frequently asked questions in +2 state board english medium business maths first chapter

12th Standard 2019 EM

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Business Maths

Don't use colour pens other than blue

Time : 01:30:00 Hrs
Total Marks : 75

    Part - A

    Answer all the following questions

    10 x 1 = 10
  1. If A=(1 2 3), then the rank of AAT is

    (a)

    0

    (b)

    2

    (c)

    3

    (d)

    1

  2. The rank of m×n matrix whose elements are unity is

    (a)

    0

    (b)

    1

    (c)

    m

    (d)

    n

  3. The rank of the unit matrix of order n is

    (a)

    n −1

    (b)

    n

    (c)

    n +1

    (d)

    n2

  4. Rank of a null matrix is

    (a)

    0

    (b)

    -1

    (c)

    \(\infty \)

    (d)

    1

  5. 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

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

    (a)

    1

    (b)

    2

    (c)

    n

    (d)

    n2

  7. 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

  8. 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

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

    (a)

    non-singular

    (b)

    singular

    (c)

    symmetric

    (d)

    not defined

  10. 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

  11. Part - B

    Answer all the following questions

    5 x 1 = 5
  12. A row having at least one non-zero element is

  13. (1)

    inconsistent

  14. For the system of equations AX = B, the solution is X = A-1 B provided

  15. (2)

    infinitely many solutions

  16. If \(\rho (A,B)=\rho (A)<n\) then the system has

  17. (3)

    non-zero row

  18. If \(\rho (A,B)=\rho (A)=n\) then the system has

  19. (4)

    unique solution

  20. If \(\rho (A,B)\neq \rho (A)\) then the system is

  21. (5)

    \(|A|\neq 0\)

    Part - C

    Answer all the following questions

    5 x 2 = 10
  22. The system of non-homogeneous equations will have.
    (a) unique solution
    (b) Infinitely many solutions
    (c) No solution
    (d) Trivial solution

  23. Rank of a 2 x 2 matrix may be
    (a) 0
    (b)1
    (c) 2
    (d)3

  24. The transition probabilities Pjk satisfy
    (a) \({ P }_{ \mu }>0\)
    (b) \(\sum _{ k }^{ 1 }{ { P }_{ jk } } =1\)
    (c) \({ P }_{ jk }\le 0\)
    (d) \({ P }_{ jk }>1\)

  25. Which is one correct?
    (a) \({ R }_{ 1 }\rightarrow { R }_{ 1 }+{ R }_{ 2 }\)
    (b) \({ C }_{ 1 }\rightarrow { C }_{ 1 }-{ 2C }_{ 2 }\)
    (c) \({ R }_{ 3 }\leftrightarrow { R }_{ 1 }\)
    (d) \({ R }_{ 1 }\leftrightarrow { C }_{ 1 }\)

  26. If IAI = 0, then
    (a) A is a singular matrix
    (b) System has either no solution or infinitely many solutions
    (c) No solution
    (d) non-singular matrix

  27. Part - C

    Answer all the following questions

    5 x 1 = 5
  28. If \(A=\left[ \begin{matrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{matrix} \right] \) then the value of |adj A| is

    ()

    a6

  29. If A is a square matrix of order n, then |Adj A|=______

    ()

    |A|n-1

  30. The system of equation x + y + z = 2,3x-y+2z= 6 and 3x+y-z=-18 has________solution

    ()

    unique

  31. The system of linear equations x + y + Z = 2, 2x + Y - z = 3, 3x + 2y + kz = 4 has a unique solution if k is_______

    ()

    Not equal to 0

  32. The value on for which the system of equations
    x + y + z = 5, x + 2y + 3z = 9, \(x+3y+\lambda z=\mu \) is

    ()

    \(\lambda \neq 5\)

  33. Part - D

    Answer all the following questions

    5 x 2 = 10
  34. Show that the equations5x+3y+7z=4,3x+26y+2z=9,7x+2y+10z =5 are consistent and solve them by rank method.

  35. For what values of the parameterl , will the following equations fail to have unique
    solution: 3x−y+lz=1,2x+y+z=2,x+2y−lz = −1 by rank method.

  36. Show that the equations x +y + Z = 6, x.+ 2y + 3z = 14 and x + 4y + 7z = 30 are consistent

  37. For what value of x, the matrix
    \(A=\left| \begin{matrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ x & 2 & -3 \end{matrix} \right| \) is singular?

  38. If \(\left( \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} \right) \left( \begin{matrix} x \\ y \\ z \end{matrix} \right) =\left( \begin{matrix} 1 \\ -1 \\ 0 \end{matrix} \right) \) find x.y- and z

  39. Part - E

    Answer all the following questions

    5 x 3 = 15
  40. Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)

  41. Find the rank of the matrix \(\left( \begin{matrix} 5 & 3 & 0 \\ 1 & 2 & -4 \\ -2 & -4 & 8 \end{matrix} \right) \)

  42. Findtherankofthematrix \(A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right) \)

  43. Show that the equations x- 3y + 4z = 3, 2x - 5y + 7z = 6, 3x - 8y + 11z = 1 are inconsistent

  44. Solve: 2x + 3y = 5, 6x + 5y= 11

  45. Part - F

    Answer all the following questions

    4 x 5 = 20
  46. The following table represents the number of shares of two companies A and B
    during the month of January and February and it also gives the amount in rupees invested
    by Ravi during these two months for the purchase of shares of two companies. Find the
    the price per share of A and B purchased during both the months
     

    Months Number of Shares of
    the company
    Amount invested by Ravi
    (in Rs)
    A B
    January 10 5 125
    February 9 12 150

     

  47. The total cost of 11 pencils and 3 erasers is Rs 64 and the total cost of 8 pencils and
    3 erasers is Rs 49. Find the cost of each pencil and each eraser by Cramer’s rule.

  48. The price of 3 Business Mathematics books, 2 Accountancy books and one
    Commerce book is Rs840. The price of 2 Business Mathematics books, one Accountancy
    book and one Commerce book is Rs 570. The price of one Business Mathematics book, one
    Accountancy book and 2 Commerce books is Rs 630. Find the cost of each book by using
    Cramer’s rule.

  49. A mixture is to be made of three foods A, B, C. The three foods A, B, C contain nutrients p, Q, R as shown below
     

    Ounces per pound of Nutrient
    Food P Q R
    A 1 2 5
    B 3 1 1
    C 4 2 1

    How to form a mixture which will have 8 ounces of P, 5 ounces of Q and 7 ounces of R? (Cramer's rule).

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