Amity MCA 2nd semester solve assignment for Numerical & Statistical Computations

Dissertation Work

Body:

Assignment A

Find the negative root of the equation x3 – 21x + 3500 = 0 correct to two decimal places by Newton Raphson Method.

Solve the following set of linear equations by Gauss Seidal method

1.2x + 2.1y + 4.2z = 9.9

5.3x + 6.1y + 4.7z = 21.6

9.2x + 8.3y + z = 15.2

Define Interpolation with the help of suitable example. Derive the relation between divided differences and ordinary differences.

Integrate the function x³ + 2x +1 with respect to x from 0 to 1 by using Trapezoidal. Divide the interval into eight equal intervals.

Fit a straight line trend by the method of least square to the following data.

Year	1991	1992	1993	1994	1995
Production	240	255	225	260	280

Estimate the likely product for the year 2000.

1. Newton-Raphson method
2. Bisection method
3. 1. SymmetricNone Solve the following differential equation by using RungaKutta fourth order method to find out y(1). y’ = x2 – y2 Given that y(0) = 1, h =0.5
    1. Findf’ (3) and f” (3) from the following table using Newton’s forward formula.
    x 3 3.2 3.4 3.6 3.8 4.0
    
    y -14 -10.032 -5.296 0.256 6.672 14
    
    8.Discuss the three available methods (Bi-Section, Regula Falsi and Newton Raphson Method) and explain the merits and demerits of each method.Assignment B 1. Compare and contrast Trapezoidal, Simpson’s 1/3 and Simpson’s 3/8 rule of integration.
    
    2.Find the value of f(x) at 3.1 and 3.9 for the following data by using the appropriate formula. x 3 3.2 3.4 3.6 3.8 4.0 y -14 -10.032 -5.296 0.256 6.672 14
    
    3.Define Interpolation. Prove that E-?=1, where E is the shift operator. (b)?4y0=y4-4y3+6y2-4y1+y0 Assignment C 1.Which one is a method for getting solution to non linear algebraic equation?
    
    Options
    1. RungaKutta Method
    2. Newton Raphson Method
    3. Jacobi Method
    4. Divided Difference Formula
    2.y=mx+c is the equation of a–
    
    Options
    1. Polygon
    2. Circle
    3. Line
    4. None
    3.Which one of the following is not a method for finding the root of an algebraic equation?
    
    Options
    1. Newton Raphson Method
    2. Bi-Section Method
    3. Gregory’s Method
    4. Regula Falsi Method
    4.The formula for Newton Raphson method is
    
    Options
    
    5.For x3 – 5x +3 =0, the root lies in between
    
    Options
    1. [0, 1]
    2. [4, 5]
    3. [3, 4]
    4. [0, -1]
    6.The value of Δ f(x) is
    
    Options
    1. f(x1) + f(x0)
    2. f(x1) – f(x0)
    3. f(x1)
    4. None of these
    7.Which one is not a method for numerical integration
    
    Options
    1. Trapezoidal Rule
    2. Gauss Method
    3. Simpson’s 1/3 Rule
    4. Simpson’s 3/8 Rule
    8.The Formula for Bi-section method is
    
    Options
    1. (x1+x2)/2
    2. (x1-x2)/2
    3. (x1x2)/2
    4. None of these
    9.The value of f(x) is
    
    Options
    1. y3-3y2+3y1-y0
    2. y3+3y2+3y1+y0
    3. y0-3y1+3y2-y3
    4. None of these 10.In forward difference formula ‘h’ is Options
      1. The difference between two consecutive y.
      2. The difference between two consecutive x
      3. The difference between first and last x values
      4. The difference between first and last y values
      11.In line fitting method, the general equation of a line is
      
      Options
      1. y = a + bx
      2. y2 = a + bx
      3. y = a + bx2
      4. None of these
      12.For Trapezoidal rule the Generalized Quadrature formula uses
      
      Options
      1. n=1
      2. n=2
      3. n=3
      4. None of these
      13.Gauss elimination method is used to solve the set of linear algebraic equations
      
      Options
      1. True
      2. False
      14.For f(a) and f(b)are of same sign then equation f(x)=0 has at least one root with in [a,b].
      
      Options
      1. True
      2. False
      15.C (n, r) or nCr. = n! / (n+r)! r!
      
      Options
      1. True
      2. False
      16.In Gauss Elimination method, coefficient matrix A is reduced to upper triangle matrix by using the elementary row operations
      
      Options
      1. True
      2. False
      17.Modified Euler is a modified version of Euler Method.
      
      Options
      1. True
      2. False
      18.Gauss Elimination method reduces the system of equations to an equivalent upper triangular matrix.
      
      Options
      1. True
      2. False
      19.Regula Falsi Method converges fastest among Bi-section, Regula Falsi and Newton Raphson Method.
      
      Options
    1. True
    2. False
    20.The number of distinguishable words that can be formed from the letters of MISSISSIPPI is 34650.
    
    Options
    1. True
    2. False
    21.The set of linear algebraic equations can be arranged in matrix for AX=B, where A is the coefficient matrix, X is the variable matrix.
    
    Options
    1. True
    2. False
    22.Numerical methods give always-exact solutions to the problems
    
    Options
    1. True
    2. False
    23.Simpson’s method is used to interpolate the value of the function at some given point.
    
    Options
    1. True
    2. False
    24.The set of equation 3x+2y = 0 and 2x+7y = 9 can be solved by using Bi-Section method.
    
    Options
    1. True
    2. False
    25.In solving simultaneous equation by Gauss- Jordan method , the coefficient matrix is reduced to ————- matrix Options
    1. Null
    2. Unit
    3. Skew
    4. Diagonal
    26.The order of convergence in Newton Raphson method is
    
    Options
    1. 2
    2. 3
    3. 0
    4. None of these
    27.Which of the following is a step by step method
    
    Options
    1. Taylor`s
    2. Adams-Bashforth
    3. Picard`s
    4. Euler`s
    28.In the case of Bisection method , the convergence is
    
    Options
    1. LINEAR
    2. Quadratic
    3. Very slow
    4. None
    29.Solutions of simultaneous non- linear equations can be obtained using
    
    Options
    1. Method of iteration
    2. Newton-Raphson method
    3. Bisection method
    4. None
    30.Bessel`s formula is most appropriate when p lies between
    
    Options
    1. -0.25 and 0.25
    2. 25 and 0.75
    3. 75 and 1
    4. None of the above
    31.The order of the matrix [473] is.
    
    Options
    1. 3*1
    2. 1*3
    3. 3*3
    4. 1*1
    32.If B is square matrix and BT = – B, then B is called
    
    Options
    1. Symmetric
    2. Skew symmetric
    3. Singular
    4. Non Singular
    33.Find the coefficient of x³ in the Taylor series about x = 0 for f(x) =sin2x ?
    
    Options
    1. -2/3
    2. -4/3
    3. 4/3
    4. 2/3
    34.The bisection method of finding roots of nonlinear equations falls under the category of a (an) —————- method.
    
    Options
    1. Open
    2. Bracketing
    3. Random
    4. Graphical
    35.A unique polynomial of degree —————–passes through n+1 data points.
    
    Options
    1. n+1
    2. n
    3. n or less
    4. n+1 or less
    36.Interpolation is the technique to find the value of dependent variable for the given value of independent variable
    
    Options
    1. True
    2. False
    37.By increasing the iterations of any Numerical methods, we increase the correctness of the solution.
    
    Options
    1. True
    2. False
    38.Lagrange’s Interpolation method can be used only for equal interval problems.
    
    Options
    1. True
    2.False
  39.Trapezoidal Integration Method is derived by putting
  
  Options
  1. n =0
  2. n=1
  3. n=2
  4. n=4
  40.If f(x) is a real continuous function in [a,b], and f(a)f(b)<0, then for f(x),there is (are)………….in the domain [a,b].
  
  Options
  1. One root
  2. An undeterminable number of roots
  3. No root
  4.At least on root

Title:

Amity MCA 2nd semester solve assignment for Numerical & Statistical Computations (General)

Short Name or Subject Code: Numerical & Statistical Computations

Short Description: Click to view question first .

University: Amity

Select Type:

General everyone

Service Type: Assignments

Select Semester: Semester- II Select Cource: MCA

commerce line item type:

Price:

₹300.00

Product:

Amity MCA 2nd semester solve assignment for Numerical & Statistical Computations

Dissertation Work

Filll this form and get price list instantly

Academic Assignment Writing Services

Academic Assignment Writing Services Work :

Search form

Amity MCA 2nd semester solve assignment for Numerical & Statistical Computations

Dissertation Work

Academic Assignment Writing Services Work :