Generate KERALA UNIVERSITY Class 1 engineering mathematics i Question Paper

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Sample Questions

Find the radius of curvature at the point $(1,1)$ on the curve $y=x^{3}$.
If $z=\frac{x^{2}+y^{2}}{\sqrt{x+y}}$, prove that $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}=\frac{3 z}{2}$
If $u=\frac{y z}{x}, v=\frac{z x}{y}$ and $w=\frac{x y}{z}$, show that $J\left(\frac{u, v, w}{x, y, z}\right)=4$
The position vector of a particle moving in space is given by $\vec{r}(t)=4 \cos \pi t \vec{i}+4 \sin \pi t \vec{j}+t \vec{k}$. Find the instantaneous velocity, speed and acceleration at $t=1$
Find the orthogonal trajectories of the parabolas $y^{2}=4 a x$