DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
End Semester Examination — May 2019
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Course: B. Tech in -Civil Engineering Sem : IV
Subject Name: Numerical Methods in Engineering Subject Code:BTCVE404A
Max Marks: 60 Date:- 22/05/2019 Duration:-3 Hr.
Instructions to the Students:
- Each question carries 12 marks.
- Attempt any five questions of the following.
- Illustrate your answers with neat sketches, diagram etc., wherever necessary.
- If some part or parameter is noticed to be missing, you may appropriately assume it and mention it clearly.
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Q.1 A) Solve the following equations by using Gauss Jordan method 6
2x1+ 4x2 - 6x3=-8
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x1+ 3x2+x3= 10
2x1-4x2-2x3=-12
B) Write the working rule of Gauss Seidel method for the following equations 6
a1x + b1y+c1z=d1
a2x + b2y+c2z=d2
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a3x + b3y+c3z=d3
Q.2 A) If dy/dx = x+y2 and y= 1 at x= 0, find an approximate value of y at x=0.2 6
By Euler’s modified method taking h= 0.1.
B) Using Secant method find the root of the equation x2 + 2x - 0.5 = 0 upto 3 6
decimal places.
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Q.3 A) Find the polynomial f(x) by using Lagrange’s formula and hence find f(3) for 6
| X | 0 | 1 | 2 | 5 |
|---|---|---|---|---|
| f(x) | 2 | 3 | 12 | 147 |
B) A simply supported beam of span L and constant EI supports a concentrated 6
load P at centre of span. Estimate maximum deflection in the beam.
Q.4 A) Evaluate the following integral using Simpson’s 1/3 rule 6
1) ?exdx , ?sin(x) dx
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B) Explain trapezoidal rule and Simpsons 3/8 rule. 6
Q.5 A) Fit a second order polynomial to the data in the table below: 6
| X | 1.0 | 2.0 | 3.0 | 4.0 |
|---|---|---|---|---|
| y | 6.0 | 11.0 | 18.0 | 27.0 |
(B) Calculate mean and standard deviation for the data 6
| X | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| f(x) | 5 | 7 | 10 | 16 | 11 |
Q.6 A) Write the algorithm for Bisection method 6
B) Write the algorithm for Newton Raphson Method 6
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End
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