Question - 2

The value of the determinant

\(\left| \begin{matrix} x+1 & x+2 & x+4 \\ x+3 & x+5 & x+8 \\ x+7 & x+10 & x+14 \end{matrix} \right| \) is

Question - 3

If \(a\neq b\neq c\),one value of x which satisfies the equation

\(\left| \begin{matrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x-c & 0 \end{matrix} \right| =0\) is given by

Question - 4

If x,y,z are all different and

\(\left| \begin{matrix} x & { x }^{ 2 } & 1+{ x }^{ 3 } \\ y & y^{ 2 } & 1+{ y }^{ 3 } \\ z & { z }^{ 2 } & 1+z^{ 3 } \end{matrix} \right| =0\) then value of xyz is

Question - 5

If a,b,c>0 then the value o the determinant

\(\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right| \) is

Question - 6

The value of the determinant, where \(a\neq b\neq c\),

\(\left| \begin{matrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{matrix} \right| \) is

Question - 7

If 1,\(\omega \),\({ \omega }^{ 2 }\) are cube roots of unity, the value of the determinant

\(\left| \begin{matrix} 1 & \omega & { \omega }^{ 2 } \\ \omega & { \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & \omega \end{matrix} \right| \) is

Question - 8

Let \(p{ \lambda }^{ 4 }+p{ \lambda }^{ 2 }+r{ \lambda }^{ 2 }+s{ \lambda }+t\)

\(=\left| \begin{matrix} { \lambda }^{ 2 }-3\lambda & \lambda -1 & \lambda +3 \\ \lambda +1 & -2\lambda & \lambda -4 \\ \lambda -3 & \lambda +4 & 3\lambda \end{matrix} \right| \)
be identity if \(\lambda \),where p,q,r,s,t are constants.The value of t is

Question - 9

The determinants
\(\left| \begin{matrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{matrix} \right| \) and \(\left| \begin{matrix} 1 & a & a^{ 2 } \\ 1 & b & { b }^{ 2 } \\ 1 & c & { c }^{ 2 } \end{matrix} \right| \) are

Question - 10

Let \({ \triangle }_{ 1 }=\left| \begin{matrix} a & b & c \\ c & a & b \\ b & c & a \end{matrix} \right| \quad and \quad{ \triangle }_{ 2 }=\left| \begin{matrix} b+c & c+a & a+b \\ a+b & b+c & c+a \\ c+a & a+b & b+c \end{matrix} \right| \)