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Most answered questions in Engineering Mathematics
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81
GATE Electrical 2014 Set 3 | Question: 28
The function $f(x)=e^x-1$ is to be solved using Newton-Raphson method. If the initial value of $x_0$ is taken as $1.0$, then the absolute error observed at $2^{nd}$ iteration is _______.
The function $f(x)=e^x-1$ is to be solved using Newton-Raphson method. If the initial value of $x_0$ is taken as $1.0$, then the absolute error observed at $2^{nd}$ iter...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Numerical Methods
gate2014-ee-3
numerical-methods
newton-raphson-method
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–
0
votes
0
answers
82
GATE Electrical 2014 Set 3 | Question: 26
Integration of the complex function $f(z)=\dfrac{z^2}{z^2-1}$ , in the counterclockwise direction, around $\mid z-1 \mid = 1$, is $-\pi i$ $0$ $\pi i$ $2 \pi i$
Integration of the complex function $f(z)=\dfrac{z^2}{z^2-1}$ , in the counterclockwise direction, around $\mid z-1 \mid = 1$, is$-\pi i$$0$$\pi i$$2 \pi i$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Complex Variables
gate2014-ee-3
complex-variables
complex-functions
cauchys-integral-theorem
+
–
0
votes
0
answers
83
GATE Electrical 2014 Set 3 | Question: 5
A function $f(t)$ is shown in the figure. The Fourier transform $F(\omega)$ of $f(t)$ is real and even function of $\omega$ real and odd function of $\omega$ imaginary and odd function of $\omega$ imaginary and even function of $\omega$
A function $f(t)$ is shown in the figure.The Fourier transform $F(\omega)$ of $f(t)$ isreal and even function of $\omega$real and odd function of $\omega$imaginary and od...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Transform Theory
gate2014-ee-3
transform-theory
fourier-transform
+
–
0
votes
0
answers
84
GATE Electrical 2014 Set 3 | Question: 1
Two matrices $A$ and $B$ are given below: $A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$ If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is $N/2$ $N – 1$ $N$ $2N$
Two matrices $A$ and $B$ are given below:$A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$If the rank of...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Linear Algebra
gate2014-ee-3
linear-algebra
matrices
rank-of-matrix
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–
0
votes
0
answers
85
GATE Electrical 2014 Set 3 | Question: 3
Let $\nabla .(fv)=x^2y+y^2z+z^2x$ , where $f$ and $v$ are scalar and vector fields respectively. If $v=yi+zj+xk$ then $v.\Delta f$ is $x^2y+y^2z+z^2x$ $2xy+2yz+2zx$ $x+y+z$ $0$
Let $\nabla .(fv)=x^2y+y^2z+z^2x$ , where $f$ and $v$ are scalar and vector fields respectively. If $v=yi+zj+xk$ then $v.\Delta f$ is$x^2y+y^2z+z^2x$$2xy+2yz+2zx$$x+y+z$...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-3
calculus
field-vectors
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–
0
votes
0
answers
86
GATE Electrical 2014 Set 3 | Question: 4
Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x$ is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ years respectively, then the value of $k$ is ________.
Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x$ is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2014-ee-3
probability-and-statistics
probability
random-variable
probability-density-function
numerical-answers
+
–
0
votes
0
answers
87
GATE Electrical 2014 Set 2 | Question: 18
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
The state transition matrix for the system$\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{b...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Linear Algebra
gate2014-ee-2
linear-algebra
matrices
transition-matrix
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0
votes
0
answers
88
GATE Electrical 2014 Set 2 | Question: 26
To evaluate the double integral $\displaystyle \int_{0}^{8} \bigg (\int_{(y/2)}^{y/2+1} \bigg (\dfrac{2x-y}{2} \bigg)dx \bigg)dy$ , we make the substitution $u=\bigg (\dfrac{2x-y}{2} \bigg)$ and $v=\dfrac{y}{2}$ ... $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{2}u \: du \bigg ) dv$
To evaluate the double integral $\displaystyle \int_{0}^{8} \bigg (\int_{(y/2)}^{y/2+1} \bigg (\dfrac{2x-y}{2} \bigg)dx \bigg)dy$ , we make the substitution $u=\bigg (\df...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-2
calculus
definite-integral
double-integral
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0
votes
0
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89
GATE Electrical 2014 Set 2 | Question: 27
Let $X$ be a random variable with probability density function $f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \text{otherwise } \end{cases} \\$ The probability $P(0.5 < X < 5)$ is ______.
Let $X$ be a random variable with probability density function$f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \tex...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2014-ee-2
probability-and-statistics
probability
random-variable
probability-density-function
numerical-answers
+
–
0
votes
0
answers
90
GATE Electrical 2014 Set 2 | Question: 28
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is $20$ $28$ $16$ $32$
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is$20$$28$$16$$32$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-2
calculus
maxima-minima
+
–
0
votes
0
answers
91
GATE Electrical 2014 Set 2 | Question: 5
Consider the differential equation $x^2\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-y=0$. Which of the following is a solution to this differential equation for $x>0$? $e^x$ $x^2$ $1/x$ $\ln x$
Consider the differential equation $x^2\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-y=0$. Which of the following is a solution to this differential equation for $x>0$?$e^x$$x^2$$1/...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Differential Equations
gate2014-ee-2
derivatives
equations
+
–
0
votes
0
answers
92
GATE Electrical 2014 Set 2 | Question: 3
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to $-\infty$ $0$ $1$ $\infty$
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to$-\infty$$0$$1$$\infty$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-2
calculus
maxima-minima
+
–
0
votes
0
answers
93
GATE Electrical 2014 Set 2 | Question: 4
All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ are purely imaginary. real and non-negative on the unit circle. equal in real and imaginary parts.
All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ arepurely imaginary.real and non-negativeon the unit circle.equal in real and imaginary part...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Complex Variables
gate2014-ee-2
complex-variables
complex-functions
+
–
0
votes
0
answers
94
GATE Electrical 2014 Set 1 | Question: 46
A system matrix is given as follows. $A=\begin{bmatrix} 0 & 1 & -1\\ -6 & -11 &6 \\ -6& -11& 5 \end{bmatrix}$ The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
A system matrix is given as follows.$A=\begin{bmatrix} 0 & 1 & -1\\ -6 & -11 &6 \\ -6& -11& 5 \end{bmatrix}$The absolute value of the ratio of the maximum eigenvalue to t...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Linear Algebra
gate2014-ee-1
linear-algebra
matrices
eigen-values
numerical-answers
+
–
1
votes
0
answers
95
GATE Electrical 2014 Set 1 | Question: 27
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is $2^{-n}$ $0$ $^{n}C_{n-3}2^{-n}$ $2^{-n+3}$
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is$2^{-n}$$0$$^{n}C_{n-3}2^{-n}$$2^{-n+3}$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2014-ee-1
probability-and-statistics
probability
coins
+
–
0
votes
0
answers
96
GATE Electrical 2014 Set 1 | Question: 28
The line integral of function $F = yzi$, in the counterclockwise direction, along the circle $x^2+y^2 = 1$ at $z = 1$ is $-2\pi$ $-\pi$ $\pi$ $2\pi$
The line integral of function $F = yzi$, in the counterclockwise direction, along the circle $x^2+y^2 = 1$ at $z = 1$ is$-2\pi$$-\pi$$\pi$$2\pi$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-1
calculus
line-integral
circle-equation
+
–
0
votes
0
answers
97
GATE Electrical 2014 Set 1 | Question: 17
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence ofonl...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-1
calculus
polynomial
routh-hurwitz-array
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–
0
votes
0
answers
98
GATE Electrical 2014 Set 1 | Question: 1
Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its solutions The system has a unique solution for any given $b_1$ and $b_2$ The system will have infinitely many solutions for any given $b_1$ ... exists depends on the given $b_1$ and $b_2$ The system would have no solution for any values of $b_1$ and $b_2$
Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Linear Algebra
gate2014-ee-1
linear-equation
system-of-linear-equations
+
–
0
votes
0
answers
99
GATE Electrical 2014 Set 1 | Question: 2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is $e^{-1}$ $e$ $1-e^{-1}$ $1+e^{-1}$
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is$e^{-1}$$e$$1-e^{-1}$$1+e^{-1}$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-1
calculus
maxima-minima
+
–
0
votes
0
answers
100
GATE Electrical 2014 Set 1 | Question: 3
The solution for the differential equation $\dfrac{d^2x}{dt^2}=-9x,$ with initial conditions $x(0)=1$ and $\dfrac{dx}{dt}\bigg \vert_{t=0}=1$ , is $t^2+t+1 \\$ $\sin 3t+\dfrac{1}{3}\cos3t+\dfrac{2}{3} \\$ $\dfrac{1}{3}\sin3t+\cos 3t \\$ $\cos 3t+t$
The solution for the differential equation $\dfrac{d^2x}{dt^2}=-9x,$ with initial conditions $x(0)=1$ and $\dfrac{dx}{dt}\bigg \vert_{t=0}=1$ , is$t^2+t+1 \\$$\sin 3t+\df...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Differential Equations
gate2014-ee-1
differential-equations
boundary-limits
+
–
0
votes
0
answers
101
GATE Electrical 2014 Set 1 | Question: 5
Let $S$ be the set of points in the complex plane corresponding to the unit circle. $(\text{That is}, S = \{z :\:\: \mid z \mid =1\}).$ Consider the function $f(z)=zz^{\ast}$ where $z^{\ast}$ denotes the complex ... following in the complex plane unit circle horizontal axis line segment from origin to $(1, 0)$ the point $(1, 0)$ the entire horizontal axis
Let $S$ be the set of points in the complex plane corresponding to the unit circle. $(\text{That is}, S = \{z :\:\: \mid z \mid =1\}).$ Consider the function $f(z)=zz^{\a...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Complex Variables
gate2014-ee-1
complex-conjugate
complex-variables
+
–
0
votes
0
answers
102
GATE Electrical 2015 Set 2 | Question: 27
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the ... is TRUE? The coin tosses are independent. $R$ is fair, $S$ is not. $S$ is fair, $R$ is not. The coin tosses are dependent.
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2015-ee-2
probability-and-statistics
probability
+
–
0
votes
0
answers
103
GATE Electrical 2015 Set 2 | Question: 28
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Differential Equations
gate2015-ee-2
differential-equations
numerical-answers
+
–
0
votes
0
answers
104
GATE Electrical 2015 Set 2 | Question: 26
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-2
calculus
volume-integral
numerical-answers
+
–
0
votes
0
answers
105
GATE Electrical 2015 Set 2 | Question: 3
Match the following. ... $P-4; Q-1; R-3; S-2$ $P-4; Q-3; R-1; S-2$ $P-3; Q-4; R-2; S-1$
Match the following.$\begin{array}{|l|l|l|l|} \hline P. & \text{Stokes’s Theorem} & 1. & ∯ D.ds = Q \\ \hline Q. & \text{Gauss’s Theorem} & 2. & \oint f(z) dz =0 \\...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-2
calculus
divergence
+
–
0
votes
0
answers
106
GATE Electrical 2015 Set 2 | Question: 4
The Laplace transform of $f(t)= 2\sqrt{t/\pi}$ is $s^{-3/2}$. The Laplace transform of $g(t)=\sqrt{1/\pi t}$ is. $3s^{-5/2} /2$ $s^{-1/2}$ $s^{1/2}$ $s^{3/2}$
The Laplace transform of $f(t)= 2\sqrt{t/\pi}$ is $s^{-3/2}$. The Laplace transform of $g(t)=\sqrt{1/\pi t}$ is.$3s^{-5/2} /2$$s^{-1/2}$$s^{1/2}$$s^{3/2}$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Transform Theory
gate2015-ee-2
transform-theory
laplace-transform
+
–
0
votes
0
answers
107
GATE Electrical 2015 Set 2 | Question: 1
Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE? If $f(z)$ is differentiable at $z_{0}$, then $g(z)$ and $h(z)$ are also differentiable ... $z_{0}$. If $f(z)$ is differentiable at $z_{0}$, then so are its real and imaginary parts
Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE?If $f(z)$ is differentia...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Complex Variables
gate2015-ee-2
complex-variables
complex-valued-functions
+
–
0
votes
0
answers
108
GATE Electrical 2015 Set 2 | Question: 2
We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equivalent statements. P: There is a unique solution. Q: The equations ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$
We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equiva...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Linear Algebra
gate2015-ee-2
linear-algebra
system-of-linear-equations
eigen-values
+
–
0
votes
0
answers
109
GATE Electrical 2015 Set 1 | Question: 26
The maximum value of "a" such that the matrix $\begin{pmatrix} -3&0&-2 \\ 1&-1&0 \\ 0&a&-2 \end{pmatrix}$ has three linearly independent real eigenvectors is $\dfrac{2}{3\sqrt{3}} \\$ $\dfrac{1}{3\sqrt{3}} \\$ $\dfrac{1+2\sqrt{3}}{3\sqrt{3}} \\$ $\dfrac{1+\sqrt{3}}{3\sqrt{3}}$
The maximum value of "a" such that the matrix $\begin{pmatrix} -3&0&-2 \\ 1&-1&0 \\ 0&a&-2 \end{pmatrix}$ has three linearly independent real eigenvectors is$\dfrac{2}{...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Linear Algebra
gate2015-ee-1
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
0
answers
110
GATE Electrical 2015 Set 1 | Question: 27
A solution of the ordinary differential equation $\dfrac{d^{2}y}{dt^{2}}+5\dfrac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\dfrac{1-3e}{e^{3}}$. The value of $\dfrac{dy}{dt}(0)$ is _______.
A solution of the ordinary differential equation $\dfrac{d^{2}y}{dt^{2}}+5\dfrac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\dfrac{1-3e}{e^{3}}$. The value of $\df...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Differential Equations
gate2015-ee-1
differential-equations
ordinary-differential-equation
numerical-answers
+
–
0
votes
0
answers
111
GATE Electrical 2015 Set 1 | Question: 1
A random variable $X$ has probability density function $f(x)$ as given below: $ f(x)= \begin{cases} a+bx & \text{ for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$ If the expected value $E[x] = 2/3$, then $Pr[x < 0.5]$ is __________.
A random variable $X$ has probability density function $f(x)$ as given below:$ f(x)= \begin{cases} a+bx & \text{ for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$If...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2015-ee-1
probability-and-statistics
probability
random-variable
probability-density-function
expectation
numerical-answers
+
–
0
votes
0
answers
112
GATE Electrical 2015 Set 1 | Question: 2
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE? $f(a) . f(b)=0$ $f(a) . f(b) < 0$ $f(a) . f(b) > 0$ $f(a) / f(b) \leq 0$
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE?$f(a) . f(b)=0$$f(a) . f(b) < 0$$f(a) . ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-1
calculus
continuity
+
–
0
votes
0
answers
113
GATE Electrical 2015 Set 1 | Question: 3
If the sum of the diagonal elements of a $2 \times 2$ matrix is $-6$, then the maximum possible value of determinant of the matrix is ________
If the sum of the diagonal elements of a $2 \times 2$ matrix is $-6$, then the maximum possible value of determinant of the matrix is ________
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-1
linear-algebra
matrices
determinant
numerical-answers
+
–
0
votes
0
answers
114
GATE Electrical 2016 Set 2 | Question: 49
Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ corresponding to distinct eigenvalues $\lambda_{1}$ and $\lambda_{2}$ respectively. Then the ... $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ co...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Linear Algebra
gate2016-ee-2
linear-algebra
eigen-values
eigen-vectors
+
–
0
votes
0
answers
115
GATE Electrical 2016 Set 2 | Question: 33
Let the probability density function of a random variable, $X$, be given as: $f_{x}(x)=\frac{3}{2}e^{-3x}u(x)+ae^{4x}u(-x)$ where u(x) is the unit step function. Then the value of 'a' and prob $\left\{X \leq 0\right\}$, respectively are $2, \frac{1}{2}$ $4, \frac{1}{2}$ $2, \frac{1}{4}$ $4, \frac{1}{4}$
Let the probability density function of a random variable, $X$, be given as:$f_{x}(x)=\frac{3}{2}e^{-3x}u(x)+ae^{4x}u(-x)$where u(x) is the unit step function.Then the va...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Probability & Statistics
gate2016-ee-2
probability-and-statistics
probability
random-variable
probability-density-function
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–
0
votes
0
answers
116
GATE Electrical 2016 Set 2 | Question: 29
The value of the integral $2\int_{-\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to $0$ $0.5$ $1$ $2$
The value of the integral $2\int_{-\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to$0$$0.5$ $1$$2$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-2
calculus
definite-integral
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–
0
votes
0
answers
117
GATE Electrical 2016 Set 2 | Question: 30
Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then the value of $y(1)$ is _________.
Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Differential Equations
gate2016-ee-2
differential-equations
numerical-answers
+
–
0
votes
0
answers
118
GATE Electrical 2016 Set 2 | Question: 32
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ ... with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3\end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix}x\\ y\end{pmatrix}$ such that $a^{2}+b^{2}=1$ where $\begin{pmatrix}...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Linear Algebra
gate2016-ee-2
linear-algebra
matrices
eigen-values
eigen-vectors
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–
0
votes
0
answers
119
GATE Electrical 2016 Set 2 | Question: 9
The value of the line integral $\int_{c}^{} (2xy^{2}dx+2x^{2}y dy+dz)$ along a path joining the origin $(0, 0, 0)$ and the point $(1, 1, 1)$ is $0$ $2$ $4$ $6$
The value of the line integral$\int_{c}^{} (2xy^{2}dx+2x^{2}y dy+dz)$along a path joining the origin $(0, 0, 0)$ and the point $(1, 1, 1)$ is$0$ $2$ $4$ $6$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-2
calculus
line-integral
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–
0
votes
0
answers
120
GATE Electrical 2016 Set 2 | Question: 10
Let $f(x)$ be a real, periodic function satisfying $f(-x)=-f(x)$. The general form of its Fourier series representation would be $f(x)=a_{0}+\sum_{k=1}^{\infty}a_{k}\cos(kx)$ $f(x)=\sum_{k=1}^{\infty}b_{k}\sin(kx)$ $f(x)=a_{0}+\sum_{k=1}^{\infty}a_{2k}\cos(kx)$ $f(x)=\sum_{k=0}^{\infty}a_{2k+1}\sin(2k+1)x$
Let $f(x)$ be a real, periodic function satisfying $f(-x)=-f(x)$. The general form of its Fourier series representation would be$f(x)=a_{0}+\sum_{k=1}^{\infty}a_{k}\cos(k...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-2
calculus
fourier-series
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