Determinants Te...

If $$A = \begin{bmatrix}2 & 5\\ 1 & 3\end{bmatrix}$$ then $$adj\ A = ?$$

$$\begin{vmatrix} \cos { { 15 }^{ o } }  & \sin { { 15 }^{ o } }  \\ \sin { { 15 }^{ o } }  & \cos { { 15 }^{ o } }  \end{vmatrix}=$$?

When the determinant $$\begin{vmatrix} \cos { 2x }  & \sin ^{ 2 }{ x }  & \cos { 4x }  \\ \sin ^{ 2 }{ x }  & \cos { 2x }  & \cos ^{ 2 }{ x }  \\ \cos { 4x }  & \cos ^{ 2 }{ x }  & \cos { 2x }  \end{vmatrix}$$ is expanded in powers of $$\sin x$$, then the constant term in that expression is

If the determinant $$\begin{vmatrix} \cos  2x & \sin ^{ 2 } x & \cos  4x \\ \sin ^{ 2 } x & \cos  2x & \cos ^{ 2 } x \\ \cos  4x & \cos ^{ 2 } x & \cos  2x \end{vmatrix}$$ is expanded in powers of $$\sin x$$ then the constant term in the expansion is 

If $$\begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & a+b & c \end{vmatrix}=0$$, then the line $$ax+by+c=0$$ passes through the fixed point whcih is

If A is singular matrix , then adj A is 

There are two values of a which makes determinant $$ \Delta =\left| \begin{matrix} 1\quad  & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \end{matrix} \right| =86 $$ then sum of these number is

If $$ \begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix}=\begin{vmatrix} 6 & -2 \\ 7 & 3 \end{vmatrix}$$ then value of $$ x $$ is

Choose the correct answer from the given alternatives in the following question:
If $$ A = \begin{bmatrix} 2 & -4 \\ 3 & 1  \end{bmatrix} $$, then the adjoint of matrix $$A$$ is 

Choose the correct answer from the given alternatives in the following question:
If $$ A = \begin{bmatrix} 1 & 2 \\ 2 & 1  \end{bmatrix} $$ and $$ A ({\text{adj}} A) = KI $$ , then the value of $$k$$ is