Determinants Te...

If $$a_{1}, a_{2}, ...., a_{n}$$, ..... are in G.P. then $$\begin{vmatrix}\log a_{n} & \log a_{n + 1} & \log a_{n + 2}\\ \log a_{n + 3} & \log a_{n + 4} & \log a_{n + 5}\\ \log a_{n + 6} & \log a_{n + 7} & \log a_{n + 8}\end{vmatrix}$$ is

The coefficient of $${x}^{2}$$ in the expansion of the determinant
$$\begin{vmatrix} { x }^{ 2 } & { x }^{ 3 }+1 & { x }^{ 5 }+2 \\ { x }^{ 3 }+3 & { x }^{ 2 }+x & { x }^{ 3 }+{ x }^{ 4 } \\ x+4 & { x }^{ 3 }+{ x }^{ 4 } & { 2 }^{ 3 } \end{vmatrix}$$ is

The value of $$x$$ satisfying the equation $$\begin{vmatrix}\cos 2x & \sin 2x & \sin 2x\\ \sin 2x & \cos 2x & \sin 2x\\ \sin 2x & \sin 2x & \cos 2x\end{vmatrix} = 0$$ and $$x\epsilon \left [0, \dfrac {\pi}{4}\right ]$$ is

If the determinant $$\begin{vmatrix} a+p & 1+x & u+f \\ b+q & m+y & v+g \\ c+r & n+z & w+h \end{vmatrix}$$ splits into exactly K determinants of order 3, each element of which contains only one term, then the value of K is

 Points (a, 0), (0, b) and (1, 1)are collinear, if:

If planes $$x-cy-bz=0, cx-y+az=0$$ and $$bx+ay-z=0$$ pass through a straight line then $${ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=$$

The value of the determinant $$\begin{vmatrix} b^2-ab & b-c & bc-ac \\ ab -a^2 & a-b & b^2-ab \\ bc-ac & c-a & ab -a^2 \end{vmatrix}$$ =

If  $$B$$ is a square matrix of order 4 such that $$ |B|= 24$$ ,then the value of $$|adj B|$$ is equal to

If $$A$$ is $$3*3$$ show symmetric matrix then $$|A| = ?: - $$

$$\begin{vmatrix} a^2
+2a & 2 a + 1 & 1 \\ 2a+1 & a+2 & 1 \\ 3 & 3 & 1
\end{vmatrix} =$$