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Recent questions tagged gate1993-ec

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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) $(0,0, \alpha)$ $(\alpha, 0,0)$ $(0,0,1)$ $(0, \alpha, 0)$
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)...
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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
The differential equation, $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+\sin$ $y=0$, islinearnon-linearhomogeneousof 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 $1$ $2$ $3$ $4$
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree$1$$2$$3$$4$
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GATE ECE 1993 | Question 1.4
Which of the following is (are) valid $\text{FORTRAN} 77$ statement(s)? $\mathrm{DO} \; 131=1$ $\mathrm{A}=\mathrm{DIM}^{* * *} 7$ $\text{READ}$ $=15.0$ $\text{GOTO}$ $3=10$
Which of the following is (are) valid $\text{FORTRAN} 77$ statement(s)?$\mathrm{DO} \; 131=1$$\mathrm{A}=\mathrm{DIM}^{* * *} 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 $f(x)=\left\{\begin{array}{ll}0 & -\pi < x<0 \\ x & 0<x<\pi\end{array}\right.$ ... $\frac{\pi^2}{4}$ $\frac{\pi^2}{6}$ $\frac{\pi^2}{8}$ $\frac{\pi^2}{12}$
Fourier series of the periodic function (period $2 \pi$ ) defined by$f(x)=\left\{\begin{array}{ll}0 & -\pi < x<0 \\ x & 0<x<\pi\end{array}\right.$ is$\frac{\pi}{4}+\sum_1...
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GATE ECE 1993 | Question 1.6
Which of the following improper integrals is (are) convergent? $\int_{0}^{1} \frac{\sin x}{1-\cos x} d x$ $\int_{0}^{\infty} \frac{\operatorname{cox} x}{1+x} d x$ $\int_{0}^{x} \frac{x}{1+x^{2}} d x$ $\int_{0}^{1} \frac{1-\cos x}{x^{5 / 2}} d x$
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}^...
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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
The function $f(x, y)=x^{2} y-3 x y+2 y+x$, hasno local extremumone local minimum but no local maximumone local maximum but no local minimumone local minimum and one loca...
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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
$\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}$ is
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GATE ECE 1993 | Question 2.2
The radius of convergence of the power series $\sum_{0}^{\infty} \frac{(3 m) !}{(m !)^{3}} x^{3m}$ is ___________.
The radius of convergence of the power series$\sum_{0}^{\infty} \frac{(3 m) !}{(m !)^{3}} x^{3m}$ is ___________.
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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 __________.
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 $\vec{w}$ a...
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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 _________.
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 sec...
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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 $I=-2^{* *} 2+5.0 ^* X / X ^* 3+\frac{3}{4} \text { is}$___________.
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
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
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 t...
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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 _________.
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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