Old Exam Papers June 2012 (Set 2)

fuEufyf[kr dks ifjHkkf"kr dhft;s %
(i) o.kZekyk,¡
(ii) 'kCn
(iii) Hkk"kk
(iv) O;kdj.k
l q l q l q
0 1 0 1 2 2 0
(b) If , , S s , s , s , Y s , s is initial
state and f is transition function, where :
b g b g
b 0g b 1g
b 0g b 1g
f s , 0 s , f s , 1 s ,
0 0 0 1
f s , s , f s , s ,
1 0 1 2
f s , s , f s , s ,
2 0 2 2
then draw the transition diagram for :
n s
FSA, A , S, Y , s , f
0
l q l q l q
0 1 0 1 2 2 0
;fn , , S s , s , s , Y s , s izkjfEHkd
voLFkk rFkk f laØe.k Qyu gS] tgk¡ %
b g b g
b 0g b 1g
b 0g b 1g
f s , 0 s , f s , 1 s ,
0 0 0 1
f s , s , f s , s ,
1 0 1 2
f s , s , f s , s ,
2 0 2 2
600 4 MT-01
(b) Find generating function of a 3r 2, r 0 .
a 3r 2, r 0 dk tud Qyu Kkr dhft;sA
r
7. (a) Find numeric function for generating function :
G x
bg
1
10 7x
x
fuEu tud Qyu ds fy, la[;kad Qyu Kkr dhft;s %
G x
bg
1
10 7x
x
(b) Prove that numeric function (sequence) (1, 2, 3,....,
r+1, ....), r 0 satisfies recurrence relation :
a 2a a r 2
r r 1 r2
;
fl) dhft;s fd la[;kad Qyu ¼vuqØe½ (1, 2, 3,....,
r+1, ....), r 0 , iqujko`fÙk lEcU/k %
a 2a a r 2
r r 1 r2
;
dks lUrq"V djrk gSA
8. (a) Solve following recurrence relation :
a a a , r 0, a 0, a 1
r r1 r 2
0 1
MT-01 7 PTO
2
2
r