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GATE Mechanical 2014 Set 1 | Question: 3

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Arjun asked Feb 24, 2017
GATE2016-1-3
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as $-x^2 + y^2 + $ constant $x^2 – y^2 +$ constant $x^2 + y^2 +$ constant $-(x^2 + y^2) +$ constant
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as$-x^2 + y^2 + $ const...
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Arjun asked Feb 19, 2017
GATE Mechanical 2014 Set 1 | Question: 27
If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .
If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .
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Arjun asked Feb 19, 2017
GATE Mechanical 2014 Set 1 | Question: 26
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to$0$$\frac{-\p...
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Arjun asked Feb 19, 2017
GATE Mechanical 2014 Set 1 | Question: 2
$\displaystyle{} \lim_{x\rightarrow 0}\dfrac{x- \sin x}{1- \cos x}$ is $0$ $1$ $3$ not defined
$\displaystyle{} \lim_{x\rightarrow 0}\dfrac{x- \sin x}{1- \cos x}$ is$0$$1$$3$not defined
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