KERALA UNIVERSITY Class 1 engineering mathematics Question Paper 2022

Practice authentic previous year questions for better exam preparation.

Sample Questions

If $z=\frac{x^{2}+y^{2}}{\sqrt{x+y}}$, prove that $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}=\frac{3 z}{2}$
(a) Find the centre of curvature of the curve $x^{2}+y^{2}=2$ at the point ( 1,1 ).
The matrix $A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 0 & 1 & -1 \\ 0 & 2 & 4\end{array}\right]$ has an eigen value 3 with corresponding eigen vector $X=\left[\begin{array}{c}1 \\ 1 \\ -2\end{array}\right]$ find $A^{7} X$.
Find the eigen values and eigen vectors of the matrix $A=\left[\begin{array}{ccc}-2 & 2 & -3 \\ 2 & 1 & -6 \\ -1 & -2 & 0\end{array}\right]$.
If $u=\frac{y z}{x}, v=\frac{z x}{y}$ and $w=\frac{x y}{z}$, show that $J\left(\frac{u, v, w}{x, y, z}\right)=4$