Old Exam Papers June 2012 (Set 2)

(b) Evaluate :
2 5
O
eku Kkr dhft;s %
2 5
O
2. State and prove Newton-Gregory backward interpolation
formula.
U;wVu&xzsxksjh i'p vUrosZ'ku lw= fyf[k;s rFkk fl) dhft;sA
3. (a) Using Newton's divided difference formula, find
f xbg at x 2 from the following table :
x f (x)
0 8
1 68
8 123
fuEu lkj.kh ls U;wVu foHkkftr vUrj lw= }kjk x 2
ij f xbg dk eku Kkr dhft;s %
x f (x)
0 8
600 2 MT-06
dy
dx
y
2 where y = 2 when x = 1
x
¼h = .05 ysrs gq,] x = 1.10 ij½
vk;yj fof/k }kjk fuEu vody lehdj.k dks y ds fy, gy
dhft;s %
dy
dx
y
2 tgk¡ y = 2 tc x = 1
x
¼h = .05 ysrs gq,] x = 1.10 ij½
9. (a) If
2
a t i tj b2 t 1gk
and b 2ti
j tk
then find the value of d
dt a.b
b g.
b g rFkk b ti j tk
2 ;fn a t i tj 2t 1
k 2
gks rks d
dt a.b
b g dk eku Kkr dhft;sA
2
(b) If F x yi 2xzj 2 yzk , then find curl F at the
point (1, 1, 1).
2 ;fn F x yi 2xzj 2yzk gks rks fcUnq (1, 1, 1)
ij curl F dk eku Kkr dhft;sA
MT-06 7 PTO