131. Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

1. 1. linear

   
   
   

   2. parabolic

   
   
   

   3. logarithmic

   
   
   

   4. hyperbolic

   
   
   

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1. View Hint View Answer Discuss in Forum

   Trapezoidal rule gives best result when function is linear in nature.

   Correct Option: A

   Trapezoidal rule gives best result when function is linear in nature.

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132. The values of function f(x) at 5 discrete points are given below:
     
     Using Trapezoidal rule step size of 0.1, the value of ∫^0.4₀ f (x) dx is

1. 1. 11

   
   
   

   2. 21

   
   
   

   3. 33

   
   
   

   4. 22

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   =	h	[ (y0 + y4) + 2(y1 + y2 + y3) ]
   	2

   
   

   =	0.1	[ (0 + 160) + 2(10 + 40 + 90) ] = 22
   	2

   Correct Option: D

   
   

   =	h	[ (y0 + y4) + 2(y1 + y2 + y3) ]
   	2

   
   

   =	0.1	[ (0 + 160) + 2(10 + 40 + 90) ] = 22
   	2

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133. Using a unit step size, the volume of integral ∫²₁ xlnxdx by trapezoidal rule is ______

1. 1. 0.693

   
   
   

   2. 0.669

   
   
   

   3. 0.653

   
   
   

   4. 0.623

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   ∴ I =	h	[ y0 + yn ]
   	2

   
   

   I =	1	[ 0 + 2 In 2 ]
   	2

   
   = In 2 = 0.693

   Correct Option: A

   
   

   ∴ I =	h	[ y0 + yn ]
   	2

   
   

   I =	1	[ 0 + 2 In 2 ]
   	2

   
   = In 2 = 0.693

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134. If x is the mean of data 3, x, 2 and 4, then the mode is

1. 1. 6

   
   
   

   2. 5

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   3, x, 2 and 4
   

   Mean, x =	3 + x + 2 + 4
   	4

   
   ⇒ 4x = 9 + x
   ⇒ 3x = 9 x = 3
   So, 3, 3, 2 and 4
   Mode = 3

   Correct Option: C

   3, x, 2 and 4
   

   Mean, x =	3 + x + 2 + 4
   	4

   
   ⇒ 4x = 9 + x
   ⇒ 3x = 9 x = 3
   So, 3, 3, 2 and 4
   Mode = 3

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135. Let X₁ and X₂ be two independent exponentially distributed random variables with means 0.5 and 0.25 respectively. Then Y = min (X₁, X₂) is

1. 1. exponentially distributed with mean 1/6

   
   
   

   2. exponentially distributed with mean 2

   
   
   

   3. normally distributed with mean 3/4

   
   
   

   4. normally distributed with mean 1/6

   
   
   

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1. View Hint View Answer Discuss in Forum

   Mean (X₁) = 0.5
   

   	1	= 0.5
   	λ1

   
   

   λ1 =	1	= 2
   	0.5

   
   Mean (X₂) = 0.25
   

   	1	= 0.25 ⇒ λ2 = 4
   	λ2

   
   y= mean (X₁, X₂)
   

   Mean (y) =	1	=	1	=	1
   	y1 + y2		2 + 4		6

   Correct Option: A

   Mean (X₁) = 0.5
   

   	1	= 0.5
   	λ1

   
   

   λ1 =	1	= 2
   	0.5

   
   Mean (X₂) = 0.25
   

   	1	= 0.25 ⇒ λ2 = 4
   	λ2

   
   y= mean (X₁, X₂)
   

   Mean (y) =	1	=	1	=	1
   	y1 + y2		2 + 4		6

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