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#### Numerical Methods Two Marks Question

12th Standard EM

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Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Evaluate ∆(log ax).

2. 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.

3. Evaluate Δ$\left[ \frac { 1 }{ (x+1)(x+2) } \right]$ by taking ‘1’ as the interval of differencing

4. Using graphic method, find the value of y when x = 48 from the following data:

 x 40 50 60 70 y 6.2 7.2 9.1 12
5. Using Newton’s forward interpolation formula find the cubic polynomial.

 x 0 1 2 3 f(x) 1 2 1 10
6. In an examination the number of candidates who secured marks between certain interval were as follows

 Marks 0-19 20-39 40-59 60-79 80-99 No.of.candidates 41 62 65 50 17
7. The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy

 P 40 50 60 70 80 90 T 180 204 226 250 276 304

Find the melting point of the alloy containing 84 percent lead.

8. Using interpolation estimate the output of a factory in 1986 from the following data

 Year 1974 1978 1982 1990 Output in 1000 tones 25 60 80 170
9. Use Lagrange’s formula and estimate from the following data the number of workers
getting income not exceeding Rs. 26 per month

 Income not exceeding (Rs) 15 25 30 35 No. of workers 36 40 45 48
10. Prove that
(1 + Δ)(1 - ∇) = 1

11. Find f(0.5) if f(−1) = 202, f (0)= 175, f(1) = 82 and f(2) = 55

12. Prove that
∇Δ = Δ -  ∇

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

14. When h = 1, find Δ (x3).

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