BSc Sem IV 2022 2023 Mar 2023 MATHEMATICS III Question Paper - Mumbai University | munotes

Questions asked in this paper

• (ii) Figures to the right indicate marks

1. Q1 A) Attempt any ONE question from the following. 8 marks
   • i) Define the terms i) Error ii) Absolute error iii) Relative error iv) Percentage Errors
   • ii) Derive Secant method. Find roots of X*- X — 10 = 0 correct to 2 decimal places
   • B) Attempt any TWO questions from the following. 12
   • i) Given f(x) = 2X -5 = O find root lies between 2 and 3 using Newton-Raphson method
   • ii) Solve by Fixed Point method X? + X? - 100=0
   • iii) Find the absolute error and relative error and also determine the number of significant digits in the approximations of the True value of x= 2.71828182 and Approximate value of x=2.7182
2. Q2 A) Attempt any ONE question from the following. 8 marks
   • i) Derive Simpson’s 3/8th rule. Write difference between Trapezoidal,
   • B) Attempt any TWO questions from the following. 12
   • ii) Fit a second degree equation for the given data
   • iii) Evaluate integral using Trapezoidal rule J, logx dx for n =6
3. Q3 A) Attempt any ONE question from the following. 8 marks
   • ii) Derive LU decomposition method. Hence solve system of equations + = 1,
   • B) Attempt any TWO questions from the following. il) Solve by Jacobi’s iteration method 3x + 20y -z=-18, ili) Use Gauss - Seidel method to solve x +4y -2 = 6, x vcD MATHEMATICS III MARKS 75 2 HRS 30 MIN 4, Attempt any THREE question from the following. (15) 12
   • i) Use method of Re yula Fa si to find the real root between
   • ii) Using Secant m 0, roots lies between
   • iii) Evaluate the in son’s 1/3 Rule where n=4
   • iv) Find the correct to 3 decimal places, using Newton-Rap! ies between and 2
   • v) Solve usit ‘
   • vi) 18, 2x+20y-72=

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