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1521
GATE ECE 1993 | Question 2.8
Given, $\mathrm{V}=x \cos ^{2} y \hat{i}+x^{2} e^{x} \hat{j}+z \sin ^{2} y \hat{k}$ and $S$ the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes, the value of the integral $\iint_{\mathrm{S}} \overrightarrow{\mathrm{V}}, \hat{n} d \mathrm{~S}$ is _________.
Given, $\mathrm{V}=x \cos ^{2} y \hat{i}+x^{2} e^{x} \hat{j}+z \sin ^{2} y \hat{k}$ and $S$ the surface of a unit cube with one corner at the origin and edges parallel to...
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1522
GATE ECE 1993 | Question 2.9
The differential equation $y+y=0$ is subjected to the boundary conditions \[y(0)+0 y(\lambda)=0\] In order that the equation has non-trivial solution (s), the general value of $\eta$ is __________.
The differential equation $y+y=0$ is subjected to the boundary conditions\[y(0)+0 y(\lambda)=0\]In order that the equation has non-trivial solution (s), the general value...
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1523
GATE ECE 1993 | Question 2.10
The Laplace transform of the periodic function $f(t)$ described by the curve below, i.e. $f(t)=\left\{\begin{array}{c}\sin t \text { if }(2 n-1) \pi \leq t \leq 2 n \pi(n=1,2,3, \ldots) \\ 0\end{array}\right.$ otherwise is_________.
The Laplace transform of the periodic function $f(t)$ described by the curve below, i.e.$f(t)=\left\{\begin{array}{c}\sin t \text { if }(2 n-1) \pi \leq t \leq 2 n \pi(n=...
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1524
GATE ECE 1993 | Question 3.1
Two particles of masses $M_{1}$ and $M_{2}\left(M_{1}>M_{2}\right)$ attract each other with a force inversely proportional to the square of the distance between them. The particles are initially at rest and then released. The centre of mass relative to a ... $\sqrt{\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}}$
Two particles of masses $M_{1}$ and $M_{2}\left(M_{1}>M_{2}\right)$ attract each other with a force inversely proportional to the square of the distance between them. The...
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1526
GATE ECE 1993 | Question 3.3
Although a laser heam is highly directional, its beam width increases with propagation. This increase is due to coherence diffraction polarization interference
Although a laser heam is highly directional, its beam width increases with propagation. This increase is due tocoherencediffractionpolarizationinterference
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1528
GATE ECE 1993 | Question 3.5
While you are listening to a programme from a radio, if a near-by electric light bulb is switched on or switched off, you hear a momentary noise in your radio. This is due to electromagnetic radiation emitted by __________.
While you are listening to a programme from a radio, if a near-by electric light bulb is switched on or switched off, you hear a momentary noise in your radio. This is du...
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1529
GATE ECE 1993 | Question 3.6
Nuclear fusion reactions require very high temperatures so as to overcome. nuclear forces van der waals forces coulomb forces gravitational forces
Nuclear fusion reactions require very high temperatures so as to overcome.nuclear forcesvan der waals forcescoulomb forcesgravitational forces
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1530
GATE ECE 1993 | Question 3.7
In radioactive decay, the disintegration rate of the nuclei is constant at all times inversely proportional to half-life of the nuclei inversely proportional to the number of nuclei at any time directly proportional to the number of nuclei at any time
In radioactive decay, the disintegration rate of the nuclei isconstant at all timesinversely proportional to half-life of the nucleiinversely proportional to the number o...
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1531
GATE ECE 1993 | Question 3.8
In an hydrogen atom $10.2 . \mathrm{eV}$ is given out as radiation when an electron is de-excited to the ground state. The principal quantum number of the excited state is ___________.
In an hydrogen atom $10.2 . \mathrm{eV}$ is given out as radiation when an electron is de-excited to the ground state. The principal quantum number of the excited state i...
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1532
GATE ECE 1993 | Question 3.9
Typical current voltage characteristic of a solar cell is given in the following figure by curve $A$ curve $B$ curve $C$ curve $D$
Typical current voltage characteristic of a solar cell is given in the following figure bycurve $A$curve $B$curve $C$curve $D$
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1533
GATE ECE 1993 | Question 3.10
Consider a solid sphere and a hollow sphere, both of mass $M$, radius $R$ ... solid sphere is $(2 / 5) \mathrm{MR}^{2}$, and for a hollow sphere $(2 / 3) \mathrm{MR}^{2}$ ]
Consider a solid sphere and a hollow sphere, both of mass $M$, radius $R$ and initially at rest, which start rolling down the same inclined plane without slipping. At the...
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1535
GATE ECE 1993 | Question 3.12
For a uniformly charged sphere of radius $R$ and charge density $\rho$, the ratio of magnitude of electric fields at distances $R / 2$ and $2 R$ from the centre, i.e., $\frac{\mathrm{E}(r=\mathrm{R} / 2}{\mathrm{E}(r=2 \mathrm{R})}$ is $\ldots .$
For a uniformly charged sphere of radius $R$ and charge density $\rho$, the ratio of magnitude of electric fields at distances $R / 2$ and $2 R$ from the centre, i.e., $\...
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1536
GATE ECE 1993 | Question 3.13
A long solenoid of radius $\mathrm{R}$, and having $\mathrm{N}$ turns per unit length carries a time dependent current $I \; (t)=I_{0} \cos (\omega t)$. The magnitude of induced electric field at a distance $R / 2$ ... $\frac{\mathrm{R}}{2} \mu_{0} N I_{0} \omega \cos (\omega t)$
A long solenoid of radius $\mathrm{R}$, and having $\mathrm{N}$ turns per unit length carries a time dependent current $I \; (t)=I_{0} \cos (\omega t)$. The magnitude of ...
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1537
GATE ECE 1993 | Question 3.14
In an electron diffraction experiment, planes of a crystal with spacing $1 \mathrm{~A}^{\circ}$ between them yield the first maximum at a Bragg angle of $\theta=30^{\circ}$. The momentum of the electrons is __________ $\text{J – s/m}.$
In an electron diffraction experiment, planes of a crystal with spacing $1 \mathrm{~A}^{\circ}$ between them yield the first maximum at a Bragg angle of $\theta=30^{\circ...
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1538
GATE ECE 1993 | Question 3.15
A conventional unit cell of close packed face centered cubic $\text{(FCC)}$ structure made up of hard spheres has a cube edge of a $\mathrm{A}^{\circ}$. The radius of the sphere is __________ $A^{\circ}$.
A conventional unit cell of close packed face centered cubic $\text{(FCC)}$ structure made up of hard spheres has a cube edge of a $\mathrm{A}^{\circ}$. The radius of the...
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1542
GATE ECE 1993 | Question 4.2
In the series circuit shown in figure for series resonance, the value of the coupling coefficient $K$ will be $0.25$ $0.5$ $0.999$ $1.0$
In the series circuit shown in figure for series resonance, the value of the coupling coefficient $K$ will be$0.25$$0.5$$0.999$$1.0$
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1543
GATE ECE 1993 | Question 4.3
If the secondary winding of the ideal transformer shown in the circuit of Fig. $4.3.$ has $40$ turns, the number of turns in the primary winding for maximum power transfer to the $2^{\circ}$ resistor will be $20$ $40$ $80$ $160$
If the secondary winding of the ideal transformer shown in the circuit of Fig. $4.3.$ has $40$ turns, the number of turns in the primary winding for maximum power transfe...
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1546
GATE ECE 1993 | Question 4.6
For the amplifier circuit of the figure is the transistor a $\mathrm{B}$ of $800$ . The midband voltage gain $\mathrm{V}^{0} / \mathrm{V}^{1}$, of the circuit will be $0$ $<1$ $\approx 1$ $800$
For the amplifier circuit of the figure is the transistor a $\mathrm{B}$ of $800$ . The midband voltage gain $\mathrm{V}^{0} / \mathrm{V}^{1}$, of the circuit will be$0$$...
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1547
GATE ECE 1993 | Question 4.7
The waveshape of $\mathrm{V}^{0}$ in the figure will be
The waveshape of $\mathrm{V}^{0}$ in the figure will be
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1548
GATE ECE 1993 | Question 4.8
For the logic circuit shown in the figure is the output $Y$ is equal to $\overline{\mathrm{ABC}}$ $\overline{\mathrm{A}}+\overline{\mathrm{B}}+\overline{\mathrm{C}}$ $\overline{\mathrm{AB}}+\overline{\mathrm{BC}}+\overline{\mathrm{A}}+\overline{\mathrm{C}}$
For the logic circuit shown in the figure is the output $Y$ is equal to$\overline{\mathrm{ABC}}$$\overline{\mathrm{A}}+\overline{\mathrm{B}}+\overline{\mathrm{C}}$$\overl...
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1549
GATE ECE 1993 | Question 4.9
In the figure, is in ideal moving iron voltmeter $M$ will read $7.07 \mathrm{~V}$ $12.24 \mathrm{~V}$ $14.14 \mathrm{~V}$ $20.0 \mathrm{~V}$
In the figure, is in ideal moving iron voltmeter $M$ will read$7.07 \mathrm{~V}$$12.24 \mathrm{~V}$$14.14 \mathrm{~V}$$20.0 \mathrm{~V}$
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1550
GATE ECE 1993 | Question 6.1
A network contains linear resistors and ideal voltage sources. If values of all the resistors are doubled, then the voltage across each resistor is halved doubled increased by four times not changed
A network contains linear resistors and ideal voltage sources. If values of all the resistors are doubled, then the voltage across each resistor ishalveddoubledincreased ...
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1552
GATE ECE 1993 | Question 6.3
In the figure is $\mathrm{A}^{1} \mathrm{~A}^{2}$ and $\mathrm{A}^{3}$ are ideal ammeters. If $\mathrm{A}^{1}$ reads $5 \mathrm{A}, \mathrm{~A}^{2}$ reads $12 \mathrm{A}$, then $\mathrm{A}^{3}$ should read. $7 \mathrm{~A}$ $12 \mathrm{~A}$ $13 \mathrm{~A}$ $17 \mathrm{~A}$
In the figure is $\mathrm{A}^{1} \mathrm{~A}^{2}$ and $\mathrm{A}^{3}$ are ideal ammeters. If $\mathrm{A}^{1}$ reads $5 \mathrm{A}, \mathrm{~A}^{2}$ reads $12 \mathrm{A}$...
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1553
GATE ECE 1993 | Question 6.4
If $\tau \mathrm{F}(\mathrm{s})=[f(t)]=\frac{\mathrm{K}}{(\mathrm{s}+1)\left(\mathrm{s}^{2}+4\right)}$ then $\lim _{t \rightarrow \infty} f(t)$ is given by $\mathrm{K} / 4$ zero infinite undefined
If $\tau \mathrm{F}(\mathrm{s})=[f(t)]=\frac{\mathrm{K}}{(\mathrm{s}+1)\left(\mathrm{s}^{2}+4\right)}$ then $\lim _{t \rightarrow \infty} f(t)$ is given by$\mathrm{K} / 4...
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1554
GATE ECE 1993 | Question 6.5
If $s^{3}+3 s^{2}+4 s+A=0$, then all the roots of this equation are in the left half plane provided that $\mathrm{A}>12$ $-3<\mathrm{A}<4$ $0<\mathrm{A}<12$ $5<\mathrm{A}<12$
If $s^{3}+3 s^{2}+4 s+A=0$, then all the roots of this equation are in the left half plane provided that$\mathrm{A}>12$$-3<\mathrm{A}<4$$0<\mathrm{A}<12$$5<\mathrm{A}<12$...
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1555
GATE ECE 1993 | Question 6.7
$\alpha$ - cut off frequency of a bipolar junction transistor increases with the increase in base width increases with the increase in emitter width increases with increase in the collector width increases with decrease in the base width.
$\alpha$ - cut off frequency of a bipolar junction transistorincreases with the increase in base widthincreases with the increase in emitter widthincreases with increase ...
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1556
GATE ECE 1993 | Question 6.8
Negative feedback in amplifiers improves the signal to noise ratio at the input improves the signal to noise ratio at the output does not affect the signal to noise ratio at the output reduces distortion
Negative feedback in amplifiersimproves the signal to noise ratio at the inputimproves the signal to noise ratio at the outputdoes not affect the signal to noise ratio at...
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1557
GATE ECE 1993 | Question 6.9
In a multi-stage $\text{R-C}$ coupled amplifier the coupling capacitor limits the low frequency response limits the high frequency response does not affect the frequency response blocks the $d.c.$ component without affecting the frequency response
In a multi-stage $\text{R-C}$ coupled amplifier the coupling capacitorlimits the low frequency responselimits the high frequency responsedoes not affect the frequency res...
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1558
GATE ECE 1993 | Question 6.10
The bandwidth of an $n$-stage tuned amplifier, with each stage having a band width of $B$, is given by $\mathrm{B} / n$ $\mathrm{B} / \sqrt{n}$ $\mathrm{B} \sqrt{2^{1 / n}-1}$ $\mathrm{B} / \sqrt{2^{1 / n}-1}$
The bandwidth of an $n$-stage tuned amplifier, with each stage having a band width of $B$, is given by$\mathrm{B} / n$$\mathrm{B} / \sqrt{n}$$\mathrm{B} \sqrt{2^{1 / n}-1...
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1559
GATE ECE 1993 | Question 6.11
In a transistor push-pull amplifier there is no $d.c.$ present in the output there is no distortion in the output there are no even harmonics in the output there are no odd harmonics in the output
In a transistor push-pull amplifierthere is no $d.c.$ present in the outputthere is no distortion in the outputthere are no even harmonics in the outputthere are no odd h...
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1560
GATE ECE 1993 | Question 6.12
$2$'s complement representation of a $16$ – bit number (one sign bit and $15$ magnitude bits) is $\text{FFFI}$. Its magnitude in decimal representation is $0$ $1$ $32,767$ $65,535$
$2$'s complement representation of a $16$ – bit number (one sign bit and $15$ magnitude bits) is $\text{FFFI}$. Its magnitude in decimal representation is$0$$1$$32,767$...
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