Numerical Method 2019 year Question paper solution (BCA Fourth Semester) TU

2019 BCA Fourth SEMESTER

Subject: Numerical Method

1. Which one of the following can causes a blunders in system?

• Human imperfection
• Numerical Methods
• Computing Methods
• Measuring Methods

2. Which one of the following be possible solution of system of linear equation with equations 2x-y = 5    and  3x-3/2y=4 ?

• Unique Solution
• No solution
• Infinite Solution
• Iii-condition

3. In which method improved rood x1 is calculated as x0-f(x0)/f’(x0)?

• Bisection Method
• Secant Method
• Newton-Raphson Method
• False Point Method

4. Which one of the following is not an open end method (extrapolation method) of solving non linear equattions?

• Bisection Method
• Newton -Raphson Method
• Secant Method
• Fixed Point Method

5. Which one of the following is an iteration method of solving the system of linear equations?

• Gauss-jardon Method
• Matrix inverse Method
• Trangular Factorization Method
• Gauss-seidel Method

6. Which of the following is a cubic splines with zero second derivatives at the end points?

• Quadratic Splines
• Natural cubic Splines
• Semi-cubic Splines
• No Splines

7. Which one of the following is correct value of Romberg estimate R(0,0) for 1∫2 1/x dx ?

• 70
• 85
• 75
• 80

8. Which one of the following is an Elliptic Equation?

• Laplace Equation
• Crank Nicolson Method
• Bender-Schmid Equation
• Newton-Gregory Method

9. Which one of the following method is similar to two stage Runge Kutta Method?

• Tayler Series Method
• Euler’s Method
• Picard’s Method
• Heun’s Method

10. Which one of the following is the correct value off eigen values for 8×1 – 4×2 = ʵx1 and 2×1 – 2×2 = ʵx2?

• 4,5
• 6,4
• 8,2
• 4,2

Group B

2. why is the study of errors important to a computational scientist ? Differentiate between inherent and numerical errors.
3. Find the root of equation x^{2 –} 4x – 10 = 0 using bisection method where root lies between 5 and 6.
4. Find the square root of 3.5 using second order Larange interpolation polynomial using the following data table.

5. Write a program to calculate the integral using Trapezoidal Rules?
6. solve the following set of equation using Gauss-Jardon Method

3x-5y+ 2z = 15

4x – y + z = 2

X – 3y + 7z = 22

7. Use classical Runge -Kutta Method to estimate (0.2) when y’(x) = x² + y²  with y(0) = 0 and h = 0.2
8. solve the poisson equation over the square domain 0 ≤ x≤ 3 and 0≤ y≤ 3 with f = 0

GROUP C

9. a) Factroize the matrix

1   2   3

2   8   22                                Using Cholesky’s Method

22   8  2

(b) Locate the root of equation x² + x – 2 = 0 using the fixed point method?

10 (a) Fit a straight line to the following set of data points.

(b)Differentiate between ordinary and partial differential equations with their applications

11. Given the data points:

Estimate the function value f at x = 2-5  using cubic splines

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