# ECE - Questions and solutions set-19

Electronics and communication Engineering Questions and solutions set-19
Question:-
Option (A)
r = (2d2/l)
Option (B)
r = (2d/l)
Option (C)
r = (d/l)
Option (D)
r = (2d/l2)
Correct Option:
A
Question:-
Option (A)
e2t cos 3t + e2t sin 3t
Option (B)
e2t cos 3t + 2/Ö3 sin 3t
Option (C)
e2t cos 3t + 2/3 sin 3t
Option (D)
e2t cos 3t + (2/3)e2t sin 3t
Correct Option:
D
Question Solution:
L-1 (f(s)) = L-1 {(s-2)+2/(s-2)2+32} = L-1 {(s-2)/(s-2)2+32} + 2/3 L-1 {3/(s-2)2+32}
= e2t cos 3t + 2/3 e2t sin 3t
Hence (D)
Question:-
Option (A)
-Ak
Option (B)
Ak
Option (C)
-Ak-1
Option (D)
Ak-1
Correct Option:
B
Question Solution:
By Cayley Hamilton’s theorem (Matrix A will satisfy its characteristic equations)
I + A + A2 + A3 + .....+ Ak = 0
Þ (Ak+1-I)/(A-I) = 0
Or, Ak+1-I = 0
Or, A,-1, Ak+1 = A-1I,
Þ A-1 = Ak
Question:-
Option (A)
8, 16
Option (B)
10, 12
Option (C)
9 , 15
Option (D)
8, 14
Correct Option:
B
Question:-
Option (A)
D = 0 , C = 0
Option (B)
D ¹ 0 , C = 0
Option (C)
D = 0 , C ¹ 0
Option (D)
D ¹ 0 , C ¹ 0
Correct Option:
D
Question:-
Option (A)