Question

Write the degree of the differential equation : $\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-2{\frac{d^{2}y}{d x^{2}}}-{\frac{d y}{d x}}+1=0.$

Write the number of vectors of unit length perpendicular to both the vector $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{2i}+\stackrel{\wedge}{j}+\stackrel{\wedge}{2k}$ and ${\vec{b}}={\hat{j}}+{\hat{k}}\,.$

If A' = $\left(\begin{array}{l l }3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l l }-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right)$ then find A' – B'.

Find ‘λ’ when the projection of $\stackrel{\rightarrow}{a}\$ = $λ\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ on $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ is 4 units.

Find : $\int{\frac{3\,x}{3\,x-1}}\,d x$

Find the projection of vector $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} +2\stackrel{\wedge}{k}$ on the vector $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$

Write the value of the determinant $\begin{vmatrix}p & p+1 \\ p-1 & p\end{vmatrix}$