Let the equation of a straight line passing through point $A(\alpha,\beta,\gamma)$ and having direction ratios $l,m,n$ be $\dfrac{x-\alpha}{l}=\dfrac{y-\beta}{m}=\dfrac{z-\gamma}{n}=r$ Suppose $P$ is any arbitrary point on this line with coordinates $(\alpha+lr,\beta+mr,\gamma+nr)$. Geometrically, $r$ is
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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
$\dfrac{\partial(x,y,z)}{\partial(u,v,w)}$
…
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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…
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Let $f(x,y) = x^3 + y^3$ for all $(x,y) \in \mathbb{R}^2$. Then
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Find the missing
B : 16 :: D : ?
Topic: AMU MCA 2021
Find the missing sequence
1, 1, 2, 3, ____, 8, 13
Topic: AMU MCA 2021
Find the missing (?)
$\frac{1}{2} : 2 :: \frac{x}{7} : ?$
Topic: AMU MCA 2021
Select the pair that has the same relationship as the original pairEast : Orient
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The empirical relationship between mean, median and mode is
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Find the missing sequence:25, 49, 121, 169, _____
Topic: AMU MCA 2021
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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
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
If $\lambda$ is an eigenvalue of a non-singular matrix $A$, then the characteristic root of adj $A$ is
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The solution of
$y' = 2px + \tan^{-1}(xp^2)$
(where $p=\dfrac{dy}{dx}$)
is
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The extremal of functional
$\iint_D\left[\left(\frac{\partial z}{\partial x}\right)^2+\left(\frac{\partial z}{\partial…
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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?
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The solution of the differential equation
$ \dfrac{d^2y}{dx^2} - 2\dfrac{dy}{dx} + y = xe^x \sin x $
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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…
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