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Hot questions in Engineering Mathematics

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61
GATE Electrical 2017 Set 1 | Question: 17
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{-4}$. The value of $I$ equals _________. (Give the answer up to two decimal places.)
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{-4}$. The value of $I$ equals _________. (Give the answer up to two...
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62
GATE Electrical 2017 Set 2 | Question: 18
Consider a function $f(x, y, z)$ given by $f(x, y, z)=(x^{2}+y^{2}-2z^{2})(y^{2}+z^{2})$ The partial derivative of this function with respect to $x$ at the point, $x=2, y=1$ and $z=3$ is _______.
Consider a function $f(x, y, z)$ given by$f(x, y, z)=(x^{2}+y^{2}-2z^{2})(y^{2}+z^{2})$The partial derivative of this function with respect to $x$ at the point, $x=2, y=1...
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64
GATE Electrical 2017 Set 2 | Question: 20
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
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GATE Electrical 2017 Set 2 | Question: 28
The eigenvalues of the matrix given below are $\begin{bmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & -3 & -4 \end{bmatrix}$ $(0, -1, -3)$ $(0, -2, -3)$ $(0, 2, 3)$ $(0, 1, 3)$
The eigenvalues of the matrix given below are$\begin{bmatrix}0 & 1 & 0\\ 0 & 0 & 1\\ 0 & -3 & -4\end{bmatrix}$$(0, -1, -3)$$(0, -2, -3)$$(0, 2, 3)$$(0, 1, 3)$
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GATE Electrical 2017 Set 2 | Question: 27
The value of the contour integral in the complex plane $\oint \frac{z^{3}-2z+3}{z-2} dz$ along the contour $\mid z \mid =3$, taken counter- clockwise is $-18 \pi i$ $0$ $14 \pi i$ $48 \pi i$
The value of the contour integral in the complex plane $\oint \frac{z^{3}-2z+3}{z-2} dz$ along the contour $\mid z \mid =3$, taken counter- clockwise is$-18 \pi i$$0$$14...
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GATE Electrical 2017 Set 2 | Question: 3
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ ... $\bigtriangledown . \vec{X}=0,\bigtriangledown \times \vec{Y} = 0, \bigtriangledown \times \vec{Z}=0$
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ respectively. Which one of the following choices is true?$\bigtriangl...
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GATE Electrical 2017 Set 1 | Question: 28
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below. The value of $I$ is $\frac{1}{2}i \\ $ $\frac{2}{3}i \\ $ $\frac{3}{4}i \\ $ $\frac{4}{5}i$
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below.The value of $I$ is$\frac{1}{2}i \\ $$\frac{2}{3}i \\ ...
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GATE Electrical 2017 Set 1 | Question: 27
Consider the differential equation $(t^{2}-81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belongs to the interval $(-2, 2)$ $(-10, 10)$ $(-10, 2)$ $(0, 10)$
Consider the differential equation $(t^{2}-81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belong...
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GATE Electrical 2017 Set 1 | Question: 2
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is $-2i$ $-i$ $i$ $2i$
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is$-2i$$-i$$i$$2i$
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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...
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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$$2\pi$
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GATE Electrical 2014 Set 1 | Question: 27
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is $2^{-n}$ $0$ $^{n}C_{n-3}2^{-n}$ $2^{-n+3}$
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is$2^{-n}$$0$$^{n}C_{n-3}2^{-n}$$2^{-n+3}$
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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...
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