Question

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

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ , write the value of x.

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.

Give an example of a skew symmetric matrix of order 3.

Write the value of x - y + z from following equation. $\left(\begin{array}{l }x+y+z \\ x+z \\ y+z\end{array}\right)$ = $\left(\begin{array}{l }9 \\ 5 \\ 7\end{array}\right)$

If A is a 3 × 3 matrix, whose elements are given by $a_{i j}={\frac{1}{3}}|-3i+j\,|$ , then write the value of $a_{23}$.

If x ∈ N and $\begin{vmatrix}x+3 & -2 \\ -3x & 2x\end{vmatrix}$ = 8, then find the value of x.