Determinants Te...

A= $$\begin{bmatrix}
 b^{2}c^{2}& bc & b+c\\
 c^{2}a^{2}& ca &c+a \\
 a^{2}b^{2}& ab & a+b
\end{bmatrix}$$ then $$\left | A \right |$$ =?

$$\mathrm{y}=\sin \mathrm{x},\ y_{n}=\displaystyle \frac{d^{n}(\sin x)}{dx^{n}}$$
then $$\begin{vmatrix}
y& y_{1} & y_{2}\\
 y_{3}& y_{4} &y_{5} \\
 y_{6}& y_{7} & y_{8}
\end{vmatrix}$$ =?

$${A}=\begin{bmatrix}
-1 & -2 & -2\\
2 & 1 & -2\\
2 & -2 & 1
\end{bmatrix}$$ then $$Adj(A)=$$ 

If $$\Delta $$ = $$\begin{vmatrix} cos\frac{\theta }{2} &1  &1 \\   1&cos\frac{\theta }{2}  &-cos\frac{\theta }{2} \\ -cos\frac{\theta }{2} &1  & -1
\end{vmatrix}$$ the minimum of $$\Delta $$ is $$m_{1}$$ and maximum of $$\Delta $$ is $$m_{2}$$ then $$[m_{1} , m_{2}]$$ is

$$f(x)=$$ $$\begin{vmatrix}
\cos x &x &1 \\
2 \sin x & x^{2} &2x \\
\tan x& x & 1
\end{vmatrix}$$ then $$ \displaystyle \lim _{ x\rightarrow 0 }{ f(x) } =$$

If $$[\mathrm{x}]$$ stands greatest integer $$\leq \mathrm{x}$$ then the value of $$\begin{vmatrix}
\left [ e \right ]& \left [ \pi \right ] &\left [ \pi ^{2}-6 \right ]\\
\left [ \pi \right ] & \pi ^{2}-6 & \left [ e \right ]\\
\left [ \pi ^{2}-6 \right ]&\left [ e \right ] & \left [ \pi \right ]
\end{vmatrix}$$ equals 

If $$\alpha,\ \beta$$ are the roots of  $$\begin{vmatrix}
x & 1 & 2\\
0 & 1& 1\\
1 & x & 2
\end{vmatrix}$$ = 0 then $$\alpha^{n}+\beta^{n}=?$$ 

$$A=\begin{bmatrix}4 &-2&5\end{bmatrix}$$, $$ B=$$ $$\begin{bmatrix}
2\\
0\\
3\end{bmatrix}$$, then $$Adj(BA)=$$ 

The straight lines $$\mathrm{x}+2\mathrm{y}-9=0,3\mathrm{x}+5\mathrm{y}-5=0$$ and $$\mathrm{a}\mathrm{x}+\mathrm{b}\mathrm{y}-1=0$$ are concurrent if the straight line $$22\mathrm{x}-35\mathrm{y}-1=0$$ passes through the point 

If x, y, z are in A.P., then the value of the det A. Where A=$$\begin{vmatrix}
4 &5 & 6 & x\\
5& 6 & 7 &y \\
6& 7& 8 &z \\
x & y & z & 0
\end{vmatrix}$$