12th Standard cbse -- Maths - Determinants

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Question - 1

If \(\begin{vmatrix} 2x & -1 \\ 4 & 2 \end{vmatrix}=\begin{vmatrix} 3 & 0 \\ 2 & 1 \end{vmatrix}\) then x is

  • A 3
  • B \(\frac { 2 }{ 3 } \)
  • C \(\frac { 3 }{ 2 } \)
  • D \(-\frac { 1 }{ 4 } \)

Question - 2

The value \(\left| \begin{matrix} 6 & 0 & -1 \\ 2 & 1 & 4 \\ 1 & 1 & 3 \end{matrix} \right| \) is

  • A -7
  • B 7
  • C 8
  • D 10

Question - 3

Let Δ = \(\left| \begin{matrix} { Ax }^{ 2 } & x^{ 3 } & 1 \\ { By }^{ 2 } & { y }^{ 3 } & 1 \\ { Cz }^{ 2 } & { z }^{ 3 } & 1 \end{matrix} \right| \) and \({ \triangle }_{ 1 }=\left| \begin{matrix} Ax & By & Cz \\ { x }^{ 2 } & { y }^{ 2 } & { z }^{ 2 } \\ yz & zx & xy \end{matrix} \right| \), then

  • A Δ + Δ1 = 0
  • B Δ ≠ Δ1
  • C Δ = xΔ1
  • D Δ - Δ1 = 0

Question - 4

Let A be a square matrix of order 2 × 2, then |KA| is equal to

  • A K|A|
  • B K²|A|
  • C K3|A|
  • D 2K|A|

Question - 5

Let f(x) = \(\left| \begin{matrix} cos \ x & 2 \ sin \ x & sin \ x \\ x & x & x \\ 1 & 2x & x \end{matrix} \right| \), then \(\lim _{ x\rightarrow 0 }{ \frac { f(x) }{ { x }^{ 2 } } } \) is equal to

  • A 0
  • B -1
  • C 2
  • D 3

Question - 6

Let x, yeR, then the determinant \(\triangle =\) \(\left| \begin{matrix} cosx & -sinx & 1 \\ sinx & cosx & 1 \\ cos(x+y) & -sin(x+y) & 0 \end{matrix} \right| \), lies in the interval

  • A \([-\sqrt { 2 } ,\sqrt { 2 } ]\)
  • B [-1, 1]
  • C \([-\sqrt { 2 } ,1]\)
  • D \([-1,\sqrt { 2 } ]\)

Question - 7

If \(\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] \) and Aij is cofactor of aij, then the value of Δ is given by

  • A a11A31 + a12A32 + a13A33
  • B a11A11 + a12A21 + a13A31
  • C a21A11 + a22A12 + a23A13
  • D a11A11 + a21A21 + a31A31

Question - 8

A and B are invertible matrices of the same order such that |(AB)-1| = 8, If |A| = 2, then |B| is

  • A 16
  • B 4
  • C 6
  • D \(\frac{1}{16}\)

Question - 9

\(\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix}=\begin{vmatrix} 6 & 2 \\ 18 & 6 \end{vmatrix}\) , then x is equal to

  • A 6
  • B 土6
  • C -6
  • D 0

Question - 10

Let A be a square matrix of order 3 × 3, then |kA| is equal to

  • A k|A|
  • B k2 |A|
  • C k3 |A|
  • D 3k |A|
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