BCA 4th Semester
Numerical Method Board Question Paper 2023

Explain absolute and relative error. Find the relative error of number 5.6 if both of its digits are correct.

On what type of equations Newton's methods can be applicable. Justify.

Solve the following equations by using Gauss-Jordan method.
2x+3y+4z=5      3x+4y+5z=6     4x+5y+6z=7

Use the Romberg method to get an improved estimate of the integral from x = 1.8 to x = 3.4 from the data in the table with h = 0.4.

Write a program to compute integral ∫₀^{π/2} √sinx dx Simpson's 1/3 rule.

Using Runge-Kutta method of 4th order solve the following equation taking each step h = 0.1
$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{4x}}{y}$ - xy given y(0) = 3.3 calculate y at x = 0.1 and 0.2.

Solve the given set of linear equations using Dolittle LU decomposition method:
  3x ₁ + 2x ₂ + x ₃ = 10
  2x ₁ + 3x ₂ + 2x ₃ = 14
  3x ₁ + 2x ₂ + 3x ₃ = 14

Define initial value problems and final value problems. Using heun’s method, find value of y when x=0.3 given that $\frac{\mathrm{dy}}{\mathrm{dx}}$ = x + y and y=1 when x=0.

How can x we use Laterpolation techniques (methods) to approximate the value of the root for the functions whose derivative can't be found? Explain. Write a program to solve sin x - 2x + 1 = 0 using Bisection method.