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521
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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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$$1500$
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523
GATE2013-7
In the transistor circuit as shown below, the value of resistance $R_E$ in $k\Omega$ is approximately, $1.0$ $1.5$ $2.0$ $2.5$
In the transistor circuit as shown below, the value of resistance $R_E$ in $k\Omega$ is approximately, $1.0$$1.5$$2.0$$2.5$
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524
GATE2012-49
With $\text{10 V}$ dc connected at port $\text{A}$ in the linear nonreciprocal two-port network shown below, the following were observed: $\text1\;\Omega$ connected at port $\text{B}$ draws a current of $\text{3 A}$ $\text2.5\;\Omega$ connected at port $\text{B}$ draws a current of $\text{2 A}$ For the same network, with $\text{6 V}$ dc connected ... $\text{A}$, the open circuit voltage at port $\text{B}$ is $\text{6 V}$ $\text{7 V}$ $\text{8 V}$ $\text{9 V}$
With $\text{10 V}$ dc connected at port $\text{A}$ in the linear nonreciprocal two-port network shown below, the following were observed:$\text1\;\Omega$ connected at por...
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525
GATE2012-50
The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.001F\;x^2[1-\frac{x}{3}]m.$ The angular deformation $\theta$ at the end of the cantilever is measured by reflecting a laser beam off a mirror $\text{M}$ as shown in the ... light on the photodetector when a force of $F=\text{1 N}$ is applied to the cantilever is $\text{1 mm}$ $\text{3 mm}$ $\text{6 mm}$ $\text{12 mm}$
The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.0...
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526
GATE2012-51
The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.001Fx^2[1-\frac{x}{3}]m.$ The angular deformation $\theta$ at the end of the cantilever is measured by reflecting a laser beam off a mirror $\text{M}$ as shown ... the cantilever to measure the effect of time varying forces, the ratio of their output is $\frac{12}{7}$ $\frac{40}{11}$ $\frac{176}{23}$ $\frac{112}{15}$
The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.0...
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527
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}$$\text...
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GATE2012-53
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}\;\text{rad/s}$ $\sqrt{3}\;\text{rad/s}$ $\sqrt{6}\;\text{rad/s}$ $\frac{1}{\sqrt{3}}\;\text{rad/s}$
The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$The phase of the above lead compensator is maximum at $\sqrt{2}\;\text{rad/s}$$\sqrt{3}\;\tex...
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529
GATE2012-54
The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$
The power factor of the load is$0.45$$0.50$$0.55$$0.60$
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530
GATE2012-55
If $R_L=5\;\Omega,$ the approximate power consumption in the load is $700\;\text{W}$ $750\;\text{W}$ $800\;\text{W}$ $850\;\text{W}$
If $R_L=5\;\Omega,$ the approximate power consumption in the load is $700\;\text{W}$$750\;\text{W}$$800\;\text{W}$$850\;\text{W}$
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GATE2012-41
The double convex lens is used to couple a laser beam of diameter $5\;\text{mm}$ into an optical fiber with a numerical aperture of $0.5$. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is $1.44\;\text{mm}$ $2.50\;\text{mm}$ $4.33\;\text{mm}$ $5.00\;\text{mm}$
The double convex lens is used to couple a laser beam of diameter $5\;\text{mm}$ into an optical fiber with a numerical aperture of $0.5$. The minimum focal length of the...
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GATE2012-42
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20\;\text{k}\Omega$, it reads $400\;\text{V}$ and with a multiplier setting of $80\;\text{k}\Omega$, it reads $352\;\text{V}$. For a multiplier setting of $40\;\text{k}\Omega$, the voltmeter reads $371\;\text{V}$ $383\;\text{V}$ $394\;\text{V}$ $406\;\text{V}$
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20\;\text{k}\Omega$, it reads $400\;\text{V}$ and with a multiplier setting of $80\;\...
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533
GATE2012-43
The open loop transfer function of a unity negative feedback control system is given by $G(s)=\frac{150}{s(s+9)(s+25)}$. The gain margin of the system is $10.8\;\text{dB}$ $22.3\;\text{dB}$ $34.1\;\text{dB}$ $45.6\;\text{dB}$
The open loop transfer function of a unity negative feedback control system is given by $G(s)=\frac{150}{s(s+9)(s+25)}$. The gain margin of the system is $10.8\;\text{dB}...
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534
GATE2012-44
A dynamometer arm makes contact with the piezoelectric load cell as shown. The $g-$constant of the piezoelectric material is $50\times10^{-3}\;\text {Vm/N}$ and the surface area of the load cell is $4\;{cm^2}$. If a torque $\tau=20 \;\text{Nm}$ is applied to the dynamometer, the output voltage $\text{V}_\circ$ of the load cell is $\text{4 V}$ $\text{5 V}$ $\text{10 V}$ $\text{16 V}$
A dynamometer arm makes contact with the piezoelectric load cell as shown. The $g-$constant of the piezoelectric material is $50\times10^{-3}\;\text {Vm/N}$ and the surf...
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535
GATE2012-45
Water $\text{(density:}\;1000\;\text{kgm}^{-3})$ stored in a cylindrical drum of diameter $1\;\text{m}$ is emptied through a horizontal pipe of diameter $0.05\;\text{m}$. A pitot-static tube is placed inside the pipe facing the flow. At the time when the difference between the stagnation and static pressure measured by the pitot-static tube is $10\;\text{kPa}$, the ... $\frac{1}{75\sqrt{10}}\text{ms}^{-1}$ $\frac{1}{50\sqrt{10}}\text{ms}^{-1}$ $\frac{1}{40\sqrt5}\text{ms}^{-1}$
Water $\text{(density:}\;1000\;\text{kgm}^{-3})$ stored in a cylindrical drum of diameter $1\;\text{m}$ is emptied through a horizontal pipe of diameter $0.05\;\text{m}$....
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536
GATE2012-46
A U-tube manometer of tube diameter $D$ is filled with a liquid of zero viscosity. If the volume of the liquid filled is $V$, the natural frequency of oscillations in the liquid level about its mean position, due to small perturbations, is $\frac{D}{2\sqrt{2\pi}}\sqrt{\frac{g}{V}}$ $\frac{2\sqrt2}{\sqrt\pi}$\frac{\sqrt{gV}}{D^2}$ $\frac{1}{2\sqrt\pi}$\frac{\sqrt{gD}}{V^{1/3}}$ $\frac{1}{\sqrt{\pi}}\sqrt{\frac{g}{D}}$
A U-tube manometer of tube diameter $D$ is filled with a liquid of zero viscosity. If the volume of the liquid filled is $V$, the natural frequency of oscillations in the...
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537
GATE2012-47
The open loop transfer function of a unity gain negative feedback control system is given by $G(s)=\frac{s^2+4s+8}{s(s+2)(s+8)}.$ The angle $\theta$ , at which the root locus approaches the zeros of the system, satisfies $|\theta|=\pi-\tan^{-1}[\frac{1}{4}]$ $|\theta|=\frac{3\pi}{4}-\tan^{-1}[\frac{1}{3}]$ $|\theta|=\frac{\pi}{2}-\tan^{-1}[\frac{1}{4}]$ $|\theta|=\frac{\pi}{4}-\tan^{-1}[\frac{1}{3}]$
The open loop transfer function of a unity gain negative feedback control system is given by $G(s)=\frac{s^2+4s+8}{s(s+2)(s+8)}.$ The angle $\theta$ , at which the root l...
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GATE2012-48
With $\text{10 V}$ dc connected at port $\text{A}$ in the linear nonreciprocal two-port network shown below, the following were observed: $\text1\;\Omega$ connected at port $\text{B}$ draws a current of $\text{3 A}$ $\text2.5\;\Omega$ connected at port $\text{B}$ draws a current of $\text{2 A}$ With $\text{10 V}$ dc connected at port $\text{A}$, the ... $\text{B}$ is $\frac{3}{7}\;\text{A}$ $\frac{5}{7}\;\text{A}$ $\text{1 A}$ $\frac{9}{7}\;\text{A}$
With $\text{10 V}$ dc connected at port $\text{A}$ in the linear nonreciprocal two-port network shown below, the following were observed:$\text1\;\Omega$ connected at por...
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GATE2012-34
The state variable description of an $\text{LTI}$ system is given by $\begin{bmatrix}\dot{x_1}\\\dot{x_2\\\dot{x_3}}\end{bmatrix}=\begin{bmatrix}0 & a_1 & 0\\0 & 0 & a_2\\a_3 & 0 & 0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}+\begin{bmatrix}0\\0\\1\end{bmatrix}u$ ... $a_2=0,$ $a_3\neq 0$ $a_1= 0,$ $a_2\neq 0,$ $a_3\neq 0$ $a_1=0,$ $a_2\neq 0,$ $a_3=0$ $a_1\neq 0,$ $a_2\neq 0,$ $a_3=0$
The state variable description of an $\text{LTI}$ system is given by $$\begin{bmatrix}\dot{x_1}\\\dot{x_2\\\dot{x_3}}\end{bmatrix}=\begin{bmatrix}0 & a_1 & 0\\0 & 0 & a_2...
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GATE2012-35
The state transition diagram for the logic circuit shown is
The state transition diagram for the logic circuit shown is
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GATE2012-37
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(1/2)^n\;u[n]$ and $g[n]$ is a causal sequence. If $y[0]=1$ and $y[1]=1/2$, then $g[1]$ equals $0$ $1/2$ $1$ $3/2$
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(1/2)^n\;u[n]$ and $g[n]$ is a causal sequence. If $y[0]=1$ and $y =1/2$, then $g $ equals$0$$1/2$$1$$...
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GATE2012-38
The feedback system shown below oscillates at $2\;\text{rad/s}$ when $K=2$ and $a=0.75$ $K=3$ and $a=0.75$ $K=4$ and $a=0.5$ $K=2$ and $a=0.5$
The feedback system shown below oscillates at $2\;\text{rad/s}$ when$K=2$ and $a=0.75$$K=3$ and $a=0.75$$K=4$ and $a=0.5$$K=2$ and $a=0.5$
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GATE2012-39
The circuit shown is a low pass filter with $\text{f}_{3\text{dB}}=\frac{1}{(R_1+R_2)C}\;\text{rad/s}$ high pass filter with $\text{f}_{3\text{dB}}=\frac{1}{R_1C}\;\text{rad/s}$ low pass filter with $\text{f}_{3\text{dB}}=\frac{1}{R_1C}\;\text{rad/s}$ high pass filter with $\text{f}_{3\text{dB}}=\frac{1}{(R_1+R_2)C}{rad/s}$
The circuit shown is alow pass filter with $\text{f}_{3\text{dB}}=\frac{1}{(R_1+R_2)C}\;\text{rad/s}$high pass filter with $\text{f}_{3\text{dB}}=\frac{1}{R_1C}\;\text{ra...
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GATE2012-40
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\int^{t}_{-\infty}x(\tau)\cos(3\tau)d\tau$. The system is time-invariant and stable stable and not time-invariant time-invariant and not stable not time-invariant and not stable
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\int^{t}_{-\infty}x(\tau)\cos(3\tau)d\tau$. The system is time-invariant and stablestable and not time...
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GATE2012-31
If $\text{V}_\text{A}-\text{V}_\text{B}=6\;\text{V}$, then $\text{V}_\text{C}-\text{V}_\text{D}$ is $-5\;\text{V}$ $2\;\text{V}$ $3\;\text{V}$ $6\;\text{V}$
If $\text{V}_\text{A}-\text{V}_\text{B}=6\;\text{V}$, then $\text{V}_\text{C}-\text{V}_\text{D}$ is $-5\;\text{V}$$2\;\text{V}$$3\;\text{V}$$6\;\text{V}$
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GATE2012-32
Assuming both the voltage sources are in phase, the value of $\text{R}$ for which maximum power transferred from circuit $\text{A}$ to circuit $\text{B}$ is $0.8\;\Omega$ $1.4\;\Omega$ $2\;\Omega$ $2.8\;\Omega$
Assuming both the voltage sources are in phase, the value of $\text{R}$ for which maximum power transferred from circuit $\text{A}$ to circuit $\text{B}$ is $0.8\;\Omega$...
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GATE2012-33
The voltage gain $A_v$ of the circuit shown below is $|A_v|\approx 200$ $|A_v|\approx 100$ $|A_v|\approx 20$ $|A_v|\approx 10$
The voltage gain $A_v$ of the circuit shown below is$|A_v|\approx 200$$|A_v|\approx 100$$|A_v|\approx 20$$|A_v|\approx 10$
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GATE2012-19
The transfer function of a Zero-Order-Hold system with sampling interval $T$ is $\frac{1}{s}(1-e^{-Ts})$ $\frac{1}{s}(1-e^{-Ts})^2$ $\frac{1}{s}e^{-Ts}$ $\frac{1}{s^2}e^{-Ts}$
The transfer function of a Zero-Order-Hold system with sampling interval $T$ is$\frac{1}{s}(1-e^{-Ts})$$\frac{1}{s}(1-e^{-Ts})^2$$\frac{1}{s}e^{-Ts}$$\frac{1}{s^2}e^{-Ts}...
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GATE2012-20
An $\text{LED}$ emitting at $1\;\mu\text{m}$ with a spectral width of $50\;\text{nm}$ is used in a Michelson interferometer. To obtain a sustained interference, the maximum optical path difference between the two arms of the interferometer is $200\;\mu\text{m}$ $20\;\mu\text{m}$ $1\;\mu\text{m}$ $50\;\text{nm}$
An $\text{LED}$ emitting at $1\;\mu\text{m}$ with a spectral width of $50\;\text{nm}$ is used in a Michelson interferometer. To obtain a sustained interference, the maxim...
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GATE2012-21
Light of wavelength $630\;\text{nm}$ in vacuum, falling normally on a biological specimen of thickness $10\;\mu\text{m}$, splits into two beams that are polarized at right angles. The refractive index of the tissue for the two polarizations are $1.32$ and $1.333$. When the two beams emerge, they are out of phase by $0.13^\circ$ $74.3^\circ$ $90.0^\circ$ $128.6^\circ$
Light of wavelength $630\;\text{nm}$ in vacuum, falling normally on a biological specimen of thickness $10\;\mu\text{m}$, splits into two beams that are polarized at righ...
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GATE2012-22
The responsivity of the $\text{PIN}$ photodiode shown is $0.9\;A/W.$ To obtain $V_\text{out}$ of $-1\;\text{V}$ for an in optical power of $1\;\text{mW},$ the value of $R$ to be used is $0.9\;\Omega$ $1.1\;\Omega$ $0.9\;k\Omega$ $1.1\;k\Omega$
The responsivity of the $\text{PIN}$ photodiode shown is $0.9\;A/W.$ To obtain $V_\text{out}$ of $-1\;\text{V}$ for an in optical power of $1\;\text{mW},$ the value of $R...
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GATE2012-23
A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil $\text{(PMMC)}$ meter connected across the same load reads $4\;\text{V}$ $5\;\text{V}$ $8\;\text{V}$ $10\;\text{V}$
A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil $\text{(PMMC)}$ meter connected across the same load reads$...
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GATE2012-24
For the circuit shown in the figure, the voltage and current expressions are $v(t)=E_1\sin(\omega t)+E_3\sin(3\omega t)$ and $i(t)=I_1\sin(\omega t-\phi_1)+I_3\sin(3\omega t-\phi_3)+I_5\sin(5\omega t).$ The average power measured by the Wattmeter is $\frac{1}{2}E_1I_1\cos\phi_1$ $\frac{1}{2}[E_1I_1\cos\phi_1+E_1I_3\cos\phi_3+E_1I_5]$ $\frac{1}{2}[E_1I_1\cos\phi_1+E_3I_3\cos\phi_3]$ $\frac{1}{2}[E_1I_1\cos\phi_1+E_3I_1\cos\phi_1]$
For the circuit shown in the figure, the voltage and current expressions are $v(t)=E_1\sin(\omega t)+E_3\sin(3\omega t)$ and $i(t)=I_1\sin(\omega t-\phi_1)+I_3\sin(3\omeg...
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GATE2012-25
The bridge method commonly used for finding mutual inductance is Heaviside Campbell bridge Schering bridge De Sauty bridge Wien bridge
The bridge method commonly used for finding mutual inductance is Heaviside Campbell bridgeSchering bridgeDe Sauty bridgeWien bridge
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GATE2012-15
If $x[n]=(1/3)^{|n|}-(1/2)^nu[n],$ then the region of convergence $\text{(ROC)}$ of its $Z-$transform in the $Z-$plane will be $\frac{1}{3}<|z|<3$ $\frac{1}{3}<|z|<\frac{1}{2}$ $\frac{1}{2}<|z|<3$ $\frac{1}{3}<|z|$
If $x[n]=(1/3)^{|n|}-(1/2)^nu[n],$ then the region of convergence $\text{(ROC)}$ of its $Z-$transform in the $Z-$plane will be $\frac{1}{3}<|z|<3$$\frac{1}{3}<|z|<\frac{1...
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GATE2012-16
A capacitive motion transducer circuit is shown. The gap $d$ between the parallel plates of the capacitoes is varied as $d(t)=10^{-3}[1+0.1\sin(1000\pi t)]\;\text{m}.$ If the value of the capacitance is $2\text{pF}$ at $t=0\text{ms},$ the output voltage $\text{V}_\circ$ at $t=2\;\text{ms}$ is $\frac{\pi}{2}\text{mV}$ $\pi\;\text{mV}$ $2\pi\;\text{mV}$ $4\pi\;\text{mV}$
A capacitive motion transducer circuit is shown. The gap $d$ between the parallel plates of the capacitoes is varied as $d(t)=10^{-3}[1+0.1\sin(1000\pi t)]\;\text{m}.$ If...
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GATE2012-17
A psychrometric chart is used to determine $\text{pH}$ $\text{Sound velocity in glasses}$ $\text{CO}_2 \text{concentration}$ $\text{Relative humidity}$
A psychrometric chart is used to determine $\text{pH}$$\text{Sound velocity in glasses}$$\text{CO}_2 \text{concentration}$$\text{Relative humidity}$
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GATE2012-18
A strain gauge is attached on a cantilever beam as shown. If the base of the cantilever vibrates according to the equation $x(t)=\sin\omega_1t+\sin\omega_2t,$ where $2\;\text{rad/s}<\omega_1,\;\omega_2<3\;\text{rad/s},$ then the output of the strain gauge is proportional to $x$ $\frac{dx}{dt}$ $\frac{d^2x}{dt^2}$ $\frac{d(x-y)}{dt}$
A strain gauge is attached on a cantilever beam as shown. If the base of the cantilever vibrates according to the equation $x(t)=\sin\omega_1t+\sin\omega_2t,$ where $2\;\...
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GATE2012-6
The average power delivered to an impedance $(4-j3)\Omega$ by a current $5\cos(100\pi t+100)\text{A}$ is $44.2\;\text{W}$ $50\;\text{W}$ $62.5\;\text{W}$ $125\;\text{W}$
The average power delivered to an impedance $(4-j3)\Omega$ by a current $5\cos(100\pi t+100)\text{A}$ is $44.2\;\text{W}$ $50\;\text{W}$ $62.5\;\text{W}$ $125\;\text{W}$...
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GATE2012-7
In the circuit shown below, the current through the inductor is $\frac{2}{1+j}\text{A}$ $\frac{-1}{1+j}\text{A}$ $\frac{1}{1+j}\text{A}$ $0\text{A}$
In the circuit shown below, the current through the inductor is $\frac{2}{1+j}\text{A}$$\frac{-1}{1+j}\text{A}$$\frac{1}{1+j}\text{A}$$0\text{A}$
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