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Recent questions tagged gate2013-ec

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GATE ECE 2013 | Question: 62
Find the sum to $n$ terms of the series $10+84+ 734 +\dots $ $\frac{9(9^n+1)}{10}+1$ $\frac{9(9^n-1)}{8}+1$ $\frac{9(9^n-1)}{8}+n$ $\frac{9(9^n-1)}{8}+n^2$
Find the sum to $n$ terms of the series $10+84+ 734 +\dots $$\frac{9(9^n+1)}{10}+1$$\frac{9(9^n-1)}{8}+1$$\frac{9(9^n-1)}{8}+n$$\frac{9(9^n-1)}{8}+n^2$
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GATE ECE 2013 | Question: 65
What is the chance that a leap year, selected at random, will contain $53$ Saturdays? $2/7$ $3/7$ $1/7$ $5/7$
What is the chance that a leap year, selected at random, will contain $53$ Saturdays?$2/7$$3/7$$1/7$$5/7$
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GATE ECE 2013 | Question: 64
The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is $(-\infty ,0)$ $(0,1)$ $(1,\infty )$ $(0,\infty )$
The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is$(-\infty ,0)$$(0,1)$$(1,\infty )$$(0,\infty )$
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GATE ECE 2013 | Question: 61
A car travels $8 \: km$ in the first quarter of an hour, $6\: km$ in the second quarter and $16\: km$ in the third quarter. The average speed of the car in $km$ per hour over the entire journey is $30$ $36$ $40$ $24$
A car travels $8 \: km$ in the first quarter of an hour, $6\: km$ in the second quarter and $16\: km$ in the thirdquarter. The average speed of the car in $km$ per hour ...
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GATE ECE 2013 | Question: 60
They were requested not to $\textbf{quarrel}$ with others. Which one of the following options is the closest in meaning to the word $\textbf{quarrel}$? make out call out dig out fall out
They were requested not to $\textbf{quarrel}$ with others.Which one of the following options is the closest in meaning to the word $\textbf{quarrel}$?make outcall outdig ...
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GATE ECE 2013 | Question: 55
The state diagram of a system is shown below. A system is described by the state-variable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ The state transition matrix $e^{At}$ ... $\begin{bmatrix} e^{-t}&-te^{-t} \\ 0 &e^{-t} \end{bmatrix}$
The state diagram of a system is shown below. A system is described by the state-variable equations $$\dot{X}= AX+Bu;\:\: y = CX+Du$$The state transition matrix $e^{At}$ ...
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GATE ECE 2013 | Question: 59
Complete the sentence: Dare _______________ mistakes. commit to commit committed committing
Complete the sentence:Dare _______________ mistakes.committo commitcommittedcommitting
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GATE ECE 2013 | Question: 56
Choose the grammatically CORRECT sentence: Two and two add four. Two and two become four. Two and two are four. Two and two make four.
Choose the grammatically CORRECT sentence:Two and two add four.Two and two become four.Two and two are four.Two and two make four.
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GATE ECE 2013 | Question: 54
The state diagram of a system is shown below. A system is described by the state-variable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ ...
The state diagram of a system is shown below. A system is described by the state-variable equations$$\dot{X}= AX+Bu;\:\: y = CX+Du$$The state-variable equations of the sy...
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GATE ECE 2013 | Question: 50
Consider the following figure The current $I_{S}$ in $\text{Amps}$ in the voltage source, and voltage $V_{S}$ in Volts across the current source respectively, are $13, − 20$ $8, − 10$ $− 8, 20$ $− 13, 20$
Consider the following figure The current $I_{S}$ in $\text{Amps}$ in the voltage source, and voltage $V_{S}$ in Volts across the current source respectively, are$13, −...
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GATE ECE 2013 | Question: 51
Consider the following figure The current in the $1\Omega$ resistor in $\text{Amps}$ is $2$ $3.33$ $10$ $12$
Consider the following figure The current in the $1\Omega$ resistor in $\text{Amps}$ is$2$$3.33$ $10$ $12$
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GATE ECE 2013 | Question: 52
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
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GATE ECE 2013 | Question: 53
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
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GATE ECE 2013 | Question: 45
There are four chips each of $1024\:\text{bytes}$ connected to a $16\:\text{bit}$ address bus as shown in the figure below. $RAMs\: 1, 2, 3$ and $4$ ... $0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH$ $0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH$
There are four chips each of $1024\:\text{bytes}$ connected to a $16\:\text{bit}$ address bus as shown in the figure below. $RAMs\: 1, 2, 3$ and $4$ respectively are mapp...
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GATE ECE 2013 | Question: 47
Let $U$ and $V$ be two independent and identically distributed random variables such that $P(U=+1)=P(U=-1) = \dfrac{1}{2}.$ The entropy $H(U + V)$ in bits is $\frac{3}{4} \\$ $1$ $\frac{3}{2} \\$ $\log_{2}3$
Let $U$ and $V$ be two independent and identically distributed random variables such that $P(U=+1)=P(U=-1) = \dfrac{1}{2}.$ The entropy $H(U + V)$ in bits is$\frac{3}{4} ...
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GATE ECE 2013 | Question: 46
In the circuit shown below, the silicon $npn$ transistor $Q$ has a very high value of $\beta.$ The required value of $R_{2}$ in $k\Omega$ to produce $I_{C} = 1\: mA$ is $20$ $30$ $40$ $50$
In the circuit shown below, the silicon $npn$ transistor $Q$ has a very high value of $\beta.$ The required value of $R_{2}$ in $k\Omega$ to produce $I_{C} = 1\: mA$ is$2...
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GATE ECE 2013 | Question: 40
The signal flow graph for a system is given below. The transfer function $\dfrac{Y(s)}{U(s)}$ for this system is $\frac{s+1}{5s^{2}+6s+2} \\$ $\frac{s+1}{s^{2}+6s+2} \\$ $\frac{s+1}{s^{2}+4s+2} \\$ $\frac{1}{5s^{2}+6s+2}$
The signal flow graph for a system is given below. The transfer function $\dfrac{Y(s)}{U(s)}$ for this system is $\frac{s+1}{5s^{2}+6s+2} \\$$\frac{s+1}{s^{2}+6s+2} \\$$\...
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GATE ECE 2013 | Question: 41
In the circuit shown below the $\text{op-amps}$ are ideal. Then $V_{\text{out}}$ in $\text{Volts}$ is $4$ $6$ $8$ $10$
In the circuit shown below the $\text{op-amps}$ are ideal. Then $V_{\text{out}}$ in $\text{Volts}$ is$4$$6$$8$$10$
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GATE ECE 2013 | Question: 39
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ ... $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}$
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ consider the...
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GATE ECE 2013 | Question: 33
The impulse response of a continuous time system is given by $h(t) = \delta(t-1) + \delta(t-3).$ The value of the step response at $t = 2$ is $0$ $1$ $2$ $3$
The impulse response of a continuous time system is given by $h(t) = \delta(t-1) + \delta(t-3).$ The value of the step response at $t = 2$ is $0$$1$$2$$3$
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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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