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#### Numerical Methods Model Questions

12th Standard EM

Reg.No. :
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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