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122
GATE Electrical 2016 Set 2 | Question: 7
A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$
A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are$1, 1, −1$$1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆...
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125
GATE Electrical 2016 Set 1 | GA Question: 5
In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\dfrac{\alpha^{n}+\beta^{n}}{\alpha^{-n}+\beta^{-n}}$ $n^{4}$ $4^{n}$ $2^{2n-1}$ $4^{n-1}$
In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\dfrac{\alpha^{n}+\beta^{n}}{\alpha^{-n}+\beta^{-n}}$$n^{4}$$4...
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129
GATE Electrical 2016 Set 1 | Question: 33
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
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130
GATE Electrical 2016 Set 1 | Question: 9
The value of $\int_{-\infty}^{+\infty} e^{-t} \delta (2t-2){d}t$, where $\delta (t)$ is the Dirac delta function, is $\dfrac{1}{2e} \\$ $\dfrac{2}{e} \\$ $\dfrac{1}{e^{2}} \\$ $\dfrac{1}{2e^{2}}$
The value of $\int_{-\infty}^{+\infty} e^{-t} \delta (2t-2){d}t$, where $\delta (t)$ is the Dirac delta function, is$\dfrac{1}{2e} \\$$\dfrac{2}{e} \\$$\dfrac{1}{e^{2}} \...
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131
GATE Electrical 2016 Set 1 | Question: 1
The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.
The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.
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132
GATE Electrical 2016 Set 1 | Question: 2
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.
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133
GATE Electrical 2016 Set 1 | Question: 4
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation $\dfrac{d^{2}y}{dt^{2}}+2\dfrac{dy}{dt}+y=0$. Then $y(2)$ is $5e^{-1}$ $5e^{-2}$ $7e^{-1}$ $7e^{-2}$
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation$\dfrac{d^{2}y}{dt^{2}}+2\dfrac{dy}{dt}+y=0$. Then $y(2)$ is$5e^{-1}$$...
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