The extremal of functional $\iint_D\left[\left(\frac{\partial z}{\partial x}\right)^2+\left(\frac{\partial z}{\partial y}\right)^2+\left(\frac{\partial^2 z}{\partial x\partial y}\right)^2\right]dxdy$ is
Previous 10 Questions — AMU MCA 2021
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The solution of
$y' = 2px + \tan^{-1}(xp^2)$
(where $p=\dfrac{dy}{dx}$)
is
Topic: AMU MCA 2021
If $\lambda$ is an eigenvalue of a non-singular matrix $A$, then the characteristic root of adj $A$ is
Topic: AMU MCA 2021
If
$U={(x,y)\in\mathbb R^2\mid y=mx}$
and
$W={(x,y)\in\mathbb R^2\mid y=tx,\ t\ne m}$
Then $\dim(U+W)$ is
Topic: AMU MCA 2021
The volume of the solid generated by revolving the region between the y-axis and the curve
$x=2\sqrt{y}, \ 0\le y\le4$…
Topic: AMU MCA 2021
Let the equation of a straight line passing through point $A(\alpha,\beta,\gamma)$ and having direction ratios $l,m,n$ …
Topic: AMU MCA 2021
The polar coordinates of pole are
Topic: AMU MCA 2021
If
$x + y + z = u$
$y + z = uv$
$z = uvw$
then the value of the Jacobian
$\dfrac{\partial(x,y,z)}{\partial(u,v,w)}$
…
Topic: AMU MCA 2021
Let $T : P_2(x) \to P_2(x)$ be a linear transformation on vector space $P_2(x)$ (polynomials of degree $\le 2$ over $\m…
Topic: AMU MCA 2021
Let $f(x,y) = x^3 + y^3$ for all $(x,y) \in \mathbb{R}^2$. Then
Topic: AMU MCA 2021
Find the missing
B : 16 :: D : ?
Topic: AMU MCA 2021
Next 10 Questions — AMU MCA 2021
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The complete solution of
$(p^2+q^2)=qz$
is
Topic: AMU MCA 2021
Which of the following function is continuous at origin?
Topic: AMU MCA 2021
The solution of the differential equation
$ \dfrac{d^2y}{dx^2} - 2\dfrac{dy}{dx} + y = xe^x \sin x $
Topic: AMU MCA 2021
The centre of a rectangular hyperbola lies on the line $y=2x$. If one of the asymptotes is $x+y+c=0$, then the other as…
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The derivative of $f(x,y)=x^2+xy$ at $P_0(1,1)$ in the direction of unit vector
$\vec{u}=\left(\frac{1}{\sqrt{2}}\righ…
Topic: AMU MCA 2021
If $u=f(x-y,y-z,z-x)$, then the value of
$\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u…
Topic: AMU MCA 2021
The continuous function $f:\mathbb{R}\to\mathbb{R}$ defined by
$f(x)=\sqrt{x^2+1}$
is
Topic: AMU MCA 2021
Let $\mathbb{R}^3={(x,y,z)}$ and $W$ be the subspace generated by ${(1,2,-3)}$. Geometrically, $W$ represents
Topic: AMU MCA 2021
Let
$f(x,y)=\begin{cases}
0,& xy\ne0\
1,& xy=0
\end{cases}$
Which is true?
Topic: AMU MCA 2021
Let
$f(x,y)=\begin{cases}
0,& xy\ne0\
1,& xy=0
\end{cases}$
Which is true?
Topic: AMU MCA 2021
