Numerical Methods Model Questions

12th Standard EM

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    10 x 1 = 10
  1. Δf(x) =

    (a)

    f(x+ h)

    (b)

    f(x) − f(x+h)

    (c)

    f(x + h) − f(x)

    (d)

    f (x) − f(x−h)

  2. If m and n are positive integers then ΔmΔnf(x) =

    (a)

    Δm+nf (x)

    (b)

    Δmf(x)

    (c)

    Δnf (x)

    (d)

    Δm-nf (x)

  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. Lagrange’s interpolation formula can be used for

    (a)

    equal intervals only

    (b)

    unequal intervals only

    (c)

    both equal and unequal intervals

    (d)

    none of these.

  5. If f (x)=x+ 2x + 2 and the interval of differencing is unity then Δf (x)

    (a)

    2x −3

    (b)

    2x +3

    (c)

    x + 3

    (d)

    x − 3

  6. E2.f(x) =

    (a)

    f(x + h)

    (b)

    f(x + 2h)

    (c)

    f(2h)

    (d)

    f(2x)

  7. If c is a constant, then Δc.f(x)

    (a)

    0

    (b)

    c.f(Δx)

    (c)

    c.Δf(x)

    (d)

    f(Δcx)

  8. Δ[f{x) . g(x)] = __________

    (a)

    Δf(x). Δg(x)

    (b)

    f(x) . Δg(x) + g(x) .Δf(x)

    (c)

    f(x) . Δg(x)

    (d)

    f(Δx) . g(Δx)

  9. E-nf(x) is

    (a)

    F(x + nh)

    (b)

    F(x - nh)

    (c)

    F(-nh)

    (d)

    f(x - n)

  10. (1 + Δ) (1 - ∇) is

    (a)

    0

    (b)

    1

    (c)

    -1

    (d)

    (1 - ∇ . Δ)

  11. 5 x 2 = 10
  12. Evaluate ∆(log ax).

  13. If y = x− x+ x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

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

  15. If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.

  16. Find the second order backward differences of f(x).

  17. 5 x 3 = 15
  18. Construct a forward difference table for y = f(x) = x3+2x+1 for x = 1,2,3,4,5

  19. Evaluate \(\Delta \)\(\left[ \frac { 5x+12 }{ { x }^{ 2 }+5x+6 } \right] \) by taking ‘1’ as the interval of differencing.

  20. Given U0 = 1, U1 = 11, U2 = 21, U3 = 28 and U4 = 29 find Δ2U0

  21. Find y when x = 0.2 given that

    x 0 1 2 3 4
    y 176 185 194 202 212
  22. If y75 = 2459, y50 = 2018, y85 = 1180, and y90 =402, find y82

    x 75 80 85 90
    y 2459 2018 1180 402
  23. 3 x 5 = 15
  24. 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

  25. 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
  26. 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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