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481
GATE2016-16
In the circuit given below, the opamp is ideal. The output voltage $V_o$ in volt is $\_\_\_\_\_\_\_\_.$
In the circuit given below, the opamp is ideal. The output voltage $V_o$ in volt is $\_\_\_\_\_\_\_\_.$
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482
GATE2016-17
In the circuit given below, the diodes $D_1$ and $D_2$ have a forward voltage drop of $0.6\;V$. The opamp used is ideal.The $\text{magnitude}$ of the negative peak value of the output $V_0$ in $\text{volt}$ is ___________.
In the circuit given below, the diodes $D_1$ and $D_2$ have a forward voltage drop of $0.6\;V$. The opamp used is ideal.The $\text{magnitude}$ of the negative peak value ...
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483
GATE2016-18
The Boolean expression $XY+(X’+Y’)Z$ is equivalent to $XYZ’+X’Y’Z$ $X’Y’Z’+XYZ$ $(X+Z)(Y+Z)$ $(X’+Z)(Y’+Z)$
The Boolean expression $XY+(X’+Y’)Z$ is equivalent to$XYZ’+X’Y’Z$$X’Y’Z’+XYZ$$(X+Z)(Y+Z)$$(X’+Z)(Y’+Z)$
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484
GATE2016-19
In the digital circuit given below, $F$ is $XY+Y\overline{Z}$ $XY+\overline{Y}Z$ $\overline{X}\overline{Y}+Y\overline{Z}$ $XZ+\overline{Y}$
In the digital circuit given below, $F$ is$XY+Y\overline{Z}$$XY+\overline{Y}Z$$\overline{X}\overline{Y}+Y\overline{Z}$$XZ+\overline{Y}$
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485
GATE2016-20
A $3\frac{1}{2}$ digit $DMM$ has an accuracy specification of $\pm 1$% of full scale (accuracy class $1$). A reading of $\text{100.0 mA}$ is obtained on its $\text{200 mA}$ full scale range. The worst case error in the reading in $\text{milliampere}$ is $\pm$______________.
A $3\frac{1}{2}$ digit $DMM$ has an accuracy specification of $\pm 1$% of full scale (accuracy class $1$). A reading of $\text{100.0 mA}$ is obtained on its $\text{200 m...
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487
GATE2016-22
In the circuit given below, each input terminal of the opamp draws a bias current of $\text{10 nA}$. The effect due to these input bias currents on the output voltage $V_0$ will be zero, if the value of $R$ chosen in $\text{kilo-ohm}$ is ____________.
In the circuit given below, each input terminal of the opamp draws a bias current of $\text{10 nA}$. The effect due to these input bias currents on the output voltage $V_...
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488
GATE2016-23
A peizo-electric type pressure sensor has a sensitivity of $\text{1 mV/kPa}$ and a bandwidth of $\text{300 Hz to 300 kHz.}$ For a constant (dc) pressure of $\text{100 kPa}$, the steady state output of the sensor in $\text{mllivolt}$ is $\_\_\_\_\_\_\_.$
A peizo-electric type pressure sensor has a sensitivity of $\text{1 mV/kPa}$ and a bandwidth of $\text{300 Hz to 300 kHz.}$ For a constant (dc) pressure of $\text{100 kPa...
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489
GATE2016-24
The signal $m(t)=cos(\omega_mt)$ is $SSB$ (single side-band) modulated with a carrier $\cos(\omega_ct)$ to get $s(t)$. The signal obtained by passing $s(t)$ through an ideal envelope detector is $\cos(\omega_mt)$ $\sin(\omega_mt)$ $\cos(\omega_mt)+\sin(\omega_mt)$ 1
The signal $m(t)=cos(\omega_mt)$ is $SSB$ (single side-band) modulated with a carrier $\cos(\omega_ct)$ to get $s(t)$. The signal obtained by passing $s(t)$ through an id...
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491
GATE2016-26
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
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493
GATE2016-28
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_\_.$
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_...
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495
GATE2016-30
The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in the complex plane is $\_\_\_\_\_\_\_\_.$
The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in th...
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496
GATE2016-31
The current $I_X$ in the circuit given below in $\text{milliampere}$ is $\_\_\_\_\_\_\_.$
The current $I_X$ in the circuit given below in $\text{milliampere}$ is $\_\_\_\_\_\_\_.$
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497
GATE2016-32
In the circuit shown below, $V_s=101\angle 0V, R=10\Omega$ and $\omega L=100\Omega$. The current $I_s$ is in phase with $V_s$. The magnitude of $I_s$ in $\text{milliampere}$ is $\_\_\_\_\_\_\_\_.$
In the circuit shown below, $V_s=101\angle 0V, R=10\Omega$ and $\omega L=100\Omega$. The current $I_s$ is in phase with $V_s$. The magnitude of $I_s$ in $\text{milliamper...
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500
GATE2016-35
The voltage $v(t)$ shown below is applied to the given circuit. $v(t)=3V$ for $t<0$ and $v(t)=6V$ for $t>0$. The value of current $i(t)$ at $t=1s$, in ampere is ____________.
The voltage $v(t)$ shown below is applied to the given circuit. $v(t)=3V$ for $t<0$ and $v(t)=6V$ for $t>0$. The value of current $i(t)$ at $t=1s$, in ampere is _________...
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501
GATE2016-36
For the periodic signal $x(t)$ shown below with period $T=8s$, the power in the 10th harmonic is __________. $0$ $\frac{1}{2} \left (\frac{2}{10\pi} \right)^2$ $\frac{1}{2} \left (\frac{4}{10\pi} \right)^2$ $\frac{1}{2} \left (\frac{4}{5\pi} \right)^2$
For the periodic signal $x(t)$ shown below with period $T=8s$, the power in the 10th harmonic is __________.$0$$\frac{1}{2} \left (\frac{2}{10\pi} \right)^2$$\frac{1}{2} ...
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502
GATE2016-37
The fundamental period $N_0$ of the discrete-time sinusoid $x[n]=\sin \left (\frac {301}{4}\pi n \right)$ is ____________.
The fundamental period $N_0$ of the discrete-time sinusoid $x[n]=\sin \left (\frac {301}{4}\pi n \right)$ is ____________.
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503
GATE2016-38
The transfer function $G(s)$ of a system which has the asymptotic Bode plot shown below is $10^4 \frac {(s-1)^2}{(s+100)^2}$ $10^4 \frac {(s+1)^2}{(s+100)^2}$ $10^4 \frac {(s+1)}{(s+100)^2}$ $10^4 \frac {(s-1)^2}{(s-100)^2}$
The transfer function $G(s)$ of a system which has the asymptotic Bode plot shown below is $10^4 \frac {(s-1)^2}{(s+100)^2}$$10^4 \frac {(s+1)^2}{(s+100)^2}$$10^4 \frac {...
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504
GATE2016-39
For the feedback system given below, the transfer function $G(s)=\frac{1}{(s+1)^2}$. The system $\text{CANNOT}$ be stabilized with $C(s)=1+\frac{3}{s}$ $C(s)=3+\frac{7}{s}$ $C(s)=3+\frac{9}{s}$ $C(s)=\frac{1}{s}$
For the feedback system given below, the transfer function $G(s)=\frac{1}{(s+1)^2}$. The system $\text{CANNOT}$ be stabilized with$C(s)=1+\frac{3}{s}$$C(s)=3+\frac{7}{s}$...
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505
GATE2016-40
Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below. $P(s)-(3), Q(s)-(2), R(s)-(1)$ $P(s)-(1), Q(s)-(2), R(s)-(3)$ $P(s)-(2), Q(s)-(1), R(s)-(3)$ $P(s)-(1), Q(s)-(3), R(s)-(2)$
Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below.$P(s)-(3), Q(s)-(2), R(s)-(1)$$P(s)-(1), Q(s)-(2), R(s)-(3)$$...
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506
GATE2016-41
An ideal opamp is used to realize a difference amplifier circuit given below having a gain of $10$. If $x=0.025$, the $CMRR$ of the circuit in $dB$ is $\_\_\_\_\_\_\_\_$.
An ideal opamp is used to realize a difference amplifier circuit given below having a gain of $10$. If $x=0.025$, the $CMRR$ of the circuit in $dB$ is $\_\_\_\_\_\_\_\_$....
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507
GATE2016-42
In the circuit given below, the opamp is ideal. The input $v_x$ is a sinusoid. To ensure $v_y=v_x$, the value of $C_N$ in $\text{picofarad}$ is $\_\_\_\_\_\_\_$.
In the circuit given below, the opamp is ideal. The input $v_x$ is a sinusoid. To ensure $v_y=v_x$, the value of $C_N$ in $\text{picofarad}$ is $\_\_\_\_\_\_\_$.
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508
GATE2016-43
In the circuit given below, the opamp is ideal. The value of current $I_L$ in $\text{microampere}$ is $\_\_\_\_\_\_\_\_.$
In the circuit given below, the opamp is ideal. The value of current $I_L$ in $\text{microampere}$ is $\_\_\_\_\_\_\_\_.$
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515
GATE2016-50
In the circuit below, the opamp is ideal and the sensor is an $RTD$ whose resistance $R_\theta=1000(1+0.004\;\theta)\Omega$, where $\theta$ is temperature in $^0C$. The output sensitivity in $mV/^0C$ is $\_\_\_\_\_\_\_\_$.
In the circuit below, the opamp is ideal and the sensor is an $RTD$ whose resistance $R_\theta=1000(1+0.004\;\theta)\Omega$, where $\theta$ is temperature in $^0C$. The o...
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518
GATE2016-53
The bandgap in $eV$ of a semiconductor material required to construct an $LED$ that emits peak power at the wavelength of $620\;nm$ is $\_\_\_\_\_\_\_.$ (Plank constant $h=4.13567\times10^{-15}\;eV\;s$ and speed of light $c=2.998\times10^8\;m/s$).
The bandgap in $eV$ of a semiconductor material required to construct an $LED$ that emits peak power at the wavelength of $620\;nm$ is $\_\_\_\_\_\_\_.$(Plank constant $h...
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519
GATE2016-54
The signal $m(t)=\frac{\sin(100\;\pi t)}{100\; \pi t}$ is frequency modulated $(FM)$ with an $FM$ Modulator of frequency deviation constant of $30\;kHz/V$. Using Carson’s rule, the approximate bandwidth of the modulated wave in $\text{kilohertz}$ is $\_\_\_\_\_\_\_\_$.
The signal $m(t)=\frac{\sin(100\;\pi t)}{100\; \pi t}$ is frequency modulated $(FM)$ with an $FM$ Modulator of frequency deviation constant of $30\;kHz/V$. Using Carson�...
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520
GATE2016-55
A signal $m(t)$ varies from $-3.5\;V$ to $+3.5\;V$ with an average power of $3\;W$. The signal is quantized using a midtread type quantizer and subsequently binary encoded. With the codeword of length $3$, the signal to quantization noise ratio in $dB$ is $\_\_\_\_\_\_\_\_.$
A signal $m(t)$ varies from $-3.5\;V$ to $+3.5\;V$ with an average power of $3\;W$. The signal is quantized using a midtread type quantizer and subsequently binary encode...
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