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Recent questions tagged gate2016-in

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4
GATE2016-GA-4
The number that least fits this set$:(324,441,97$ and $64)$ is $324$ $441$ $97$ $64$
The number that least fits this set$:(324,441,97$ and $64)$ is$324$$441$$97$$64$
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6
GATE2016-GA-6
The velocity $V$ of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the $7$ seconds, how much will the odometer reading increase by (in m)? $0$ $3$ $4$ $5$
The velocity $V$ of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the $7$ seconds, how much will ...
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GATE2016-GA-9
Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant. $14.95$ $15.25$ $15.70$ $20.35$
Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant.$14.95$$15.25$$15.70$$20.35$
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10
GATE2016-GA-10
A straight line is fit to a data set $(\text{ln }x,y).$ This line intercepts the abscissa at $\text{ln } x =0.1$ and has a slope of $-0.02$. What is the value of $y$ at $x=5$ from the fit? $-0.030$ $-0.014$ $0.014$ $0.030$
A straight line is fit to a data set $(\text{ln }x,y).$ This line intercepts the abscissa at $\text{ln } x =0.1$ and has a slope of $-0.02$. What is the value of $y$ at $...
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11
GATE 2016 - 1
A straight line of the form $y=mx+c$ passes through the origin and the point $(x,y)$ =$(2,6)$. The value of $m$ is _____.
A straight line of the form $y=mx+c$ passes through the origin and the point $(x,y)$ =$(2,6)$. The value of $m$ is _____.
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12
GATE2016-2
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
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14
GATE2016-4
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______. $(i-2j+k)$ $(-i+2j-k)$ $(0i+0j+0k)$ $(4i+3j+5k)$
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______.$(i-2j+k)$ $(-i+2j-k)$$(0i+0j+0k)$$(4i+3j+5k)$
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15
GATE2016-5
In the neighborhood of $z=1$, the function $f(z)$ has a power series expansion of the form $f(z)$ = $1$ + $(1-z)$ + $(1-z)^2+ \ldots$ Then $f(z)$ is $\frac{1}{z}$ $\frac{-1}{z-2}$ $\frac{z-1}{z+}$ $\frac{1}{2z-1}$
In the neighborhood of $z=1$, the function $f(z)$ has a power series expansion of the form $f(z)$ = $1$ + $(1-z)$ + $(1-z)^2+ \ldots$Then $f(z)$ is$\frac{1}{z}$$\frac{-1}...
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16
GATE2016-6
Three currents $i_1, i_2$ and $i_3$ meet at a node as shown in the figure below. If $i_1=3\cos(\omega t)$ ampere, $i_2=4\sin(\omega t)$ ampere and $i_3=I_3\cos(\omega t+\theta)$ ampere, the value of $I_3$ in $\text{ampere}$ is $\_\_\_\_\_\_\_.$
Three currents $i_1, i_2$ and $i_3$ meet at a node as shown in the figure below. If $i_1=3\cos(\omega t)$ ampere, $i_2=4\sin(\omega t)$ ampere and $i_3=I_3\cos(\omega t+\...
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GATE2016-7
An air cored coil has a $Q$ of $5$ at a frequency of $100$ kHz. The $Q$ of the coil at $20$ kHz (neglecting skin effect) will be ________.
An air cored coil has a $Q$ of $5$ at a frequency of $100$ kHz. The $Q$ of the coil at $20$ kHz (neglecting skin effect) will be ________.
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GATE2016-8
A current $i(t)$ shown in the figure below is passed through a $\text{1 F}$ capacitor that had zero initial charge. The voltage across the capacitor for $t>2s$ in $volt$ is $\_\_\_\_\_\_\_$.
A current $i(t)$ shown in the figure below is passed through a $\text{1 F}$ capacitor that had zero initial charge. The voltage across the capacitor for $t>2s$ in $volt$ ...
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19
GATE2016-9
The signal $x[n]$ shown in the figure below is convolved with itself to get $y[n]$. The value of $y[-1]$ is $\_\_\_\_\_\_\_\_.$
The signal $x[n]$ shown in the figure below is convolved with itself to get $y[n]$. The value of $y[-1]$ is $\_\_\_\_\_\_\_\_.$
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20
GATE2016-10
In the circuit shown below $ (v_1+v_2) =[1\; \sin(2\pi10000t)] + 1\;\sin(2\pi30000t)] \;V.$ The $RMS$ value of the current through the resistor $R$ will be minimum if the value of the capacitor $C$ in $\text{microfarad}$ is ____________.
In the circuit shown below $ (v_1+v_2) =[1\; \sin(2\pi10000t)] + 1\;\sin(2\pi30000t)] \;V.$ The $RMS$ value of the current through the resistor $R$ will be minimum if th...
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21
GATE2016-11
If $X(s)$, the Laplace transform of signal $x(t)$ is given by $X(s) = \frac{(s+2)}{(s+1)(s+3)^2}$, then the value of $x(t)$ as $t\rightarrow \infty$ is ______.
If $X(s)$, the Laplace transform of signal $x(t)$ is given by $X(s) = \frac{(s+2)}{(s+1)(s+3)^2}$, then the value of $x(t)$ as $t\rightarrow \infty$ is ______.
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22
GATE2016-12
The number of times the Nyquist plot of $G(s)= \frac{s-1}{s+1}$ will encircle the origin clockwise is _______.
The number of times the Nyquist plot of $G(s)= \frac{s-1}{s+1}$ will encircle the origin clockwise is _______.
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23
GATE2016-13
The value of $a_0$ which will ensure that the polynomial $s^3$ + $3s^2$ + $2s$ + $a_0$ has roots on the left half of the $s$-plane is $11$ $9$ $7$ $5$
The value of $a_0$ which will ensure that the polynomial $s^3$ + $3s^2$ + $2s$ + $a_0$ has roots on the left half of the $s$-plane is$11$$9$$7$$5$
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24
GATE2016-14
The input $i(t)$ = $2\sin(3t+\pi)$ is applied to a system whose transfer function $G(s)=\frac{8}{(s+10)^2}$. The amplitude of the output of the system is _______.
The input $i(t)$ = $2\sin(3t+\pi)$ is applied to a system whose transfer function $G(s)=\frac{8}{(s+10)^2}$.The amplitude of the output of the system is _______.
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25
GATE2016-15
The diode $D$ used in the circuit below is ideal. The voltage drop $V_{ab}$ across the $1\;k\Omega$ resistor in $\text{volt}$ is $\_\_\_\_\_\_\_\_.$
The diode $D$ used in the circuit below is ideal. The voltage drop $V_{ab}$ across the $1\;k\Omega$ resistor in $\text{volt}$ is $\_\_\_\_\_\_\_\_.$
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26
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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27
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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28
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)$$(X’+Z)(Y’+Z)$
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29
GATE2016-19
In the digital circuit given below, $F$ is $XY+Y\overline{Z}$ $XY+\overline{Y}Z$ $\overline{X}\overline{Y}+Y\overline{Z}$ $XZ+\overline{Y}$
In the digital circuit given below, $F$ is$XY+Y\overline{Z}$$XY+\overline{Y}Z$$\overline{X}\overline{Y}+Y\overline{Z}$$XZ+\overline{Y}$
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30
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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32
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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33
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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34
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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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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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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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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