First Mid Term Model Questions

12th Standard EM

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. The rank of m×n matrix whose elements are unity is

    (a)

    0

    (b)

    1

    (c)

    m

    (d)

    n

  2. 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

  3. \(\sqrt { { e }^{ x } } \) dx is

    (a)

    \(\sqrt { { e }^{ x } } +c\)

    (b)

    \(2\sqrt { { e }^{ x } } \) + c

    (c)

    \(\frac12\sqrt { { e }^{ x } } +c\)

    (d)

    \(\frac { 1 }{ 2\sqrt { { e }^{ x } } } +c\)

  4. The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

    (a)

    40

    (b)

    \(\frac{41}{2}\)

    (c)

    \(\frac{40}{3}\)

    (d)

    \(\frac{41}{5}\)

  5. If MR = 15 - 8x, then the revenue function is 

    (a)

    15x-4x2+k

    (b)

    \(\frac{15}{x}-8\)

    (c)

    -8

    (d)

    15x-8

  6. 5 x 1 = 5
  7. If \(\rho (A,B)\neq \rho (A)\) then the system is

  8. (1)

    inconsistent

  9. \(\int _{ 0 }^{ 1 }{ { e }^{ -t } } dt\quad \)

  10. (2)

    2x+5ex+k

  11. Cost function

  12. (3)

    ഽmc dx+k

  13. ഽ(2+5ex)dx

  14. (4)

    \(\int _{ 0 }^{ N }{ { Pe }^{ rt }dt } \)

  15. Amount of annuity after N payments

  16. (5)

    proper definite integer

    5 x 2 = 10
  17. Solve the following system of equations by rank method
    x+y+z=9,2x+5y+7z=52,2x−y−z =0

  18. Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)

  19. Integrate the following with respect to x.
    \(\frac { { x }^{ 3 } }{ x+2 } \)

  20. Evaluate \(\int { \frac { 2+3cosx }{ { sin }^{ 2 }x } } dx\)

  21. Find the revenue function and the demand function if the marginal revenue for x units is MR= 10 + 3x − x2.

  22. 5 x 3 = 15
  23. Find the rank of the matrix \(\left( \begin{matrix} 0 & -1 & 5 \\ 2 & 4 & -6 \\ 1 & 1 & 5 \end{matrix} \right) \)
     

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

  25. Evaluate ഽ\(\frac { dx }{ { 4x }^{ 2 }-1 } \)

  26. Using integration find the area of the region bounded between the line x = 4 and the parabola y2 = 16x.

  27. Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x)=\(\frac{x}{3000}+2.50\)

  28. 3 x 5 = 15
  29. Solve by Cramer’s rule x+y+z=4,2x−y+3z=1,3x+2y−z = 1

  30. The marginal revenue function (in thousand of rupees ) of a commodity is 10 + e−0.05x Where x is the number of units sold. Find the total revenue from the sale of 100 units (e−5 = 0.0067)

  31. Find the area of the region bounded by the parabola y2 = 4x and the line 2x - Y = 4.

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