#### Matrices And Determinants One Mark Questions

11th Standard

Reg.No. :
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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)

(b)

(c)

(d)

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