#### important multiple choice questions in state board english medium business maths chapter one

12th Standard EM

Reg.No. :
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Use blue pen only
Time : 00:20:00 Hrs
Total Marks : 25

Part - A

25 x 1 = 25
1. If $\rho (A)$ =r then which of the following is correct?

(a)

all the minors of order r which does not vanish

(b)

A has at least one minor of order r which does not vanish

(c)

A has at least one (r+1) order minor which vanishes

(d)

all (r+1) and higher order minors should not vanish

2. IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

(a)

0

(b)

1

(c)

2

(d)

3

3. If the rank of the matrix  $\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right)$  is 2. Then $\lambda$ is

(a)

1

(b)

2

(c)

3

(d)

only real number

4. The rank of the diagonal matrix$\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right)$

(a)

0

(b)

2

(c)

3

(d)

5

5. if T= $_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right)$ is a transition probability matrix, then the value of x is

(a)

0.2

(b)

0.3

(c)

0.4

(d)

0.7

6. Which of the following is not an elementary transformation?

(a)

${ R }_{ i }\leftrightarrow { R }_{ j }$

(b)

${ R }_{ i }\rightarrow { 2R }_{ i }+{ 2c }_{ j }$

(c)

${ R }_{ i }\rightarrow { 2R }_{ i }-{ 4R }_{ i }$

(d)

${ C }_{ i }\rightarrow { C }_{ i }+{ 5C }_{ j }$

7. if $\rho (A)=\rho (A,B)$ then the system is

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

Consistent

(d)

inconsistent

8. If $\rho (A)=\rho (A,B)$the number of unknowns, then the system is

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

inconsistent

(d)

consistent

9. if $\rho (A)\neq \rho (A,B),$ then the system is

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

inconsistent

(d)

consistent

10. In a transition probability matrix, all the entries are greater than or equal to

(a)

2

(b)

1

(c)

0

(d)

3

11. If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

(a)

$\rho (A)=\rho (A,B)>n$

(b)

$\rho (A)=\rho (A,B)<n$

(c)

$\rho (A)=\rho (A,B)=n$

(d)

none of these

12. The system of equations 4x+6y=5, 6x+9y=7 has

(a)

a unique solution

(b)

no solution

(c)

infinitely many solutions

(d)

none of these

13. For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

(a)

there is only one solution

(b)

there exists infinitely many solutions

(c)

there is no solution

(d)

None of these

14. if $\left| A \right| \neq 0,$ then A is

(a)

non- singular matrix

(b)

singular matrix

(c)

zero matrix

(d)

none of these

15. The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

(a)

4

(b)

0

(c)

-4

(d)

1

16. Cramer’s rule is applicable only to get an unique solution when

(a)

${ \triangle }_{ z }\neq 0$

(b)

${ \triangle }_{ x }\neq 0$

(c)

${ \triangle }_\neq 0$

(d)

${ \triangle }_{ y }\neq 0$

17. if $\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },{ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix};\quad { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}$ then (x,y) is

(a)

$\left( \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } \frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } } \right)$

(b)

$\left( \frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } } \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } \right)$

(c)

$\left( \frac { { \triangle }_{ 1 } }{ { \triangle }_{ 2 } } \frac { { \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right)$

(d)

$\left( \frac { { -\triangle }_{ 1 } }{ { \triangle }_{ 2 } } \frac { {- \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right)$

18. $\left| { A }_{ n\times n } \right|$=3 $\left| adjA \right|$ =243 then the value n is

(a)

4

(b)

5

(c)

6

(d)

7

19. Rank of a null matrix is

(a)

0

(b)

-1

(c)

$\infty$

(d)

1

20. For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

(a)

$\cfrac { 3 }{ 10 }$

(b)

$\cfrac { 10 }{ 3 }$

(c)

3

(d)

10

21. The rank of an n x n matrix each of whose elements is 2 is

(a)

1

(b)

2

(c)

n

(d)

n2

22. The value of $\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right|$

(a)

52

(b)

0

(c)

513

(d)

59

23. If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =

(a)

3

(b)

± 3

(c)

± 6

(d)

6

24. If A is a singular matrix, then Adj A is.

(a)

non-singular

(b)

singular

(c)

symmetric

(d)

not defined

25. If A, B are two n x n non-singular matrices, then

(a)

AB is non-singular

(b)

AB is singular

(c)

(AB)-I = A-1 B-1

(d)

(AB)-1I does not exit