126. The inverse Laplace transform of the function
     

     F (s) =	1	is given by
     	s(s + 1)

1. 1. f(t) = sin t

   
   
   

   2. f(t) = e^{- t} sint

   
   
   

   3. f(t) = e^{- t}

   
   
   

   4. f(t) = 1 – e^{- t}

   
   
   

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1. View Hint View Answer Discuss in Forum

   L-1		1		=	1	-	1
   		s(s + 1)			s		s + 1

   
   

   L-1		1	-	1		= 1 - e-t
   		s		s + 1

   Correct Option: D

   L-1		1		=	1	-	1
   		s(s + 1)			s		s + 1

   
   

   L-1		1	-	1		= 1 - e-t
   		s		s + 1

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127. The inverse Laplace transform of 1/(s² + s) is

1. 1. 1 + e^t

   
   
   

   2. 1 – e^t

   
   
   

   3. 1 – e^{- t}

   
   
   

   4. 1 + e^{- t}

   
   
   

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1. View Hint View Answer Discuss in Forum

   	1	=	1	=	1	-	1
   	(s2 + s)		s(s + 1)		s		(s + 1)

   Correct Option: C

   	1	=	1	=	1	-	1
   	(s2 + s)		s(s + 1)		s		(s + 1)

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128. Evaluation of ∫⁴₂ x³ dx using a 2-equal-segment trapezoidal rule gives value of _______.

1. 1. 63

   
   
   

   2. 55

   
   
   

   3. 45

   
   
   

   4. 51

   
   
   

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1. View Hint View Answer Discuss in Forum

   Trapezoidal Rule, h = 1
   
   

   =	1	[ (23 + 43) + 4(33) ]
   	2

   
   

   =	1	[ 8 + 64 + 54 ] = 63
   	2

   Correct Option: A

   Trapezoidal Rule, h = 1
   
   

   =	1	[ (23 + 43) + 4(33) ]
   	2

   
   

   =	1	[ 8 + 64 + 54 ] = 63
   	2

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129. P(0, 3), Q(0.5, 4) and R(1, 5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits x = 0 and x = 1 for the curve. The difference between the two results will be

1. 1. 0

   
   
   

   2. 0.25

   
   
   

   3. 0.5

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   By Trapezoidal rule
   
   

   =	0.5	[ (3 + 5) + 2(4) ] = 4
   	2

   
   By Simpson rule
   
   

   =	0.5	[ (3 + 5) + 4(4) ] = 4
   	3

   
   Difference between these two results will be 0.

   Correct Option: A

   
   By Trapezoidal rule
   
   

   =	0.5	[ (3 + 5) + 2(4) ] = 4
   	2

   
   By Simpson rule
   
   

   =	0.5	[ (3 + 5) + 4(4) ] = 4
   	3

   
   Difference between these two results will be 0.

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130. The error in numerically computing the integral ∫^π₀ (sinx + cosx) dx using the trapezoidal rule with three intervals of equal length between 0 and π is _________.

1. 1. 0.1860

   
   
   

   2. 0.1863

   
   
   

   3. 0.18

   
   
   

   4. 0.1163

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   
   = 2
   Error = Exact value – Approx Value
   = 2 – 1.8137 = 0.1863

   Correct Option: B

   
   
   = 2
   Error = Exact value – Approx Value
   = 2 – 1.8137 = 0.1863

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