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2681
GATE ECE 2014 Set 1 | GA Question: 6
Find the odd one from the following group: $W,E,K,O \qquad I,Q,W,A \qquad F,N,T,X \qquad N,V,B,D$ $W,E,K,O$ $I,Q,W,A $ $F,N,T,X $ $N,V,B,D$
Find the odd one from the following group:$W,E,K,O \qquad I,Q,W,A \qquad F,N,T,X \qquad N,V,B,D$$W,E,K,O$$I,Q,W,A $$F,N,T,X $$N,V,B,D$
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2682
GATE ECE 2014 Set 1 | Question: 52
A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let $L$ be the number of tosses to get this first ‘Head’. The entropy $H(L)$ in bits is _____.
A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let $L$ be the number of tosses to get this first ‘Head’. The entropy $H(L)$ in bits i...
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2683
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$$+15\: V$
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2686
GATE ECE 2014 Set 3 | Question: 3
Match the application to appropriate numerical method. ... $P1-M3,P2-M1,P3-M4,P4-M2$ $P1-M4,P2-M1,P3-M3,P4-M2$ $P1-M2,P2-M1,P3-M3,P4-M4$
Match the application to appropriate numerical method.$\begin{array}{ll} \underline{\text{Application}} & \underline{\text{Numerical} \mid \text{Method}} \\ \text{P1: Nu...
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2687
GATE ECE 2014 Set 2 | GA Question: 8
The sum of eight consecutive odd numbers is $656$. The average of four consecutive even numbers is $87$. What is the sum of the smallest odd number and second largest even number?
The sum of eight consecutive odd numbers is $656$. The average of four consecutive even numbers is $87$. What is the sum of the smallest odd number and second largest eve...
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2688
GATE ECE 2014 Set 1 | GA Question: 4
The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four? ... K L M N
The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?$$\begin{array}{|c|c|c|}\h...
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2689
GATE ECE 2012 | Question: 11
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $tf(t)$ is $-\frac{s}{(s^2+s+1)^2}$ $-\frac{2s+1}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $tf(t)$ is$-\frac{s}{(s^2+s+1)^2}$$-\frac{2s+1}{(s^2+s+1)^2}$$\frac...
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2692
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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2693
GATE ECE 2014 Set 4 | GA Question: 6
Find the next term in the sequence: $13M, 17Q, 19S$, ___ $21W$ $21V$ $23W$ $23V$
Find the next term in the sequence: $13M, 17Q, 19S$, ___$21W$$21V$$23W$$23V$
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2695
GATE ECE 2014 Set 4 | Question: 49
Consider a communication scheme where the binary valued signal $X$ satisfies $P\{X=+1\}=0.75$ and $P\{X=-1 \}=0.25$. The received signal $Y=X+Z$, where $Z$ is a Gaussian random variable with zero mean and variance ... $\sigma ^2$
Consider a communication scheme where the binary valued signal $X$ satisfies $P\{X=+1\}=0.75$ and $P\{X=-1 \}=0.25$. The received signal $Y=X+Z$, where $Z$ is a Gaussian ...
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2696
GATE ECE 2014 Set 4 | Question: 5
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by _________.
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by...
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2699
GATE ECE 2014 Set 1 | Question: 46
Consider the state space model of a system, as given below ... The system is controllable and observable uncontrollable and observable uncontrollable and unobservable controllable and unobservable
Consider the state space model of a system, as given below$\begin{bmatrix} x_{1}\\x_{2} \\x_{3} \end{bmatrix} \begin{bmatrix} -1 &1 &0 \\ 0& -1 &0 \\ 0 & 0 & -2 \end{bmat...
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2701
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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2702
GATE ECE 2014 Set 4 | Question: 21
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is $16$ $4$ $2$ $1$
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is$16$$4$$2$$1$
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2703
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 $$12...
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2708
GATE ECE 2014 Set 1 | Question: 38
In the circuit shown the op-amp has finite input impedance, infinite voltage gain, and zero input offset voltage. The output voltage $V_{out}$ is $-I_{2}(R_{1} + R_{2})$ $I_{2}R_{2}$ $I_{1}R_{2}$ $-I_{1}(R_{1} + R_{2})$
In the circuit shown the op-amp has finite input impedance, infinite voltage gain, and zero input offset voltage. The output voltage $V_{out}$ is $-I_{2}(R_{1} + R_{2})$$...
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2711
GATE ECE 2014 Set 1 | Question: 20
The forward path transfer function of a unity negative feedback system is given by $G(s) = \frac{K}{(s+2)(s-1)}$. The value of $K$ which will place both the poles of the closed-loop system at the same location, is _______.
The forward path transfer function of a unity negative feedback system is given by $$G(s) = \frac{K}{(s+2)(s-1)}$$. The value of $K$ which will place both the poles of th...
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2713
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$$3$
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2717
GATE ECE 2014 Set 1 | Question: 3
$C$ is a closed path in the $z$-plane given by $\mid z \mid = 3.$ The value of the integral $\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}-z+4j}{z+2j}\bigg)dz$ is $-4\pi(1+j2)$ $4\pi(3-j2)$ $-4\pi(3+j2)$ $4\pi(1-j2)$
$C$ is a closed path in the $z$-plane given by $\mid z \mid = 3.$ The value of the integral $\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}-z+4j}{z+2j}\bigg)dz$ is$-4\pi(1+j2...
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2718
GATE ECE 2013 | Question: 8
The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is $\frac{t^{2}}{2}u(t)$ $\frac{t(t-1)}{2}u(t-1)$ $\frac{(t-1)^{2}}{2}u(t-1)$ $\frac{t^{2}-1}{2}u(t-1)$
The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is$\frac{t^{2}}{2}u(t)$$\frac{t(t-1)}{2}u(t-1)$$\frac{(t-1)^{2}}{2}u(t-1)$$\frac...
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2719
GATE ECE 2014 Set 1 | Question: 47
The phase margin in degrees of $G(s) = \dfrac{10}{(s+0.1)(s+1)(s+10)}$ calculated using the asymptotic Bode plot is ______.
The phase margin in degrees of $G(s) = \dfrac{10}{(s+0.1)(s+1)(s+10)}$ calculated using the asymptotic Bode plot is ______.
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