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Recent questions tagged gate2013-in

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GATE2013-64
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$$5/7$
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GATE2013-63
A car travels $8\;\text{km}$ in the first quarter of an hour, $6\;\text{km}$ in the second quarter and $16\;\text{km}$ in the third quarter. The average speed of the car in $\text{km}$ per hour over the entire journey is $30$ $36$ $40$ $24$
A car travels $8\;\text{km}$ in the first quarter of an hour, $6\;\text{km}$ in the second quarter and $16\;\text{km}$ in the third quarter. The average speed of the car ...
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GATE2013-62
The set of values of $\text{p}$ for which the roots of the equation $3\text{x}^2+2\text{x}+\text{p}\text{(p-1)}=0$ are of opposite sign is $(-\infty,\;0)$ $(0,\;1)$ $(1,\;\infty)$ $(0,\;\infty)$
The set of values of $\text{p}$ for which the roots of the equation $3\text{x}^2+2\text{x}+\text{p}\text{(p-1)}=0$ are of opposite sign is $(-\infty,\;0)$$(0,\;1)$$(1,\;\...
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GATE2013-61
Find the sum to $n$ terms of the series $10+84+734+….$ $\frac{9(9^n+1)}{10}+1$ $\frac{9(9^n-1)}{8}+1$ $\frac{9(9^n-1)}{8}+n$ $\frac{9(9^n-1)}{8}+n^2$
Find the sum to $n$ terms of the series $10+84+734+….$$\frac{9(9^n+1)}{10}+1$$\frac{9(9^n-1)}{8}+1$$\frac{9(9^n-1)}{8}+n$$\frac{9(9^n-1)}{8}+n^2$
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GATE2013-59
They were requested not to $\text{quarrel}$ with others. Which one of the following options is the closest in meaning to the word $\text{quarrel}$? make out call out dig out fall out
They were requested not to $\text{quarrel}$ with others.Which one of the following options is the closest in meaning to the word $\text{quarrel}$?make outcall outdig outf...
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GATE2013-58
Choose the grammatically $\text{CORRECT}$ sentence: Two and two add four Two and two become four Two and two are four Two and two make four
Choose the grammatically $\text{CORRECT}$ sentence:Two and two add fourTwo and two become fourTwo and two are fourTwo and two make four
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GATE2013-57
Complete the sentence: Dare _____________ mistakes. commit to commit committed committing
Complete the sentence:Dare _____________ mistakes.committo commitcommittedcommitting
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GATE2013-38
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$ $\frac{1}{s^2}[1-2e^{-s}+e^{-2s}]$
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$$...
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GATE2013-37
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$ $2$ $\pi$ $\sqrt{2}$
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$...
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25
GATE2013-43
In the circuit shown below the op-amps are ideal. Then $V_{out}$ in Volts is $4$ $6$ $8$ $10$
In the circuit shown below the op-amps are ideal. Then $V_{out}$ in Volts is$4$$6$$8$$10$
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GATE2013-42
A voltage $1000\sin \omega t$ Volts is applied across $YZ$. Assuming ideal diodes, the voltage measured across $WX$ in Volts, is $\sin \omega t$ $(\sin \omega t+|\sin \omega t|)/2$ $(\sin \omega t-|\sin \omega t|)/2$ $0$ for all $t$
A voltage $1000\sin \omega t$ Volts is applied across $YZ$. Assuming ideal diodes, the voltage measured across $WX$ in Volts, is$\sin \omega t$$(\sin \omega t+|\sin \omeg...
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GATE2013-41
The signal flow graph for a system is given below. The transfer function $\frac{Y(s)}{U(s)}$ for this system is given as $\frac{s+1}{5s^2+6s+2}$ $\frac{s+1}{s^2+6s+2}$ $\frac{s+1}{s^2+4s+2}$ $\frac{1}{5s^2+6s+2}$
The signal flow graph for a system is given below. The transfer function $\frac{Y(s)}{U(s)}$ for this system is given as $\frac{s+1}{5s^2+6s+2}$$\frac{s+1}{s^2+6s+2}$ $\f...
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GATE2013-39
In the circuit shown below, if the source voltage $V_s=100\angle 53.13^\circ$ Volts, then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_L$ is $100 \angle 90^\circ$ $800 \angle 0^\circ$ $800 \angle 90^\circ$ $100 \angle 60^\circ$
In the circuit shown below, if the source voltage $V_s=100\angle 53.13^\circ$ Volts, then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_L...
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GATE2013-40
A signal $V_i(t)=10+10\sin 100\pi t+10\sin 4000 \pi t+10\sin 100000\pi t$ is supplied to a filter circuit (shown below) made up of ideal op-amps. The least attenuated frequency component in the output will be $\text{0 Hz}$ $\text{50 Hz}$ $\text{2 kHz}$ $\text{50 kHz}$
A signal $V_i(t)=10+10\sin 100\pi t+10\sin 4000 \pi t+10\sin 100000\pi t$ is supplied to a filter circuit (shown below) made up of ideal op-amps. The least attenuated fre...
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GATE2013-34
The impulse response of a continuous time system is given by $h(t)=\delta(t-1)+\delta (t-3)$. The value of the step response at $t=2$ is $0$ $1$ $2$ $3$
The impulse response of a continuous time system is given by $h(t)=\delta(t-1)+\delta (t-3)$. The value of the step response at $t=2$ is$0$$1$$2$$3$
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GATE2013-26
While numerically solving the differential equation $\frac{dy}{dx}+2xy^2=0,\; y(0)=1$ using Euler’s predictor-corrector (improved Euler-Cauchy) method with a step size of 0.2, the value of $y$ after the first step is $1.00$ $1.03$ $0.97$ $0.96$
While numerically solving the differential equation $\frac{dy}{dx}+2xy^2=0,\; y(0)=1$ using Euler’s predictor-corrector (improved Euler-Cauchy) method with a step size ...
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GATE2013-29
Considering the transformer to be ideal, the transmission parameter $’A’$ of the 2-port network a shown in the figure below is $1.3$ $1.4$ $0.5$ $2.0$
Considering the transformer to be ideal, the transmission parameter $’A’$ of the 2-port network a shown in the figure below is $1.3$$1.4$$0.5$$2.0$
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