STUPIDSID
Solve any one question from Q.1 & Q.2
1
Determine the maximum relative error for the function \( F=3x^{2}y^{2}+5y^{2}z^{2}-7x^{2}z^{2}+38\ \ \text{For}\ x=y=z=1 \ \ \text{and}\ \ \Delta x=-0.05, \Delta y=0.001 \ \ \text{and} \ \ \Delta z=0.02.\)/
6 M
2
Find real root of cos(x) -3(x)+5 =0. Correct to four decimal places using the False Position method.
6 M
Solve any one question from Q.3 & Q.4
3
Solve the following equations by Thomas Algortihm. \[\begin{align*}& 3x_{1}-x_{2}=5\\
&2x_{1}-3x_{2}+2x_{3}=5\\
&x_{2}+2x_{3}+5x_{4}=10\\
&x_{3}x_{4}=1\end{align*}\]
6 M
4
Draw a flow chart for Gauss-Seidal Method.
6 M
Solve any one question from Q.5 & Q.6(a,b)
5
Two nproducts A and B are to be manufactured by a firm. Each of these product has to be processed on two machines M1 and M2. Product A requires 4 hours on machine M1 and 5 hours on machine M2. Product B requires 5 hours on machine M1 and 2 hours on machine M2. The available capacity per month is 100 hours and 80hour for machine M1 and M2 respectively. The profit per unit is Rs.10 and Rs.5 on product A and B resespectively. Estimate the number of units of each type to be produced per month for maximum profit by simplex Method.
8 M
6(a)
\( \begin{align*} &\text{Minimize}Z = 80x_{1}+120x_{2}\\
&\text{Subject to}\ x_{1}+x_{2}\leq 9\\
&x_{1}\geq 2\\
&x_{2}\geq 3\\
&20x_{1}+50x_{2}\leq 300\\
&x_{1},x_{2}\geq 0\end{align*}
\)/
(Use graphical method)
(Use graphical method)
6 M
6(b)
Explain following terms used in graphical method of optimization.
i) Constraints ii) Optimal solution
i) Constraints ii) Optimal solution
2 M
Solve any one question from Q.7(a,b) & Q.8(a,b)
7(a)
From the given table find the value of x for y (x) = 0.390
| x | 20 | 25 | 30 | 35 |
| f(x) | 0.342 | 0.423 | 0.5 | 0.65 |
8 M
7(b)
Fit the curve pvy=k to the following data:
| p(kg/cm2) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| v(litres) | 1620 | 1000 | 750 | 620 | 520 | 460 |
5 M
8(a)
For the following data claculate difference and obtain forward difference polynamials. Interpolate at x = 0.25 and x = 0.35
| x | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 |
| y=f(x) | 1.4 | 1.56 | 1.76 | 2.0 | 2.28 |
5 M
8(b)
Fit a parabola \( y=ax^{2}+bx+c \)/ in least square to the data.
| x | 10 | 12 | 15 | 23 | 20 |
| y | 14 | 17 | 23 | 25 | 21 |
5 M
Solve any one question from Q.9(a,b) & Q.10(a,b)
9(a)
Evaluate \( \int_{2}^{6}\log _{10}xdx \)/ by using trapezoidal rule, taking n = 8, correct to five decimal places.
8 M
9(b)
Explain Simpon's 1/3 rule graphically and drive formula for integration of a function.
8 M
10(a)
Explain what is meant by Simpson's strip for 1/3rd and 3/8th rule. Explain why Simpson's 3/8th rule give more accuracy compared to Trapezoidal and Simpson's 1/3rd rule with same number of strips.
8 M
10(b)
Solve the Trapezoidal rule \(\int_{0}^{1}\int_{0}^{1}x^{2}y^{2}.dx.dy \)/ Taking step length in x and y as 0.25.
8 M
Solve any one question from Q.11(a,b) & Q.12(a,b)
11(a)
Draw flowchart for modified Euler's method.
8 M
11(b)
Solve the Laplace equation \( \frac{\partial ^{2}T}{\partial x^{2}}+\frac{\partial ^{2}T}{\partial y^{2}}=0\)/ for the square mesh as shown in diagram below.
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10 M
12(a)
Draw the flowchart for solving the Laplace equation.
8 M
12(b)
Use Runge-Kutta method of fourth order to obtain the numercial solution of \( \frac{dy}{dx}=\sqrt{\left ( x^{2}+y \right )},\)/ Find y at x = 0.4 given y(0) = 1, take h = 0.2.
10 M
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