### Mathematics - Determinants & Matrices

#### Question - 1

The value of the determinant

$\left| \begin{matrix} 43 & 1 & 6 \\ 35 & 7 & 4 \\ 17 & 3 & 2 \end{matrix} \right|$ is

• A 0
• B 10
• C 15
• D none of these

#### 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

• A -2
• B x2+2
• C 2
• D none of these

#### 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

• A x=a
• B x=b
• C x=c
• D x=0

#### 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

• A -1
• B 0
• C 1
• D 2

#### 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

• A always positive
• B always negative
• C always zero
• D none of these

#### 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

• A -1
• B 2
• C 1
• D 0

#### 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

• A 0
• B $\omega$
• C ${ \omega }^{ 2 }$
• D 1

#### 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

• A 0
• B 1
• C ${ \lambda }^{ 2 }$
• D none of these

#### 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

• A (a) equal
• B equal in magnitude but opposite in sign
• C reciprocal of each other
• D  none of these

#### Question - 10

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

• A ${ \triangle }_{ 1 }={ \triangle }_{ 2 }$
• B ${ \triangle }_{ 1 }={2 \triangle }_{ 2 }$
• C ${ \triangle }_{ 2 }={ 2\triangle }_{ 1 }$
• D none of these