: Z$ converted into the canonica...
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2503
GATE ECE 2015 Set 1 | Question: 39
For the NMOSFET in the circuit shown, the threshold voltage is $V_{th}$, where $V_{th}>0$. The source voltage $V_{SS}$ is varied from $0$ to $V_{DD}$. Neglecting the channel length modulation, the drain current $I_D$ as a function of $V_{SS}$ is represented by
For the NMOSFET in the circuit shown, the threshold voltage is $V_{th}$, where $V_{th}>0$. The source voltage $V_{SS}$ is varied from $0$ to $V_{DD}$. Neglecting the chan...
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2504
GATE ECE 2015 Set 1 | Question: 40
In the circuit shown, assume that the opamp is ideal. The bridge output voltage $V_0$ (in mV) for $\delta=0.05$ is __________
In the circuit shown, assume that the opamp is ideal. The bridge output voltage $V_0$ (in mV) for $\delta=0.05$ is __________
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2506
GATE ECE 2015 Set 1 | Question: 42
In the circuit shown, $I_1=80$ mA and $I_2=4$ mA. Transistors $T_1$ and $T_2$ are identical. Assume that the thermal voltage $V_T$ is $26$ mV at $27^{\circ}C$. At $50^{\circ}C$, the value of the voltage $V_{12}=V_1 - V_2$ (in mV) is _______.
In the circuit shown, $I_1=80$ mA and $I_2=4$ mA. Transistors $T_1$ and $T_2$ are identical. Assume that the thermal voltage $V_T$ is $26$ mV at $27^{\circ}C$. At $50^{\c...
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2507
GATE ECE 2015 Set 1 | Question: 43
Two sequences $\begin{bmatrix}a, & b, & c \end{bmatrix}$ and $\begin{bmatrix}A, & B, & C \end{bmatrix}$ ... $\begin{bmatrix}p, & q, & r \end{bmatrix} = \begin{bmatrix} c, & b, & a \end{bmatrix}$
Two sequences $\begin{bmatrix}a, & b, & c \end{bmatrix}$ and $\begin{bmatrix}A, & B, & C \end{bmatrix}$ are related as,$$\begin{bmatrix}A \\ B \\ C \end{bmatrix} = \be...
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2508
GATE ECE 2015 Set 1 | Question: 44
For the discrete-time system shown in the figure, the poles of the system transfer function are located at $2,3 \\$ $\frac{1}{2},3 \\$ $\frac{1}{2}, \frac{1}{3} \\$ $2, \frac{1}{3}$
For the discrete-time system shown in the figure, the poles of the system transfer function are located at$2,3 \\$$\frac{1}{2},3 \\$$\frac{1}{2}, \frac{1}{3} \\$$2, \frac...
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2510
GATE ECE 2015 Set 1 | Question: 46
The open-loop transfer function of a plant in a unity feedback configuration is given as $G(s) = \frac{K(s+4)}{(s+8)(s^2-9)}$. The value of the gain $K(>0)$ for which $-1+j2$ lies on the root locus is _________.
The open-loop transfer function of a plant in a unity feedback configuration is given as $G(s) = \frac{K(s+4)}{(s+8)(s^2-9)}$. The value of the gain $K(>0)$ for which $-1...
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2511
GATE ECE 2015 Set 1 | Question: 47
A lead compensator network includes a parallel combination of $R$ and $C$ in the feed-forward path. If the transfer function of the compensator is $G_c(s)=\frac{s+2}{s+4}$, the value of $RC$ is ___________.
A lead compensator network includes a parallel combination of $R$ and $C$ in the feed-forward path. If the transfer function of the compensator is $G_c(s)=\frac{s+2}{s+4}...
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2520
GATE ECE 2014 Set 4 | GA Question: 1
Which of the following options is the closest in meaning to the word underlined in the sentence below? In a democracy, everybody has the freedom to disagree with the government. dissent descent decent decadent
Which of the following options is the closest in meaning to the word underlined in the sentence below?In a democracy, everybody has the freedom to disagree with the gover...
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