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

12th Standard 2019 EM

    Reg.No. :
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Business Maths

Use blue pen only
Time : 00:20:00 Hrs
Total Marks : 25

    Part - A

    Answer all the following questions

    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

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