GO Electronics
Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Highest voted questions in Engineering Mathematics
0
votes
0
answers
321
GATE ECE 2014 Set 1 | Question: 50
Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlation $E[X(t_{1})X(t_{2})]$ is $\cos(2\pi(t_{1} + t_{2}))$ $\sin(2\pi(t_{1} - t_{2}))$ $\sin(2\pi(t_{1} + t_{2}))$ $\cos(2\pi(t_{1} - t_{2}))$
Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlat...
Milicevic3306
16.0k
points
110
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
probability-and-statistics
statistics
uniform-distribution
correlation-and-regression-analysis
+
–
0
votes
0
answers
322
GATE ECE 2014 Set 1 | Question: 53
In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions. $\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omega t - \beta r)\hat{a_{\theta}}\: V/m$ ... free space. The average power $(W)$ crossing the hemispherical shell located at $r = 1\:km,0\leq \theta \leq \pi/2$ is ______.
In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions.$$\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omeg...
Milicevic3306
16.0k
points
128
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2014-ec-1
numerical-answers
vector-analysis
+
–
0
votes
0
answers
323
GATE ECE 2013 | Question: 52
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
Milicevic3306
16.0k
points
144
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2013-ec
vector-analysis
+
–
0
votes
0
answers
324
GATE ECE 2013 | Question: 53
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
Milicevic3306
16.0k
points
160
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2013-ec
vector-analysis
+
–
0
votes
0
answers
325
GATE ECE 2013 | Question: 36
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$ Let $x(t)$ be a rectangular pulse given by $x(t) = \begin{cases} 1&0<t<2 \\ 0&\text{otherwise} \end{cases}$ ... $\frac{e^{-2s}}{(s+2)(s+3)} \\$ $\frac{1-e^{-2s}}{s(s+2)(s+3)} $
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$Let $x(t)$ be a rectangul...
Milicevic3306
16.0k
points
122
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2013-ec
differential-equations
laplace-transform
+
–
0
votes
0
answers
326
GATE ECE 2013 | Question: 37
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing function is $x(t)$ and the initial condition is $y(0).$ If one wishes to modify the ... forcing function to $j\sqrt{2}x(t)$ change the initial condition to $−2y(0)$ and the forcing function to $−2x(t)$
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing functi...
Milicevic3306
16.0k
points
115
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2013-ec
differential-equations
+
–
0
votes
0
answers
327
GATE ECE 2013 | Question: 38
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. Then, for all values of $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. ...
Milicevic3306
16.0k
points
236
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ec
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
328
GATE ECE 2013 | Question: 39
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ ... $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}$
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ consider the...
Milicevic3306
16.0k
points
94
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2013-ec
vector-analysis
+
–
0
votes
0
answers
329
GATE ECE 2013 | Question: 26
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is$4/9$...
Milicevic3306
16.0k
points
140
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ec
probability-and-statistics
probability
random-variable
independent-events
+
–
0
votes
0
answers
330
GATE ECE 2013 | Question: 27
Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB) =$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \times k$ identity matrix. Using the above property, the determinant of the matrix given below ... $2$ $5$ $8$ $16$
Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB) =$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \time...
Milicevic3306
16.0k
points
110
views
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-ec
linear-algebra
matrices
determinant
+
–
0
votes
1
answer
331
GATE ECE 2013 | Question: 19
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
The minimum eigenvalue of the following matrix is$$\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$$$0$$1$$2$$3$
Milicevic3306
16.0k
points
947
views
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-ec
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
332
GATE ECE 2013 | Question: 20
A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive has no real roots no negative real root odd number of real roots at least one positive and one negative real root
A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive hasno real rootsno negative real rootodd number of real roots a...
Milicevic3306
16.0k
points
144
views
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-ec
calculus
polynomials
+
–
0
votes
0
answers
333
GATE ECE 2013 | Question: 6
The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta $ holds to within $10\%$ error is $10^{\circ}$ $18^{\circ}$ $50^{\circ}$ $90^{\circ}$
The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta $ holds to within $10\%$ error is$10^{\circ}$$18^{\circ}$$50^{\circ}$$90^{\circ}$
Milicevic3306
16.0k
points
117
views
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2013-ec
numerical-methods
+
–
0
votes
0
answers
334
GATE ECE 2013 | Question: 7
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$ $1/3$ $1$ $3$
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$$1/3$ $1$ $3$
Milicevic3306
16.0k
points
97
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2013-ec
vector-analysis
+
–
0
votes
0
answers
335
GATE ECE 2013 | Question: 2
Consider a vector field $\vec{A}(\vec{r}).$ The closed loop line integral $\displaystyle {} \int \vec{A}\bullet\vec{dl}$ can be expressed as $\displaystyle {} \iint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the closed surface ... by the loop $\displaystyle {} \iiint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the open surface bounded by the loop
Consider a vector field $\vec{A}(\vec{r}).$ The closed loop line integral $\displaystyle {} \int \vec{A}\bullet\vec{dl}$ can be expressed as$\displaystyle {} \iint (\tria...
Milicevic3306
16.0k
points
104
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2013-ec
vector-analysis
+
–
0
votes
0
answers
336
GATE ECE 2012 | Question: 46
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$
Milicevic3306
16.0k
points
88
views
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-ec
calculus
maxima-minima
+
–
0
votes
0
answers
337
GATE ECE 2012 | Question: 47
Given that $A=\begin{bmatrix} -5 &-3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is $15\:A+12\:I$ $19\:A+30\:I$ $17\:A+15\:I$ $17\:A+21\:I$
Given that$A=\begin{bmatrix} -5 &-3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is$15\:A+12\:I$$19\:A+30\:I$$17\:A+15\:I$...
Milicevic3306
16.0k
points
110
views
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012-ec
linear-algebra
matrices
+
–
0
votes
0
answers
338
GATE ECE 2012 | Question: 35
The direction of vector $A$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\triangledown.A=0$ is $-2$ $2$ $1$ $0$
The direction of vector $A$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\triangledown....
Milicevic3306
16.0k
points
205
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2012-ec
vector-analysis
+
–
0
votes
1
answer
339
GATE ECE 2012 | Question: 36
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is$\frac{1}{3}$$\frac{1}{2}$$\frac{2}{3}$$\frac{3}{...
Milicevic3306
16.0k
points
180
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
+
–
0
votes
0
answers
340
GATE ECE 2012 | Question: 38
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probability of error for an optimum receiver will be $\frac{7}{80}$ $\frac{63}{80}$ $\frac{9}{10}$ $\frac{1}{10}$
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probabi...
Milicevic3306
16.0k
points
239
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
+
–
0
votes
0
answers
341
GATE ECE 2012 | Question: 34
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)\big|_{t=0^-}=-2$ and $\frac{dy}{dt}\big|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}\big|_{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation$\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)\big|_{t=0^-}=-2$ and $\frac{dy}{dt}\big|_{t=0^-}=0$.The numerical val...
Milicevic3306
16.0k
points
115
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2012-ec
differential-equations
+
–
0
votes
0
answers
342
GATE ECE 2012 | Question: 23
Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}$. If $C$ is a counterclockwise path in the z-plane such that $\mid z+1 \mid=1$, the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is $-2$ $-1$ $1$ $2$
Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}$. If $C$ is a counterclockwise path in the z-plane such that $\mid z+1 \mid=1$, the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is$-2...
Milicevic3306
16.0k
points
106
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2012-ec
vector-analysis
+
–
0
votes
0
answers
343
GATE ECE 2012 | Question: 24
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is$\frac{3}{4}...
Milicevic3306
16.0k
points
102
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
independent-events
random-variable
+
–
0
votes
0
answers
344
GATE ECE 2012 | Question: 25
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{\frac{-\pi}{2}}$ $e^{\frac{\pi}{2}}$ $x$ $1$
If $x=\sqrt{-1}$, then the value of $x^x$ is$e^{\frac{-\pi}{2}}$$e^{\frac{\pi}{2}}$$x$$1$
Milicevic3306
16.0k
points
85
views
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-ec
calculus
+
–
0
votes
0
answers
345
GATE ECE 2012 | Question: 12
With initial condition $x(1)=0.5$, the solution of the differential equation, $t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$ $x=t^2-\frac{1}{2}$ $x=\frac{t^2}{2}$ $x=\frac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation,$$t\frac{dx}{dt}+x=t$$ is$x=t-\frac{1}{2}$$x=t^2-\frac{1}{2}$$x=\frac{t^2}{2}$$x=\frac{t}{2}$...
Milicevic3306
16.0k
points
87
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2012-ec
differential-equations
+
–
0
votes
0
answers
346
GATE ECE 2012 | Question: 15
A source alphabet consists of $N$ symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount $\varepsilon$ and decreases that of the second by $\varepsilon$. After encoding, the entropy of the source increases remains the same increases only if $N=2$ decreases
A source alphabet consists of $N$ symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by ...
Milicevic3306
16.0k
points
173
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
+
–
0
votes
0
answers
347
GATE ECE 2012 | Question: 18
If $x[n]=(\frac{1}{3})^{|n|}-(\frac{1}{2})^{|n|}u[n]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be $\frac{1}{3}\lt |z|\lt 3$ $\frac{1}{3}\lt |z|\lt \frac{1}{2}$ $\frac{1}{2}\lt |z|\lt 3$ $\frac{1}{3}\lt |z|$
If $x[n]=(\frac{1}{3})^{|n|}-(\frac{1}{2})^{|n|}u[n]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be$\frac{1}{3}\lt |z|\lt 3$$\frac{1}{3}...
Milicevic3306
16.0k
points
105
views
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2012-ec
numerical-methods
convergence-criteria
+
–
0
votes
0
answers
348
GATE ECE 2018 | Question: 55
Let $X\left[ k \right ] = k + 1,0\leq k\leq 7$ be $8$-point $\:\text{DFT}\:$ of a sequence $x[n]$. where $X\left [ k \right ]=\sum_{n=0}^{N-1}x \left [ n \right ]e^{-j2\pi nk/N}$. The value (correct to two decimal places) of $\sum_{n=0}^{3}x \left [ 2n \right ]$ is ________.
Let $X\left[ k \right ] = k + 1,0\leq k\leq 7$ be $8$-point $\:\text{DFT}\:$ of a sequence $x[n]$.where $X\left [ k \right ]=\sum_{n=0}^{N-1}x \left [ n \right ]e^{-j2\pi...
gatecse
1.6k
points
113
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
+
–
0
votes
0
answers
349
GATE ECE 2018 | Question: 50
The position of a particle $y\left ( t \right )$ is described by the differential equation: $\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$ The initial conditions are $y\left ( 0 \right )=1$ and $\frac{dy}{dt}\mid_{t=0}=0$. The position (accurate to two decimal places) of the particle at $t=\pi$ is _________.
The position of a particle $y\left ( t \right )$ is described by the differential equation:$$\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$$The initial conditions ar...
gatecse
1.6k
points
127
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
numerical-answers
differential-equations
second-order-differential-equation
+
–
0
votes
0
answers
350
GATE ECE 2018 | Question: 51
The contour $C$ given below is on the complex plane $z=x+j y,$ where $j=\sqrt{-1}.$ The value of the integral $\displaystyle{}\dfrac{1}{\pi j}\oint _{C}\dfrac{dz}{z^{2}-1}$ is _______.
The contour $C$ given below is on the complex plane $z=x+j y,$ where $j=\sqrt{-1}.$ The value of the integral $\disp...
gatecse
1.6k
points
417
views
gatecse
asked
Feb 19, 2018
Complex Analysis
gate2018-ec
numerical-answers
complex-analysis
+
–
0
votes
0
answers
351
GATE ECE 2018 | Question: 52
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to two decimal places) of $\dfrac{\partial r}{\partial x}$ is _________ .
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to t...
gatecse
1.6k
points
126
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
partial-derivatives
+
–
0
votes
0
answers
352
GATE ECE 2018 | Question: 40
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ where $Z$ ... $\alpha$ (accurate to two decimal places) is ________.
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ wh...
gatecse
1.6k
points
217
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
propability
random-variable
+
–
0
votes
0
answers
353
GATE ECE 2018 | Question: 34
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{x}.$ The equation that describes the curve is $\ln\left (1+\dfrac{y^{2}}{x^{2}}\right)=x-1$ ... $\ln\left (1+\dfrac{y}{x}\right)=x-1$ $\dfrac{1}{2}\ln\left (1+\dfrac{y}{x}\right)=x-1$
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{...
gatecse
1.6k
points
133
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
0
answers
354
GATE ECE 2018 | Question: 22
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value of $k$ for which the equation $Ax=0$ has infinitely many solutions is _________.
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value o...
gatecse
1.6k
points
109
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
numerical-answers
linear-algebra
system-of-equations
+
–
0
votes
0
answers
355
GATE ECE 2018 | Question: 23
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the four is ________.
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the fou...
gatecse
1.6k
points
161
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
probability
random-variable
variance
+
–
0
votes
0
answers
356
GATE ECE 2018 | Question: 24
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $$f\left ( x \right )={a}_{0}+a_{1}x+a_{2}...
gatecse
1.6k
points
191
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
taylor-series
+
–
0
votes
0
answers
357
GATE ECE 2018 | Question: 11
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements: $S1: M $ has $4$ linearly independent eigenvectors. $S2: M$ has $4$ distinct eigenvalues. $S3: M$ is non-singular (invertible). Which one among the following is TRUE? $S1$ implies $S2$ $S1$ implies $S3$ $S2$ implies $S1$ $S3$ implies $S2$
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements:$S1: M $ has $4$ linearly independent eigenvectors.$S2: M$ has $4$ distinct eigenvalues. $S...
gatecse
1.6k
points
123
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
358
GATE ECE 2018 | Question: 12
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and $y = 2$, then the relation between $a$ and $b$ is $a=\dfrac{b}{4}$ $a=\dfrac{b}{2}$ $a=2b$ $a=4b$
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and ...
gatecse
1.6k
points
113
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
359
GATE ECE 2018 | Question: 4
Let the input be $u$ and the output be $y$ ... $y=au+b,b\neq 0$ $y=au$
Let the input be $u$ and the output be $y$ of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:$\d...
gatecse
1.6k
points
132
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
0
answers
360
GATE ECE 2018 | Question: 6
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)$ is $0$ $1$ $2$ $3$
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)...
gatecse
1.6k
points
117
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
calculus
derivatives
+
–
Page:
« prev
1
...
6
7
8
9
10
next »
GO Electronics
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register