Determinants Te...

If $$f(x)=\begin{vmatrix} 1 & x & x+1\\ 2x & x(x-1) & (x+1)x\\ 3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1)\end{vmatrix}$$ then $$f(100)$$ is equal to?

The value of the determinant $$\left| \begin{matrix} { b }^{ 2 }-ab & b-c & bc-ac \\ ab-{ b }^{ 2 } & a-b & { b }^{ 2 }-ab \\ bc-ac & c-a & ab-{ b }^{ 2 } \end{matrix} \right| $$

Solve 
$$\begin{vmatrix} 1 & bc & a\left( b+c \right)  \\ 1 & ca & b\left( c+a \right)  \\ 1 & ab & c\left( a+b \right)  \end{vmatrix}$$

if $$a>0$$ and discriminant of $${ax}^{2}+{2bx}+{c}$$ is $$-ve$$, then $$\left| \begin{matrix} a & b & ax+b \\ b & c & bx+c \\ ax+b & bx+c & 0 \end{matrix} \right|$$ is

$$\left| \begin{matrix} \sqrt { 13 } +\sqrt { 3 }  & 2\sqrt { 5 }  & \sqrt { 5 }  \\ \sqrt { 15 } +\sqrt { 26 }  & 5 & \sqrt { 10 }  \\ 3+\sqrt { 65 }  & \sqrt { 15 }  & 5 \end{matrix} \right| =$$ 

The value of $$\left| \begin{matrix} 1+w & { w }^{ 2 } & -w \\ 1+{ w }^{ 2 } & w & -{ w }^{ 2 } \\ { w }^{ 2 }+w & w & -{ w }^{ 2 } \end{matrix} \right| $$ is equal to 

If $$\left[ \begin{array}{l}\cos \theta \,\,\,\, - \sin \theta \,\,\,\,\,\,0\\\sin \theta \,\,\,\,\,\,\,\,\cos \theta \,\,\,\,\,\,0\\0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,1\end{array} \right]$$, then $$adjA = $$

If the points $$A(at^{2}_{1},2at_{1}), B(at^{2}_{2},2at_{2})$$ and $$C(\alpha,0)$$ are collinear, then $$t_{1} t_{2}$$ equals

Let $$F(x)=$$$$\left | \left|  \right| \begin{matrix}1  &1+sin\ x  &1+sin\ x+cos\ x \\  2 &3+2\ sin\ x  &4+3\ sin\ x+2\ cos\ x  \\  3&6+3\ sin\ x&10+6\ sin\ x+3\ cos\ x  \end{matrix} \right |$$  then $$F'\ \left ( \dfrac{\pi}{2} \right )$$ is equal to

If $$A = \left[ {\begin{array}{*{20}{c}}a&0&0\\0&a&0\\0&0&a\end{array}} \right]$$ then find the value of $$\left| A \right|\left| {adjA} \right|$$