Page 238 - Engineering Mathematics Workbook_Final

Laplace Transforms

(a) 0, 2 respectively s + 1
2
(a)
(b) 2, 0 respectively s + 3

(c) 0, 1 respectively 1
(b)
(d) 2/5, 0 respectively s + 3

[GATE-1995-EC] (c) s + 2 1 + s + 2
2
 (s + 3 )(s + ) 2 s + 1
( ) =
L
51. If  f t then the value
s +  2 (d) None of these
2
of lim f ( ) .............t =
t→  [GATE-2000-EC]

(a) can not be determined 54. A delayed unit step function is
 0, for t  a

−
(b) zero defined as ( u t a = )  1, for t  a .


(c) unity Its Laplace transform is

(d) infinite [GATE-1998-EC] (a) a e − as (b) e − as

 3s + 1  s
52. Given L  − 1   . If e as e as
  s + 4s + (K − ) 3 s  (c) s (d) a
3
2
lim f ( ) 1t = , then the value of K is   
t→    
55. The integral    t −    6sin ( ) t dt
−  6 
(a) 1 (b) 2
evaluates to

(c) 3 (d) 4 (a) 6 (b) 3

[GATE-2010-EE] (c) 1.5 (d) 0

s + 2 [GATE-10 (IN)]
( ) =
L
53. If  f t ,
s + 1 56. Given two continuous time signal
2
t −
( ) e=
x ( ) t = e and y t − 2t which
s + 1
2
( ) =
L g t exists for t > 0 then the convolution
(s + 3 )(s + ) 2
z(t) = x(t) * y(t) is
( ) ( g t T dT−
h ( ) t =  t f T ) then t − − 2t − 2t
0 (a) e − e (b) e
L{h(t)} is ….. t − t − −
(c) e (d) e + e 3t

[GATE-2011]

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