Question

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

Find the maximum value of $\begin{vmatrix}1 & 1 & 1 \\ 1 & 1+sinθ & 1 \\ 1 & 1 & 1+cosθ\end{vmatrix}$

If ${\left[\begin{array}{l l}{x y}&{4}\\ {z+6}&{x+y}\end{array}\right]}\ ={\left[\begin{array}{l l}{8}&{w}\\ {0}&{6}\end{array}\right]},$ write the value of x + y + z.

Write the sum of the order and degree of the differential equation. $\begin{array}{r l}{\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}+\left({\frac{d y}{d x}}\right)^{3}+x^{4}\,}&{{}=0.}\end{array}$

If A is square matrix of order 2 and $|a d j A|=9,$ , find | A |.

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are unit vectors, then what is the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$, so that ${\sqrt{2}}$ $\stackrel{\rightarrow}{a}\$ -$\stackrel{\rightarrow}{b}\$ is a unit vector ?

Find the solution of the differential equation ${\frac{d y}{d x}}=x^{3}e^{-2y}$.