## Apply Picard's methods to find the solution of the differential equation :

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With x=0 , y=2 upto the third order of approximations.

## Use Stirling formula to find y28, given

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y20 = 49225, y25 = 48316, y30 = 47236,

y35 = 45926, y40 = 44306

## Solve -

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yn+2 - 2yn+1+yn = n22n

## Given the following pairs of values of x and y :

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 x 5 6 9 11 y 12 13 14 16

Interpolate the value of y at x = 10

## Apply convolution theorem to evaluate .

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${L}^{-1}\left\{\frac{P}{\left({P}^{2}+{a}^{2}\right)\left({P}^{2}+{b}^{2}\right)}\right\}$

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## 5 jobs are to be processed on machines M1 and M2 in the order M1M2, their processing times are given below :

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 Job M1 M2 J1 5 2 J2 1 6 J3 9 7 J4 3 8 J5 10 4

Determine:

1. The Job sequence
2. Total processing time
3. The idle times for M1 and M2

## A simple network is as given below:

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 Activity A B C D E F G H J K L M N Preceding Activity - - A A A C C C B,D F,J E,H,G,K E,H L,M Durations 9 3 8 2 3 2 6 1 4 1 2 3 4

## Determine the optimal sequence oh jobs that minimizes the total elapsed time on machine M1,M2, M3 in the processing order of M1M2M3:

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 Jobs → J1 J2 J3 J4 J5 J6 J7 M1 3 8 7 4 9 8 7 Hours M2 4 3 2 5 1 4 3 Hours M3 6 7 5 11 5 6 12 Hours

## Consider the following data for the activities concerning a project :

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 Name of activity Pre - operations Duration (days) A - 2 B A 3 C A 4 D B,C 6 E - 2 F E 8

1. Draw a network diagram for the above project.
2. Find the minimum time for completion of the project.
3. Describe the critical path.
4. Find Float

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Subject to

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Subject to

## Find the all basic solution for the equation.

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Show that the basic solution are non-degenerate.