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BCA Semester 2 – Mathematics II – Unit 6: Computational Method (10Hrs)

Comprehensive questions and detailed answers for Unit 6: Computational Method (10Hrs). Perfect for exam preparation and concept clarity.

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Solve the following system by Gauss-Seidel method:

$-4x + y - z = -8$

$3x + 6y + 2z = 1$

$x - y + 3z = 2$

MediumNumerical5 marks2022(TU FOHSS Final)

Using simplex method, find the optimal solution of

Z = 7x_1 + 5x_2

subject to

x_1 + 2x_2 \le 6

4x_1 + 3x_2 \le 6

x_1 \ge 0,\; x_2 \ge 0

HardNumerical10 marks2022(TU FOHSS Final)

Using Simpson’s $\tfrac{1}{3}$ rule, evaluate

\int_0^1 \frac{1}{1+x}\,dx

with 3 points of intervals.
Find the error of approximation.
How many points are to be considered to make the approximation value within $10^{-5}$ ?

HardNumerical10 marks2022(TU FOHSS Final)

Evaluate

\int_0^2 \sqrt{1+x^3}\,dx

by using Simpson’s $\tfrac{1}{3}$ rule, taking $n=4$ .

MediumNumerical5 marks2023(TU FOHSS Final)

Define $\text{pivot element}$ , $\text{pivot column}$ , and $\text{consistency }$ in a system of equations.
Using the simplex method, maximize

\quad F = 5x - 3y

subject to

3x + 2y \le 6

-x + 3y \ge -4

x \ge 0,\; y \ge 0

HardNumerical10 marks2023(TU FOHSS Final)

Compute the approximate value of the integral

\int_1^2 \frac{1}{1+x^2}\,dx

by using the $\textbf{composite trapezoidal rule}$ with three points, and compare the result with the actual value.
Determine the $\textbf{error formula}$ and numerically verify an $\textbf{upper bound}$ on it.

HardNumerical10 marks2023(TU FOHSS Final)

Using the trapezoidal rule, compute $\int_0^2 (2x^2 - 1)\,dx$ with 4 intervals.
Find the absolute error of approximation from its actual value.

MediumNumerical5 marks2024(TU FOHSS Final)

Using Newton-Raphson method, find a root of $x^3 - x - 4 = 0$ between 1 and 2 correct to three decimal places.

MediumNumerical5 marks2024(TU FOHSS Final)

Using the simplex method, find the optimal solution of the following linear programming problem.
Maximize

$z = 15x + 12y$

Subject to

2x + 3y \le 21

3x + 2y \le 24

x \ge 0,\; y \ge 0

HardNumerical10 marks2024(TU FOHSS Final)

Examine the consistency of the system. Solve it by using Gauss elimination method.

\begin{cases} 3x + y + z = 5 \\ 3x - 4y + z = -2 \\ 3x + y - 3z = -1 \end{cases}

MediumTHEORY5 marks2024(TU FOHSS Final)

Using simplex method, find the optimal solution of the following linear programming problem. Minimize $Z = 10x + 15y$ Subject to

\begin{cases} x + y \ge 8 \\ 5x + 3y \ge 30 \\ x \ge 0,\; y \ge 0 \end{cases}

MediumTHEORY5 marks2024(TU FOHSS Final)

a) Use Simpson's $\frac{1}{3}$ Rule to evaluate

\int_{0}^{1} \frac{1}{1+x^2}\,dx

taking $n=4$ . Also find the error.
b) A man who has $130$ m of fencing material wishes to enclose a rectangular garden.
Find the maximum area he can enclose.

MediumTHEORY10 marks2024(TU FOHSS Final)

Compute the approximate value of the integral

\int \frac{1}{1+x^2}\,dx

by using the composite trapezoidal rule with three points, and compare the result with the actual value.
Determine the error formula and numerically verify an upper bound on it.

MediumTHEORY10 marks2024(TU FOHSS Final)

Showing 13 questions

Sample Questions

Solve the following system by Gauss–Seidel method: \[ -4x + y - z = -8 \] \[ 3x + 6y + 2z = 1 \] \[ x - y + 3z = 2 \]

Marks: 5Chapter: Unit 6: Computational Method (10Hrs)

Using simplex method, find the optimal solution of \[ Z = 7x1 + 5x2 \] subject to \[ x1 + 2x2 \le 6 \] \[ 4x1 + 3x2 \le 6 \] \[ x1 \ge 0,\; x2 \ge 0 \]

Marks: 10Chapter: Unit 6: Computational Method (10Hrs)

Using Simpson’s $ \tfrac{1}{3} $ rule, evaluate \[ \int0^1 \frac{1}{1+x}\,dx \] with 3 points of intervals. Find the error of approximation. How many points are to be considered to make the ap

Marks: 10Chapter: Unit 6: Computational Method (10Hrs)

Evaluate \[ \int0^2 \sqrt{1+x^3}\,dx \] by using Simpson’s $ \tfrac{1}{3} $ rule, taking $ n=4 $.

Marks: 5Chapter: Unit 6: Computational Method (10Hrs)

Define $$\text{pivot element}$$, $$\text{pivot column}$$, and $$\text{consistency }$$in a system of equations. Using the simplex method, maximize \[ \quad F = 5x - 3y \] subject to \[ 3x + 2y \l

Marks: 10Chapter: Unit 6: Computational Method (10Hrs)

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BCA Semester 2 – Mathematics II – Unit 6: Computational Method (10Hrs)

Sample Questions

Solve the following system by Gauss–Seidel method: \[ -4x + y - z = -8 \] \[ 3x + 6y + 2z = 1 \] \[ x - y + 3z = 2 \]

Using simplex method, find the optimal solution of \[ Z = 7x1 + 5x2 \] subject to \[ x1 + 2x2 \le 6 \] \[ 4x1 + 3x2 \le 6 \] \[ x1 \ge 0,\; x2 \ge 0 \]

Using Simpson’s \( \tfrac{1}{3} \) rule, evaluate \[ \int0^1 \frac{1}{1+x}\,dx \] with 3 points of intervals. Find the error of approximation. How many points are to be considered to make the ap

Evaluate \[ \int0^2 \sqrt{1+x^3}\,dx \] by using Simpson’s \( \tfrac{1}{3} \) rule, taking \( n=4 \).

Define $$\text{pivot element}$$, $$\text{pivot column}$$, and $$\text{consistency }$$in a system of equations. Using the simplex method, maximize \[ \quad F = 5x - 3y \] subject to \[ 3x + 2y \l