Generate KERALA UNIVERSITY Class 1 engineering mathematics Question Paper
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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}\righ...
- Find the eigen values and eigen vectors of the matrix $A=\left[\begin{array}{ccc}-2 & 2 & -3 \\ 2 & 1 & -6 \\ -1 & -2 & 0\end{array}\right]$.
- (b) Find the maximum value of $u=x^{3} y^{2}(1-x-y)$.