#### Numerical Methods Book Back Questions

12th Standard EM

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. Δ2y0 =

(a)

y−2y+ y0

(b)

y+ 2y− y0

(c)

y2 + 2y1 + y0

(d)

y+ y+ 2y0

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

(a)

f(2x)

(b)

f(x+ h)

(c)

f (x)

(d)

Δf(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. 3 x 2 = 6
7. 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.

8. If f(x) = x+ 3x than show that Δf(x) = 2x + 4

9. Following are the population of a district

 Year (x) 1881 1891 1901 1911 1921 1931 Population (y) Thousands 363 391 421 - 467 501
10. 3 x 3 = 9
11. Evaluate ${ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right)$ by taking ‘1’ as the interval of differencing.

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

13. Estimate the production for 1964 and 1966 from the following data

 Year 1961 1962 1963 1964 1965 1966 1967 Production 200 220 260 - 350 - 430
14. 2 x 5 = 10
15. 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

16. Using appropriate interpolation formula find the number of students whose weight
is between 60 and 70 from the data given below