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#### Numerical Methods One Mark Questions

12th Standard EM

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Time : 00:30:00 Hrs
Total Marks : 15
10 x 1 = 10
1. Δ2y0 =

(a)

y−2y+ y0

(b)

y+ 2y− y0

(c)

y2 + 2y1 + y0

(d)

y+ y+ 2y0

2. Δf(x) =

(a)

f(x+ h)

(b)

f(x) − f(x+h)

(c)

f(x + h) − f(x)

(d)

f (x) − f(x−h)

3. ∇ ≡

(a)

1+E

(b)

1 - E

(c)

1− E−1

(d)

1+ E−1

4. ∇ f(a) =

(a)

f (a) + f(a−h)

(b)

f (a) − f(a + h)

(c)

f (a) − f(a − h)

(d)

f (a)

5. 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)

$y(x)=\frac { { x }_{ 1 }-{ x }_{ 0 } }{ { x }_{ 0 }-{ x }_{ 1 } } { y }_{ 0 }+\frac { { x }_{ 1 }-{ x }_{ 0 } }{ { x }_{ 1 }-{ x }_{ 0 } } { y }_{ 1 }$

(c)

$y(x)=\frac { x-{ x }_{ 1 } }{ { x }_{ 0 }-{ x }_{ 1 } } { y }_{ 1 }+\frac { x-{ x }_{ 0 } }{ { x }_{ 1 }-{ x }_{ 0 } } { y }_{ 0 }$

(d)

$y(x)=\frac { { x }_{ 1 }-{ x } }{ { x }_{ 0 }-{ x }_{ 1 } } { y }_{ 1 }+\frac { x-{ x }_{ 0 } }{ { x }_{ 1 }-{ x }_{ 0 } } { y }_{ 0 }$

6. E2.f(x) =

(a)

f(x + h)

(b)

f(x + 2h)

(c)

f(2h)

(d)

f(2x)

7. ∆f(x + 3h)

(a)

f(x + 3h) - f(x + 4h)

(b)

f(x + 4h) - f(x + 3h)

(c)

f(x + h) - f(x)

(d)

f(x + 2h) - f(x + 3h)

8. Δ can be defined as Δf(x) =f(x + h) -f(x) where h is the __________ interval of spacing

(a)

equal

(b)

unequal

(c)

equal & unequal

(d)

equal or unequal

9. If c is a constant, then Δc =

(a)

c.∆

(b)

c.∇

(c)

0

(d)

1

10. Δ(f(x) + g(x)) = ________

(a)

Δf(x) + Δg(x)

(b)

f(x) ± Δg(x)

(c)

f(x) Δ g(x)

(d)

g(x). Δf(x)

11. 5 x 1 = 5
12. E (Δf(x))

13. (1)

Δ . E. f(x)

14. When 5 values are given, the polynomial which fits the data is of degree

15. (2)

parabolic

16. When 3 values are given, the polynomial which fits the data is of

17. (3)

4

18. When k values are given, the polynomial which fits the data is of degree

19. (4)

k - 1

20. When 2 values are given the polynomial which fits the data is

21. (5)

linear