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GATE ECE 1993 | Question 6.6
The built-in potential (Diffusion Potential) in a $p-n$ junction is equal to the difference in the Fermi level of the two sides, expressed in volts increases with the increase in the doping levels of the two sides increases with the increase in temperature is equal to the average of the Fermi levels of the two sides
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GATE ECE 1993 | Question 1.1
The eigenvector(s) of the matrix $\left(\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right), a \neq 0$, is (are) $(0,0, \alpha)$ $(\alpha, 0,0)$ $(0,0,1)$ $(0, \alpha, 0)$
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GATE ECE 1993 | Question 1.2
The differential equation, $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+\sin$ $y=0$, is linear non-linear homogeneous of degree two
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GATE ECE 1993 | Question 1.3
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree $1$ $2$ $3$ $4$
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GATE ECE 1993 | Question 1.4
Which of the following is (are) valid $\text{FORTRAN} 77$ statement(s)? $\mathrm{DO} 131=1$ $\mathrm{A}=\mathrm{DIM}^{* * 7} 7$ $\text{READ}$ $=15.0$ $\text{GOTO}$ $3=10$
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GATE ECE 1993 | Question 1.5
Fourier series of the periodic function (period $2 \pi$ ) defined by $f(x)=\left\{\begin{array}{ll}0 & -\pi x x<0 \\ x & 0<x<\pi\end{array}\right.$ ... $\frac{\pi^2}{4}$ $\frac{\pi^2}{6}$ $\frac{\pi^2}{8}$ $\frac{\pi^2}{12}$
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GATE ECE 1993 | Question 1.6
Which of the following improper integrals is (are) convergent? $\int_{0}^{1} \frac{\sin x}{1-\cos x} d x$ $\int_{0}^{\infty} \frac{\operatorname{cox} x}{1+x} d x$ $\int_{0}^{x} \frac{x}{1+x^{2}} d x$ $\int_{0}^{1} \frac{1-\cos x}{x^{5 / 2}} d x$
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GATE ECE 1993 | Question 1.7
The function $f(x, y)=x^{2} y-3 x y+2 y+x$, has no local extremum one local minimum but no local maximum one local maximum but no local minimum one local minimum and one local maximum
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GATE ECE 1993 | Question 2.1
$\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}$ is
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GATE ECE 1993 | Question 2.2
The radius of convergence of the power series $\sum_{0}^{n} \frac{(3 m) !}{(m !)^{3}} x^{i m}$ is $\dots$
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GATE ECE 1993 | Question 2.3
If the linear velocity $\overrightarrow{\mathrm{V}}$ is given by $\overrightarrow{\mathrm{V}}=x^{2} y \hat{i}+$ $x y z \hat{j}-y z^{2} k$ the anguarl velocity $\vec{w}$ at the point $(1,1,-1)$ is $\dots$
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GATE ECE 1993 | Question 2.4
Given the differential equation, $\bar{y}=x-y$ with the initial condition $y(0)=0$. The value of $(0.1)$ calculated numerically upto the third place of decimal by the second order Runge-Kutta method with step size $h=0.1$ is
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GATE ECE 1993 | Question 2.5
For $\mathrm{X}=4.0$, the value of $1$ in the $\text{FORTRAN}$ $77$ statement \[ I=-2^{* *} 2+5.0 * X / X * 3+\frac{3}{4} \text { is } \]
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GATE ECE 1993 | Question 2.6
The value of the double integral $\int_{0}^{1} \int_{x}^{1 / x} \frac{x}{1+y^{2}}$ $d x d y$ is
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GATE ECE 1993 | Question 2.7
If $\mathrm{A}=\left(\begin{array}{cccc}1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i\end{array}\right)$ the matrix $\mathrm{A}^{4}$, calculated by the use of Cayley - Hamilton theorem or otherwise, is
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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
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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 $\dots$
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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 $\dots$
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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 ... $\sqrt{\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}}$
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GATE ECE 1993 | Question 3.2
The temperature of an ideal gas is held constant while its volume is increased. The pressure exerted by the gas on the walls of the container decreases because its molecules strike the walls with smaller force strike the walls with lower velocities strike the walls less frequently collide with each other more frequently
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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
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GATE ECE 1993 | Question 3.4
A plane electromagnetic wave of the form $\vec{E}=\hat{y} E_{0}\left[\cos 2 \pi\left(5 \times 10^{14} \sec ^{-1}\right) t-\left(2.5 \times 10^{6} \mathrm{~m}^{-1}\right) x\right]$ (where $E_{0}$ is a constant and $y$ is the unit vector along $y$-direction) represents a wave propagating along $+x$ direction $+y$ direction $-x$ direction $-y$ direction
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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 $\dots$
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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
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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
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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 $\dots$
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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 $D$
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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 $(2 / 3) \mathrm{MR}^{2}$ ]
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GATE ECE 1993 | Question 3.11
An optical fiber consists of a cylindrical dielectric rod of refractive index $\mathrm{n}^{1}$, surrounded by another dielectric of refractive index $n^{2}$, where $n^{2}$ $i \geq \sin ^{-1} \sqrt{n_{1}^{2}-n_{2}^{2}}$ $i<\sin ^{-1} \sqrt{n_{1}-n_{2}}$ $i \geq \sin ^{-1} \sqrt{n_{1}^{2}-n_{2}^{2}}$ $i=\sin ^{-1} \sqrt{n_{1}-n_{2}}$
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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 $\ldots .$
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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 $R / 2$ ... $\frac{\mathrm{R}}{2} \mu_{0} N I_{0} \omega \cos (\omega t)$
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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
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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 $\dots$ $A^{\circ}$.
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GATE ECE 1993 | Question 3.16
A light beam of frequency $1.2 \times 10^{15} \mathrm{~Hz}$ is incident on a metal in a photoelectric effect experiment. The corresponding maximum kinetic energy of the ejeted photoelectrons from the metal is $6.63 \times 10^{-19} \mathrm{~J}$. The characteristic cut-off frequency of the metal is $\text{Hz}$.
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GATE ECE 1993 | Question 3.17
Consider the semiconductors $\mathrm{A}$ and $\mathrm{B}$. The figure shows variation of $\ln p$ with $I / T$, where $p$ is resistivity and $\mathrm{T}$ the temperature, for the two semiconductors. Choose the correct statements (s). the bandgap ... than in B. the mamximum wavelength of light needed to create an electron hole pair is smaller in $\mathrm{A}$ than in B.
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GATE ECE 1993 | Question 4.1
A dc circuit shown in the figure is has a voltage source V, a current source 1 and several resistors. A particular resistor $\mathrm{R}$ dissipates a power of 4 Watts when $\mathrm{V}$ alone is active. The same resistor $\mathrm{R}$ dissipates a power of 9 Watts when ... both sources are active will be $1 \mathrm{~W}$ $5 \mathrm{~W}$ $13 \mathrm{~W}$ $25 \mathrm{~W}$
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GATE ECE 1993 | Question 4.2
In the series circuit shown in figure for series resonance, the value of the coupling coefficient $K$ wil be $0.25$ $0.5$ $0.999$ $1.0$
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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 $20$ $40$ $80$ $160$
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GATE ECE 1993 | Question 4.4
While starting a de shunt motor: reduced armature voltage $V_{n}$ and reduced field voltage $V_{\text {, }}$ should be applied and full regulator resistance $R$, should be included in the field circuit. reduced $V_{A}$ but full $V_{f}$ ... rated $\mathrm{V}_{a}$ and rated $\mathrm{V}_{f}$ should be applied and $\mathrm{R}_{r}$ should be maximum.
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GATE ECE 1993 | Question 4.5
A $6$ pole $3$ phase wound-rotor induction machine is driven by another machine at $180 \mathrm{rpm}$. The rotor of the induction machine is connected to a $50 \mathrm{~Hz}$ system. If the mechanical rotation of the rotor is in the same direction as the rotor ... the stator voltage will be $50 \mathrm{~Hz}$ $140 \mathrm{~Hz}$ $150 \mathrm{~Hz}$ $200 \mathrm{~Hz}$.
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