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681
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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684
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$$2.0$
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685
GATE2013-16
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0<x<\propto$. Then $\text{P{X>1}}$ is $0.368$ $0.5$ $0.632$ $1.0$
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0<x<\propto$. Then $\text{P{X>1}}$ is $0.368$$0.5$$0.632$$1.0$
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686
GATE2013-17
A band-limited signal with a maximum frequency of $5\;kHz$ is to be sampled. According to the sampling theorem, the sampling frequency in $kHz$ which is not valid is $5$ $12$ $15$ $20$
A band-limited signal with a maximum frequency of $5\;kHz$ is to be sampled. According to the sampling theorem, the sampling frequency in $kHz$ which is not valid is$5$$1...
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687
GATE2013-18
The differential pressure transmitter of a flow meter using a venturi tube reads $2.5\times 10^5\;Pa$ for a flow rate of $0.5\;m^3/s$. The approximate flow rate in $m^3/s$ for a differential pressure $0.9\times 10^5\;Pa$ is $0.30$ $0.18$ $0.83$ $0.60$
The differential pressure transmitter of a flow meter using a venturi tube reads $2.5\times 10^5\;Pa$ for a flow rate of $0.5\;m^3/s$. The approximate flow rate in $m^3/s...
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689
GATE2013-20
The impulse response of a system is $h(t)=t\;u(t)$. For an input $u(t-1),$ the output is $\frac{t^2}{2}u(t)$ $\frac{t(t-1)}{2}u(t-1)$ $\frac{(t-1)^2}{2}u(t-1)$ $\frac{t^2-1}{2}u(t-1)$
The impulse response of a system is $h(t)=t\;u(t)$. For an input $u(t-1),$ the output is$\frac{t^2}{2}u(t)$$\frac{t(t-1)}{2}u(t-1)$$\frac{(t-1)^2}{2}u(t-1)$$\frac{t^2-1}{...
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690
GATE2013-21
Consider a delta connection of resistors and its equivalent star connection as shown. If all elements of the delta connection are scaled by a factor k, k>0, the elements of the corresponding star equivalent will be scaled by a factor of $k^2$ $k$ $\frac{1}{k}$ $\sqrt{k}$
Consider a delta connection of resistors and its equivalent star connection as shown. If all elements of the delta connection are scaled by a factor k, k>0, the elements ...
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691
GATE2013-22
An accelerometer has input range of $0$ to $10g$, natural frequency $30\; Hz$ and mass $0.001\;kg$. The range of the secondary displacement transducer in mm required to cover the input range is $0\;to\;2.76$ $0\;to\;9.81$ $0\;to\;11.20$ $0\;to\;52.10$
An accelerometer has input range of $0$ to $10g$, natural frequency $30\; Hz$ and mass $0.001\;kg$. The range of the secondary displacement transducer in mm required to c...
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692
GATE2013-8
A source $v_s(t)=V\cos 100 \pi t$ 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 $v_s(t)=V\cos 100 \pi t$ has an internal impedance of $4+j3\; \Omega$. If a purely resistive load connected to this source has to extract the maximum power out o...
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694
GATE2013-10
The Operational amplifier shown in the circuit below has a slew rate of $0.8\; Volts/\mu s$. The input signal is $0.25\; \sin (\omega t).$ The maximum frequency of input in kHz for which there is no distortion in the output is $23.84$ $25.0$ $50.0$ $46.60$
The Operational amplifier shown in the circuit below has a slew rate of $0.8\; Volts/\mu s$. The input signal is $0.25\; \sin (\omega t).$ The maximum frequency of input ...
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695
GATE2013-11
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is $u(t)$ $t u(t)$ $\frac{t^2}{2}u(t)$ $e^{-t}u(t)$
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is$u(t)$$t u(t)$$\frac{t^2}{2}u(t)$$e^{-t}u(t)$
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696
GATE2013-12
The transfer function $\frac{V_2(s)}{V_1(s)}$ of the circuit shown below is $\frac{0.5s+1}{s+1}$ $\frac{3s+6}{s+2}$ $\frac{s+2}{s+1}$ $\frac{s+1}{s+2}$
The transfer function $\frac{V_2(s)}{V_1(s)}$ of the circuit shown below is $\frac{0.5s+1}{s+1}$$\frac{3s+6}{s+2}$$\frac{s+2}{s+1}$$\frac{s+1}{s+2}$
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697
GATE2013-13
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ is Parabolic Elliptic Hyperbolic Nonlinear
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ isParabolicEllipticHyperbolicNonlinear
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698
GATE2013-14
The discrete-time transfer function $\frac{1-2 Z^{-1}}{1-0.5Z^{-1}}$ is non-minimum phase and unstable minimum phase and unstable minimum phase and stable non-minimum phase and stable
The discrete-time transfer function $\frac{1-2 Z^{-1}}{1-0.5Z^{-1}}$ isnon-minimum phase and unstableminimum phase and unstableminimum phase and stablenon-minimum phase a...
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699
GATE2013-15
Match the following biomedical instrumentation techniques with their applications $\text{P-U, Q-V, R-X, S-W}$ $\text{P-V, Q-U, R-X, S-W}$ $\text{P-V, Q-W, R-U, S-X}$ $\text{P-V, Q-W, R-X, S-U}$
Match the following biomedical instrumentation techniques with their applications$\text{P-U, Q-V, R-X, S-W}$$\text{P-V, Q-U, R-X, S-W}$$\text{P-V, Q-W, R-U, S-X}$$\text{P...
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700
GATE2013-2
If the A-matrix of the state space model of a $SISO$ linear time invariant system is rank deficient, the transfer function of the system must have a pole with a positive real part a pole with a negative real part a pole with a positive imaginary part a pole at the origin
If the A-matrix of the state space model of a $SISO$ linear time invariant system is rank deficient, the transfer function of the system must have a pole with a positive ...
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701
GATE2013-3
Two systems with impulse responses $h_1(t)\;and\; h_2(t)$ are connected in cascade. Then the overall impulse response of the cascaded system is given by product of $h_1(t)\;and\;h_2(t)$ sum of $h_1(t)\;and\;h_2(t)$ convolution of $h_1(t)\;and\;h_2(t)$ subtraction of $h_2(t)\;and\;h_1(t) $
Two systems with impulse responses $h_1(t)\;and\; h_2(t)$ are connected in cascade. Then the overall impulse response of the cascaded system is given byproduct of $h_1(t)...
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702
GATE2013-4
The complex function $\tan h(s)$ is analytic over a region of the imaginary axis of the complex s-plane if the following is $\text{TRUE}$ everywhere in the region for all integers $n$ $Re(s)=0$ $Im(s)\neq n\pi$ $Im(s)\neq \frac{n\pi}{3}$ $Im(s)\neq\frac{(2n+1)\pi}{2}$
The complex function $\tan h(s)$ is analytic over a region of the imaginary axis of the complex s-plane if the following is $\text{TRUE}$ everywhere in the region for all...
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703
GATE2013-5
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$? If $\Delta.E=0,\;E$ is called solenoidal If $\Delta \times E=0,\;E$ is called conservative If $\Delta\times E=0,\;E$ is called irrotational If $\Delta.E=0,\;E$ is called irrotational
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$?If $\Delta.E=0,\;E$ is called solenoidalIf $\Delta \times E=0,\;E$ is called conservativeIf $...
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704
GATE2013-6
For a periodic signal $v(t)=30\sin 100t+10\cos 300t+6\sin (500t+\frac{\pi}{4})$, the fundamental frequency in $rad/s$ is $100$ $300$ $500$ $1500$
For a periodic signal $v(t)=30\sin 100t+10\cos 300t+6\sin (500t+\frac{\pi}{4})$, the fundamental frequency in $rad/s$ is $100$$300$$500$$1500$
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705
GATE2013-7
In the transistor circuit as shown below, the value of resistance $R_E$ in $k\Omega$ is approximately, $1.0$ $1.5$ $2.0$ $2.5$
In the transistor circuit as shown below, the value of resistance $R_E$ in $k\Omega$ is approximately, $1.0$$1.5$$2.0$$2.5$
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706
GATE2013-1
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is $0$ $1$ $2$ $3$
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is$0$$1$$2$$3$
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708
GATE2012-64
The data given in the following table summarizes the monthly budget of an average household. ... $\text{NOT}$ spent on savings is $10\%$ $14\%$ $81\%$ $86\%$
The data given in the following table summarizes the monthly budget of an average household.$$\begin{array}{|l|c|}\hline \textbf{Category} & \textbf{Amount (Rs.)} \\\hlin...
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710
GATE2012-56
Choose the most appropriate alternative from the options given below to complete the following sentence: $\text{If the tired soldier wanted to lie down, he___ the mattress out on the balcony.}$ should take shall take should have taken will have taken
Choose the most appropriate alternative from the options given below to complete the following sentence:$\text{If the tired soldier wanted to lie down, he___ the mattress...
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711
GATE2012-57
If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=$ $2.23$ $4.33$ $11.37$ $27.64$
If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=$$2.23$$4.33$$11.37$$27.64$
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713
GATE2012-59
Which one of the following options is the closest in meaning to the word given below? $\text{Latitude}$ Eligibility Freedom Coercion Meticulousness
Which one of the following options is the closest in meaning to the word given below?$\text{Latitude}$EligibilityFreedomCoercionMeticulousness
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714
GATE2012-60
Choose the most appropriate word from the options given below to complete the following sentence: $\text{Given the seriousness of the situation that he had to face, his ___ was impressive}$. beggary nomenclature jealousy nonchalance
Choose the most appropriate word from the options given below to complete the following sentence:$\text{Given the seriousness of the situation that he had to face, his __...
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715
GATE2012-61
Raju has $14$ currency notes in his pocket consisting of only $\text{Rs. 20}$ notes and $\text{Rs. 10}$ notes. The total money value of the notes is $\text{Rs. 230}$. The number of $\text{Rs. 10}$ notes that Raju has is $5$ $6$ $9$ $10$
Raju has $14$ currency notes in his pocket consisting of only $\text{Rs. 20}$ notes and $\text{Rs. 10}$ notes. The total money value of the notes is $\text{Rs. 230}$. The...
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720
GATE2012-52
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $\text{a=1, b=2}$ $\text{a=3, b=2}$ $\text{a=-3, b=-1}$ $\text{a=3, b=1}$
The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$$G_c(s)$ is a lead compensator if $\text{a=1, b=2}$$\text{a=3, b=2}$$\text{a=-3, b=-1}$$\text...
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