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Amity MBA online solve assignment for Numerical & Statistical Computations
1.Find the negative root of the equation x3 – 21x + 3500 = 0 correct to two decimal places by Newton Raphson Method.
2.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
3.Define Interpolation with the help of suitable example.
4.Derive the relation between divided differences and ordinary differences.
5.Integrate the function x³ + 2x +1 with respect to x from 0 to 1 by using Trapezoidal. Divide the interval into eight equal intervals
6.. 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.
7. 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 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
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 RungaKutta Method Newton Raphson Method Jacobi Method Divided Difference Formula
2.y=mx+c is the equation of a– Options Polygon Circle Line None
3.Which one of the following is not a method for finding the root of an algebraic equation? Options Newton Raphson Method Bi-Section Method Gregory’s Method Regula Falsi Method
4.The formula for Newton Raphson method is Options
5.For x3 – 5x +3 =0, the root lies in between Options [0, 1] [4, 5] [3, 4] [0, -1]
6.The value of Δ f(x) is Options f(x1) + f(x0) f(x1) – f(x0) f(x1) None of these
7.Which one is not a method for numerical integration Options Trapezoidal Rule Gauss Method Simpson’s 1/3 Rule Simpson’s 3/8 Rule
8.The Formula for Bi-section method is Options (x1+x2)/2 (x1-x2)/2 (x1x2)/2 None of these
9.The value of f(x) is Options y3-3y2+3y1-y0 y3+3y2+3y1+y0 y0-3y1+3y2-y3 None of these
10.In forward difference formula ‘h’ is Options The difference between two consecutive y. The difference between two consecutive x The difference between first and last x values The difference between first and last y values
11.In line fitting method, the general equation of a line is Options y = a + bx y2 = a + bx y = a + bx2 None of these
12.For Trapezoidal rule the Generalized Quadrature formula uses Options n=1 n=2 n=3 None of these
13.Gauss elimination method is used to solve the set of linear algebraic equations Options True 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 True False
15.C (n, r) or nCr. = n! / (n+r)! r! Options True False
16.In Gauss Elimination method, coefficient matrix A is reduced to upper triangle matrix by using the elementary row operations Options True False
17.Modified Euler is a modified version of Euler Method. Options True False
18.Gauss Elimination method reduces the system of equations to an equivalent upper triangular matrix. Options True False
19.Regula Falsi Method converges fastest among Bi-section, Regula Falsi and Newton Raphson Method. Options True False
20.The number of distinguishable words that can be formed from the letters of MISSISSIPPI is 34650. Options True 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 True False
22.Numerical methods give always-exact solutions to the problems Options True False
23.Simpson’s method is used to interpolate the value of the function at some given point. Options True False
24.The set of equation 3x+2y = 0 and 2x+7y = 9 can be solved by using Bi-Section method. Options True False
25.In solving simultaneous equation by Gauss- Jordan method , the coefficient matrix is reduced to ————- matrix Options Null Unit Skew Diagonal
26.The order of convergence in Newton Raphson method is Options 2 3 0 None of these
27.Which of the following is a step by step method Options Taylor`s Adams-Bashforth Picard`s Euler`s
28.In the case of Bisection method , the convergence is Options LINEAR Quadratic Very slow None
29.Solutions of simultaneous non- linear equations can be obtained using Options Method of iteration Newton-Raphson method Bisection method None
30.Bessel`s formula is most appropriate when p lies between Options -0.25 and 0.25 25 and 0.75 75 and 1 None of the above
31.The order of the matrix [473] is. Options 3*1 1*3 3*3 1*1
32.If B is square matrix and BT = – B, then B is called Options Symmetric Skew symmetric Singular Non Singular
33.Find the coefficient of x³ in the Taylor series about x = 0 for f(x) =sin2x ? Options -2/3 -4/3 4/3 2/3
34.The bisection method of finding roots of nonlinear equations falls under the category of a (an) —————- method. Options Open Bracketing Random Graphical
35.A unique polynomial of degree —————–passes through n+1 data points. Options n+1 n n or less n+1 or less
36.Interpolation is the technique to find the value of dependent variable for the given value of independent variable Options True False
37.By increasing the iterations of any Numerical methods, we increase the correctness of the solution. Options True False
38.Lagrange’s Interpolation method can be used only for equal interval problems. Options True 2.False
39.Trapezoidal Integration Method is derived by putting Options n =0 n=1 n=2 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 One root An undeterminable number of roots No root 4.At least on root
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