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522
GATE2015-11
Let $A$ be an $n\times n$ matrix with rank $r(0<r<n).$ Then $\text{Ax=0}$ has $p$ independent solutions, where $p$ is $r$ $n$ $n-r$ $n+r$
Let $A$ be an $n\times n$ matrix with rank $r(0<r<n).$ Then $\text{Ax=0}$ has $p$ independent solutions, where $p$ is$r$$n$$n-r$$n+r$
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523
GATE2015-12
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is $-2\pi i$ $0$ $2\pi i$ $4\pi i$
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is$-2\pi i$$0$$2\pi i$$4\pi i$
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524
GATE2015-13
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to $\int_0^x\int_0^y f(x,y) dx\;dy$ $\int_0^a \int_x^y f(x,y) dx\;dy$ $\int_0^a \int_x^a f(x,y) dy\;dx$ $\int_0^a \int_0^a f(x,y) dx\;dy$
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to$\int_0^x\int_0^y f(x,y) dx\;dy$$\int_0^a \int_x^y f(x,y) dx\;dy$$\int_0^a \int_x^a f(x,y) dy\;dx$$\...
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525
GATE2015-14
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is $4\sqrt{2}$ $5\sqrt{2}$ $7\sqrt{2}$ $9\sqrt{2}$
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is$4\sqrt{2}$$5\sqrt{...
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526
GATE2015-15
The figure shows a half-wave rectifier circuit with input voltage $V(t)=10\sin(100\;\pi t)$ volts. Assuming ideal diode characteristics with zero forward voltage drop and zero reverse current, the average power consumed in watts by the load resistance $R_L$ is $\_\_\_\_\_\_\_\_\_ W$.
The figure shows a half-wave rectifier circuit with input voltage $V(t)=10\sin(100\;\pi t)$ volts. Assuming ideal diode characteristics with zero forward voltage drop and...
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527
GATE2015-16
The capacitor shown in the figure is initially charged to $\text{+10 V}$. The switch closes at time $t=0$. Then the value of $V_C(t)$ in volts at time $\text{t=0 ms}$ is _____________ $V$.
The capacitor shown in the figure is initially charged to $\text{+10 V}$. The switch closes at time $t=0$. Then the value of $V_C(t)$ in volts at time $\text{t=0 ms}$ is ...
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528
GATE2015-17
The torque transmitted by a cylindrical shaft is to be measured by using two strain gauges. The angles for mounting the strain gauges relative to the axis of the shaft for maximum sensitivity are $\pm 45^\circ$ $\pm 60^\circ$ $\pm 90^\circ$ $\pm 180^\circ$
The torque transmitted by a cylindrical shaft is to be measured by using two strain gauges. The angles for mounting the strain gauges relative to the axis of the shaft fo...
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529
GATE2015-18
A p-type semiconductor strain gauge has a nominal resistance of $1000\;\Omega$ and a gauge factor of $+200$ at $25\;^\circ C$. The resistance of the strain gauge in ohms when subjected to a strain of $+10^{-4}$ m/m at the same temperature is __________ $\Omega$.
A p-type semiconductor strain gauge has a nominal resistance of $1000\;\Omega$ and a gauge factor of $+200$ at $25\;^\circ C$. The resistance of the strain gauge in ohms ...
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530
GATE2015-19
Liquid flow rate is measured using a Pirani gauge a pyrometer an orifice plate a Bourdon tube
Liquid flow rate is measured usinga Pirani gaugea pyrometeran orifice platea Bourdon tube
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531
GATE2015-20
The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by $NV_i\sin \omega t$ $-NV_i\sin \omega t$ $\frac{1}{N}V_i\sin \omega t$ $-\frac{1}{N}V_i\sin \omega t$
The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by$NV_i\sin \omega t$$-NV_i\sin \omega t$$\frac{1}{N}V_i\sin \omega ...
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532
GATE2015-21
A load resistor $R_L$ is connected to a battery of voltage $E$ with internal resistance $R_i$ through a resistance $R_s$ as shown in the figure. For fixed values of $R_L$ and $R_i$, the value of $R_s(\underline{>}0)$ for maximum power transfer to $R_L$ is $0$ $R_L-R_i$ $R_L$ $R_L+R_i$
A load resistor $R_L$ is connected to a battery of voltage $E$ with internal resistance $R_i$ through a resistance $R_s$ as shown in the figure. For fixed values of $R_L$...
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534
GATE2015-23
The logic evaluated by the circuit at the output is $X\overline{Y}+Y\overline{X}$ $(\overline{X+Y})XY$ $\overline{XY}+XY$ $\overline{X}Y+X\overline{Y}+X+Y$
The logic evaluated by the circuit at the output is $X\overline{Y}+Y\overline{X}$$(\overline{X+Y})XY$$\overline{XY}+XY$$\overline{X}Y+X\overline{Y}+X+Y$
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536
GATE2015-25
The highest frequency present in the signal $x(t)$ is $f_{max}$. The highest frequency present in the signal $y(t)=x^2(t)$ is $\frac{1}{2}f_{max}$ $f_{max}$ $2f_{max}$ $4f_{max}$
The highest frequency present in the signal $x(t)$ is $f_{max}$. The highest frequency present in the signal $y(t)=x^2(t)$ is$\frac{1}{2}f_{max}$$f_{max}$$2f_{max}$$4f_{m...
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537
GATE2015-26
The filter whose transfer function is of the form $G(s)=\frac{s^2-bs+c}{s^2+bs+c}$ is a high-pass filter a low-pass filter an all-pass filter a band-reject filter
The filter whose transfer function is of the form $G(s)=\frac{s^2-bs+c}{s^2+bs+c}$ isa high-pass filtera low-pass filteran all-pass filtera band-reject filter
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538
GATE2015-27
Let 3+4j be a zero of a fourth order linear-phase $FIR$ filter. The complex number which is $NOT$ a zero of this filter is $3-4j$ $\frac{3}{25}+\frac{4}{25}j$ $\frac{3}{25}-\frac{4}{25}j$ $\frac{1}{3}-\frac{1}{4}j$
Let 3+4j be a zero of a fourth order linear-phase $FIR$ filter. The complex number which is $NOT$ a zero of this filter is$3-4j$$\frac{3}{25}+\frac{4}{25}j$$\frac{3}{25}-...
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540
GATE2015-29
The bridge most suited for measurement of a four-terminal resistance in the range of $0.001\;\Omega$ to $0.1\;\Omega$ is Wien’s bridge Kelvin double bridge Maxwell’s bridge Schering bridge
The bridge most suited for measurement of a four-terminal resistance in the range of $0.001\;\Omega$ to $0.1\;\Omega$ isWien’s bridgeKelvin double bridgeMaxwell’s bri...
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543
GATE2015-32
A system with transfer function $G(S)=\frac{1}{s^2+1} $ has zero initial conditions. The percentage overshoot in its step response is ______________ $\%$.
A system with transfer function $G(S)=\frac{1}{s^2+1} $ has zero initial conditions. The percentage overshoot in its step response is ______________ $\%$.
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544
GATE2015-33
The voltage $(E_0)$ developed across a glass electrode for $pH$ measurement is related to the temperature $(T)$ by the relation $E_0 \varpropto \frac{1}{T^2}$ $E_0 \varpropto \frac{1}{T}$ $E_0 \varpropto T$ $E_0 \varpropto T^2$
The voltage $(E_0)$ developed across a glass electrode for $pH$ measurement is related to the temperature $(T)$ by the relation$E_0 \varpropto \frac{1}{T^2}$$E_0 \varprop...
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547
GATE2015-36
The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ are defective is 0.001 0.057 0.107 0.3
The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ ar...
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548
GATE2015-37
The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}$ is __________ .
The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}...
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549
GATE2015-38
The $z-$transform of $x[n]=\alpha ^{|n|}, 0<|\alpha|<1,$ is $X(z).$ The region of convergence of $X(z)$ is $|\alpha|<|z|<\frac{1}{|\alpha|}$ $|z|>\alpha$ $|z|>\frac{1}{|\alpha|}$ $|z|<min[|\alpha|,\frac{1}{|\alpha|}]$
The $z-$transform of $x[n]=\alpha ^{|n|}, 0<|\alpha|<1,$ is $X(z).$ The region of convergence of $X(z)$ is$|\alpha|<|z|<\frac{1}{|\alpha|}$$|z|>\alpha$$|z|>\frac{1}{|\alp...
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550
GATE2015-39
The current in amperes through the resistor $R$ in the circuit shown in the figure is ______________ $A$.
The current in amperes through the resistor $R$ in the circuit shown in the figure is ______________ $A$.
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551
GATE2015-40
The linear $I-V$ characteristics of 2-terminal non-ideal dc sources $X$ and $Y$ are shown in the figure. If the sources are connected to a $1\Omega$ resistor as shown, the current through the resistor in amperes is ______________ A.
The linear $I-V$ characteristics of 2-terminal non-ideal dc sources $X$ and $Y$ are shown in the figure. If the sources are connected to a $1\Omega$ resistor as shown, th...
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552
GATE2015-41
Consider the circuits shown in the figure. The magnitude of the ratio of the currents, i.e., $|I_1/I_2|$, is ___________.
Consider the circuits shown in the figure. The magnitude of the ratio of the currents, i.e., $|I_1/I_2|$, is ___________.
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553
GATE2015-42
The circuit shown in the figure is in series resonance at frequency $f_c\;Hz$. The value of $V_c$ in volts is _____________ $V$.
The circuit shown in the figure is in series resonance at frequency $f_c\;Hz$. The value of $V_c$ in volts is _____________ $V$.
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554
GATE2015-43
The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is $100\;kHz$. If the sensor capacitance increases by $10\% $, the output frequency in kilohertz becomes ____________ $kHz.$
The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is $100\;kHz$. If the sensor capacitance increases by $1...
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555
GATE2015-44
The Seebeck coefficients, in $\mu V/^\circ C,$ for copper, constant an and iron, with respect to platinum, are $1.9, \:-38.3$ and $13.3$, respectively. The magnitude of the thermo emf $E$ developed in the circuit shown in the figure, in millivolts is _____________ $mV$.
The Seebeck coefficients, in $\mu V/^\circ C,$ for copper, constant an and iron, with respect to platinum, are $1.9, \:-38.3$ and $13.3$, respectively. The magnitude of t...
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557
GATE2015-46
In the circuit shown in the figure, it is found that $V_{BE}=0.7\:V$ and $V_E=0\:V$. If $\beta_{dc}=99$ for the transistor, then the value of $R_B$ in kilo ohms is _______________ $k\Omega$.
In the circuit shown in the figure, it is found that $V_{BE}=0.7\:V$ and $V_E=0\:V$. If $\beta_{dc}=99$ for the transistor, then the value of $R_B$ in kilo ohms is ______...
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558
GATE2015-47
An opamp has ideal characteristics except that its open loop gain is given by the expression $Av(S)=10^4/(1+10^{-3}\;s).$ This op-amp is used in the circuit shown in the figure. The 3-dB bandwidth of the circuit, in $\text{rad/s}$, is $10^2$ $10^3$ $10^4$ $10^6$
An opamp has ideal characteristics except that its open loop gain is given by the expression $Av(S)=10^4/(1+10^{-3}\;s).$ This op-amp is used in the circuit shown in the ...
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