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12th Business Maths - Numerical Methods Model Question Paper Question Bank Software Nov-27 , 2019

Numerical Methods

12th Business Maths - Numerical Methods Model Question Paper

Numerical Methods Model Question Paper

12th Standard

    Reg.No. :
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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5

  1. If ‘n’ is a positive integer Δn[ Δ-n​ ​​​​​​f(x)] _______.

    (a)

    f(2x)

    (b)

    f(x+ h)

    (c)

    f (x)

    (d)

    Δf(x)

  2. E f (x)= _______.

    (a)

    f(x− h)

    (b)

    f (x)

    (c)

    f(x+ h)

    (d)

    f(x+ 2h)

  3. ∇ f(a) = _______.

    (a)

    f (a) + f(a−h)

    (b)

    f (a) − f(a + h)

    (c)

    f (a) − f(a − h)

    (d)

    f (a)

  4. For the given points (x0, y0) and (x1, y1) the Lagrange’s formula is _______.

    (a)

    \(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

    (b)

    \(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

    (c)

    \(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

    (d)

    \(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

  5. If c is a constant, then Δc = ______________

    (a)

    c.∆

    (b)

    c.∇

    (c)

    0

    (d)

    1

    6. 5 x 2 = 10

  6. If h = 1 then prove that (E−1Δ)x3 = 3x2 − 3x + 1.

  7. Using Newton’s forward interpolation formula find the cubic polynomial.

    x 0 1 2 3
    f(x) 1 2 1 10

  8. Find f(2.8) from the following table.

    x 0 1 2 3
    f(x) 1 2 11 34

  9. If u0 = 560, u1 = 556, u2 = 520, u4 = 385, show that u3 = 465

  10. When h = 1, find Δ (x3).

    11. 5 x 3 = 15

  11. By constructing a difference table and using the second order differences as constant, find the sixth term of the series 8,12,19,29,42…

  12. Prove that f(4) = f(3) + Δf(2) + Δ2 f(1) + Δ3 f(1) taking ‘1’ as the interval of differencing.

  13. Using graphic method, find the value of y when x=27.

    x 10 15 20 25 30
    y 35 32 29 26 23

  14. Find the number of men getting wages between Rs. 30 and Rs. 35 from the following table.

    Wages (x) 20 - 30 30 - 40 40 - 50 50 - 60
    No. of men (y) 9 30 35 42

  15. Using Lagrange's formula and y(x) from the following table.

    x 6 7 10 12
    y 13 14 15 17
    16. 4 x 5 = 20

  16. The values of y = f(x) for x = 0,1,2, ...,6 are given by

    x 0 1 2 3 4 5 6
    y 2 4 10 16 20 24 38

    Estimate the value of y (3.2) using forward interpolation formula by choosing the four values that will give the best approximation.

  17. The population of a certain town is as follows

    Year : x 1941 1951 1961 1971 1981 1991
    Population in lakhs:y 20 24 29 36 46 51

    Using appropriate interpolation formula, estimate the population during the period 1946.

  18. From the following table, estimate the premium for a policy maturing at the age of 58.

    Age (x) 40 45 50 55 60
    Premium (y) 114.84 96.16 83.32 74.48 68.48

  19. Using Lagrange's formula find the value of y when x = 4 from the following table.

    x 0 3 5 6 8
    y 276 460 414 343 110

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