Matrices And Determinants One Mark Questions

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 25
    10 x 1 = 10
  1. The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is

    (a)

    0, -1

    (b)

    0, 1

    (c)

    -1, 1

    (d)

    -1, -1

  2. The value of \(\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}\) is

    (a)

    xyz

    (b)

    x+y+z

    (c)

    2x+2y+2z

    (d)

    0

  3. The co-factor of -7 in the determinant \(\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}\) is

    (a)

    -18

    (b)

    18

    (c)

    -7

    (d)

    7

  4. If \(\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}\) then \(\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}\) is

    (a)

    \(\triangle\)

    (b)

    -\(\triangle\)

    (c)

    3\(\triangle\)

    (d)

    -3\(\triangle\)

  5. The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is

    (a)

    abc

    (b)

    0

    (c)

    a2b2c2

    (d)

    -abc

  6. If A is a square matrix of order 3, then |kA| is

    (a)

    k|A|

    (b)

    -k|A|

    (c)

    k3|A|

    (d)

    -k3|A|

  7. adj (AB) is equal to

    (a)

    adj A adj B

    (b)

    adj AT adj BT

    (c)

    adj B adj A

    (d)

    adj BT adj AT

  8. The inverse matrix of \(\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}\) is

    (a)

    \({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

    (b)

    \({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 1 }{ 5 } \end{pmatrix}\)

    (c)

    \({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

    (d)

    \({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

  9. If A = \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)such that ad - bc \(\neq\) 0 then A-1 is

    (a)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & b \\-c & a\end{pmatrix}\)

    (b)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & b \\c & a\end{pmatrix}\)

    (c)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\-c & a\end{pmatrix}\)

    (d)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\c & a\end{pmatrix}\)

  10. The number of Hawkins-Simon conditions for the viability of an input - output analysis is

    (a)

    1

    (b)

    3

    (c)

    4

    (d)

    2

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