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Most viewed questions in Engineering Mathematics
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1
GATE2019 IN: 29
A complex function f(z) = u(x,y) + i v(x,y) and its complex conjugate f*(z) = u(x,y) – i v(x,y) are both analytic in the entire complex plane, where z = x + i y and i = $\sqrt{-1}$. The function f is then given by f(z) = x + i y f(z) = x$^{2}$ – y$^{2}$ + i 2xy f(z) = constant f(z) = x$^{2}$ + y$^{2}$
A complex function f(z) = u(x,y) + i v(x,y) and its complex conjugate f*(z) = u(x,y) – i v(x,y) are both analytic in the entire complex plane, where z = x + i y and i =...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Analysis of complex variables
gate2019-in
analysis-of-complex-variables
complex-conjugate
complex-function
+
–
0
votes
0
answers
2
GATE IN 2021 | Question: 37
Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\left ( 1,4 \right )$. Then $P\left ( Y\leq X \right )$ is equal to __________________ (rounded off to two decimal places).
Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\l...
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Probability and Statistics
gatein-2021
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
3
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 _____.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
cartesian-coordinates
+
–
0
votes
0
answers
4
GATE2020 IN: 28
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1. The equation that describes this line is __________. $\text{y=-0.5x+1}$ $\text{y=x-0.5}$ $\text{y=0.5x-1}$ $\text{y=2x+1}$
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1.The equation that describes this line is __________.$\text{y=-0.5x+1}$$\text{y=x-0...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Calculus
gate2020-in
calculus
cartesian-coordinates
+
–
0
votes
0
answers
5
GATE2018IN: 37
Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for this system is $x(t) = \begin{bmatrix}e^{-t} & te^{-2t} \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1 \\1\end{bmatrix}$ ... $\begin{bmatrix}1 \\1\end{bmatrix}$ $x(t) = \begin{bmatrix}e^{-t} & 0 \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1 \\1\end{bmatrix}$
Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Numerical Methods
gate2018-in
numerical-methods
linear-system
+
–
0
votes
0
answers
6
GATE2012-27
Given that $A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is $15A+12I$ $19A+30I$ $17A+15I$ $17A+21I$
Given that$A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is$15A+12I$$19A+30I$$17A+15I$$17A+21I$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
7
GATE2019 IN: 2
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightarrow{\bigtriangledown}$ x $\overrightarrow{A}$| is -1 0 1 $\infty$
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightar...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Calculus
gate2019-in
calculus
vector-calculus
vector-identities
+
–
0
votes
0
answers
8
GATE2018IN: 27
Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red? 20% 25% 30% 40%
Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Probability and Statistics
gate2018-in
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
9
GATE2020: 16
A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ball twice. Considering each attempt to be independent, the probability that this player puts the ball into the basket only in the second attempt $\text{(rounded off to two decimal places)}$ is __________
A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ba...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Probability and Statistics
gate2020-in
numerical-answers
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
10
GATE2020 IN: 31
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Calculus
gate2020-in
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
11
GATE2020: 2
Consider the recursive equation $X_{n+1}=X_n – h(F(X_n)-X_n),$ with initial condition $X_0=1$ and h>0 being a very small valued scalar. This recursion numerically solves the ordinary differential equation ________ $\dot{X}=-F(X), X(0)=1$ $\dot{X}=-F(X)+X, X(0)=1$ $\dot{X}=F(X), X(0)=1$ $\dot{X}=F(X)+X, X(0)=1$
Consider the recursive equation $X_{n+1}=X_n – h(F(X_n)-X_n),$ with initial condition $X_0=1$ and h>0 being a very small valued scalar. This recursion numerically solve...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Differential equations
gate2020-in
differential-equations
recursive-equation
+
–
0
votes
0
answers
12
GATE2018IN: 26
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$\overrightarrow{k}$, the value of the linear integral $\int_c$\overrightarrow{F}$ . d$\overrightarrow{l}$ along the straight line c from (0,0,0) to (1,1,1) is 3/16 0 -5/12 -1
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$$\overrightarrow{k}$, the value of the linear integral $\int_c$$\ove...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018-in
calculus
vector-calculus
line-integral
+
–
0
votes
0
answers
13
GATE2019 IN: 3
A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is 4/15 7/16 ½ 8/15
A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Probability and Statistics
gate2019-in
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
14
GATE IN 2021 | Question: 6
Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ________________. $\frac{1}{s-1}$ with real part of $s< 1$ $\frac{1}{s-1}$ with real part of $s> 1$ $\frac{-1}{s-1}$ with real part of $s< 1$ $\frac{-1}{s-1}$ with real part of $s> 1$
Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ______________...
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Differential equations
gatein-2021
differential-equations
laplace-transform
+
–
0
votes
0
answers
15
GATE2019 IN: 1
$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\widehat{k}}$ and $\overrightarrow{b}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ – ${\widehat{k}}$, the vector $\overrightarrow{c}$ is parallel to $\widehat{i}+2\widehat{j}+3\widehat{k}$ $2\widehat{i} + \widehat{j}$ $2\widehat{i} – \widehat{j}$ $4\widehat{k}$
$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\wi...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Calculus
gate2019-in
calculus
vector-calculus
vector-identities
+
–
0
votes
0
answers
16
GATE2015-12
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is $-2\pi i$ $0$ $2\pi i$ $4\pi i$
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is$-2\pi i$$0$$2\pi i$$4\pi i$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Analysis of complex variables
gate2015-in
analysis-of-complex-variables
cauchys-integral-theorem
+
–
0
votes
0
answers
17
GATE IN 2021 | Question: 23
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gatein-2021
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
18
GATE2014-4
A vector is defined as $f=y\hat{i}+x\hat{j}+z\hat{k}$ where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system. The surface integral $f.ds$ over the closed surface S of a cube with vertices having the following coordinates: $(0,0,0), (1,0,0),(1,1,0),(0,1,0),(0,0,1),(1,0,1),(1,1,1),(0,1,1)$ is __________.
A vector is defined as $$f=y\hat{i}+x\hat{j}+z\hat{k}$$where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system.The surface integral $f....
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014-in
numerical-answers
calculus
vector-calculus
surface-integral
+
–
0
votes
0
answers
19
GATE2018IN: 2
Let f$_1$(Z) =Z$^2$ and f$_2$(Z) = $\overline{z}$ be two complex variable functions. Here $\overline{z}$ is the complex conjugate of z. Choose the correct answer Both f$_1$(Z) and f$_2$(Z) are analytic Only f$_1$(Z) is analytic Only f$_2$(Z) is analytic Both f$_1$(Z) and f$_2$(Z) are not analytic
Let f$_1$(Z) =Z$^2$ and f$_2$(Z) = $\overline{z}$ be two complex variable functions. Here $\overline{z}$ is the complex conjugate of z. Choose the correct answerBoth f$_1...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Analysis of complex variables
gate2018-in
analysis-of-complex-variables
complex-conjugate
+
–
0
votes
0
answers
20
GATE2017: 35
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 2, 2020
Differential equations
gate2017-in
numerical-answers
differential-equations
laplace-transform
+
–
0
votes
0
answers
21
GATE2016-27
An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same color. The probability of getting a red ball in the next draw is $\frac{65}{156}$ $\frac{67}{156}$ $\frac{79}{156}$ $\frac{89}{156}$
An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same co...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2016-in
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
22
GATE IN 2021 | Question: 25
The determinant of the matrix $\text{M}$ shown below is _______________. $M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$
The determinant of the matrix $\text{M}$ shown below is _______________. $$M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$$...
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gatein-2021
numerical-answers
linear-algebra
matrices
determinant
+
–
0
votes
0
answers
23
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 $\_\_\_\_\_\_\_.$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
24
GATE2019 IN: 26
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional to x$^{-1}$ x$^{2}$ x$^{3}$ x$^{4}$
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional tox$^{-1}$x$^{2}$x$^{3}...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Calculus
gate2019-in
calculus
functions
curves
+
–
0
votes
0
answers
25
GATE2015-37
The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}$ is __________ .
The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2015-in
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
26
GATE2018IN: 29
Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy $\frac {\partial {V(x,y)}}{\partial y}$ = x$^2$ + qy$^2$ + 2xy where p and q are constant ,V(x,y) that satisfies the above equations is p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 2xy + 6 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 5 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$ + xy p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$
Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy ...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Differential equations
gate2018-in
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
27
GATE IN 2021 | Question: 24
Let $f\left ( z \right )=\dfrac{1}{z^{2}+6z+9}$ defined in the complex plane. The integral $\oint _{c}\:f\left ( z \right )dz$ over the contour of a circle $\text{c}$ with center at the origin and unit radius is _______________.
Let $f\left ( z \right )=\dfrac{1}{z^{2}+6z+9}$ defined in the complex plane. The integral $\oint _{c}\:f\left ( z \right )dz$ over the contour of a circle $\text{c}$ wit...
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Analysis of complex variables
gatein-2021
numerical-answers
analysis-of-complex-variables
cauchys-integral-theorem
+
–
0
votes
0
answers
28
GATE2018IN: 4
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018-in
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
29
GATE2018IN: 1
Let N be a 3 by 3 matrix with real numbers entries. The matrix N is such that N$^2$ = 0. The eigen values of N are 0, 0, 0 0,0,1 0,1,1 1,1,1
Let N be a 3 by 3 matrix with real numbers entries. The matrix N is such that N$^2$ = 0. The eigen values of N are 0, 0, 00,0,10,1,11,1,1
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Linear Algebra
gate2018-in
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
30
GATE IN 2021 | Question: 26
$f\left ( Z \right )=\left ( Z-1 \right )^{-1}-1+\left ( Z-1 \right )-\left ( Z-1 \right )^{2}+ \cdots$ is the series expansion of $\frac{-1}{Z\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$ $\frac{1}{Z\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$ $\frac{1}{\left ( Z-1 \right )^{2}}$ for $\left | Z-1 \right |< 1$ $\frac{-1}{\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$
$f\left ( Z \right )=\left ( Z-1 \right )^{-1}-1+\left ( Z-1 \right )-\left ( Z-1 \right )^{2}+ \cdots$ is the series expansion of$\frac{-1}{Z\left ( Z-1 \right )}$ for $...
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Analysis of complex variables
gatein-2021
analysis-of-complex-variables
taylor-series
+
–
0
votes
0
answers
31
GATE2020: 3
A set of linear equations is given in the form $Ax=b$, where A is a $2\times 4$ matrix with real number entries and $b\neq 0.$ will it be possible to solve for $x$ and obtain a unique solution by multiplying both left and right sides of the equation by $A^T$ (the super script $T$ denotes the transpose) and ... $A^T A$ is well conditioned Yes, can obtain a unique solution provided the matrix $A$ is well conditioned
A set of linear equations is given in the form $Ax=b$, where A is a $2\times 4$ matrix with real number entries and $b\neq 0.$ will it be possible to solve for $x$ and ob...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Linear Algebra
gate2020-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
32
GATE2015-13
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to $\int_0^x\int_0^y f(x,y) dx\;dy$ $\int_0^a \int_x^y f(x,y) dx\;dy$ $\int_0^a \int_x^a f(x,y) dy\;dx$ $\int_0^a \int_0^a f(x,y) dx\;dy$
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to$\int_0^x\int_0^y f(x,y) dx\;dy$$\int_0^a \int_x^y f(x,y) dx\;dy$$\int_0^a \int_x^a f(x,y) dy\;dx$$\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
calculus
definite-integrals
double-integrals
+
–
0
votes
0
answers
33
GATE2019 IN: 28
The dynamics of the state $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ of a sytem is governed by the differential equation $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ = $\begin{bmatrix}1 & 2 \\-3 & -4\end{bmatrix}$\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ + $ ... is $\begin{bmatrix}-30 \\-40\end{bmatrix}$ $\begin{bmatrix}-20 \\-10\end{bmatrix}$ $\begin{bmatrix}5\\-15\end{bmatrix}$ $\begin{bmatrix}50 \\-35\end{bmatrix}$
The dynamics of the state $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ of a sytem is governed by the differential equation $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ = ...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Differential equations
gate2019-in
differential-equations
+
–
0
votes
0
answers
34
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 __________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
limits
+
–
0
votes
0
answers
35
GATE2013-27
One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\begin{bmatrix}0&-1\\1&0\end{bmatrix}$ is $\begin{bmatrix}1\\-j\end{bmatrix}$,$\begin{bmatrix}j\\-1\end{bmatrix}$ $\begin{bmatrix}0\\1\end{bmatrix}$,$\begin{bmatrix}-1\\0\end{bmatrix}$ $\begin{bmatrix}1\\j\end{bmatrix}$,$\begin{bmatrix}0\\1\end{bmatrix}$ $\begin{bmatrix}1\\j\end{bmatrix}$,$\begin{bmatrix}j\\1\end{bmatrix}$
One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\begin{bmatrix}0&-1\\1&0\end{bmatrix}$ is$\begin{bmatrix}1\\-j\end{bmatrix}$,$\begin{bmatrix}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-in
linear-algebra
matrices
eigen-values
eigen-vectors
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–
0
votes
0
answers
36
GATE2012-36
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$$1/2$$1$$2$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
fourier-transform
+
–
0
votes
0
answers
37
GATE IN 2021 | Question: 1
Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is $1$ $2$ $3$ $4$
Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is$1$$2$$3$$4$
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gatein-2021
linear-algebra
matrices
rank-of-matrix
vectors
+
–
0
votes
0
answers
38
GATE2020: 19
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Differential equations
gate2020-in
numerical-answers
differential-equations
fourier-transform
+
–
0
votes
0
answers
39
GATE2017: 10
A system is described by the following differential equation: $\frac {dy(t)}{dt}+2y(t)=\frac {dx(t)}{dt}+x(t),\;x(0)=y(0)=0$ where $\text{x(t)}$ and $\text{y(t)}$ are the input and output variables respectively. The transfer function of the inverse system is $\frac {s+1}{s-2}$ $\frac {s+2}{s+1}$ $\frac{s+1}{s+2}$ $\frac {s-1}{s-2}$
A system is described by the following differential equation:$\frac {dy(t)}{dt}+2y(t)=\frac {dx(t)}{dt}+x(t),\;x(0)=y(0)=0$where $\text{x(t)}$ and $\text{y(t)}$ are the i...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 1, 2020
Differential equations
gate2017-in
differential-equations
+
–
0
votes
0
answers
40
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}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Analysis of complex variables
gate2016-in
analysis-of-complex-variables
taylor-series
+
–
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