 #### What are the problems with polynomial interpolation for a large number of data set? How such problems are addressed? Explain with an example. #### Calculate the real root of the given equation using fixed point iteration correct up to 3 significant figures. 2×3 – 2x = 5 #### How boundary value problems differs from initial value problems? Discuss shooting method for solving boundary value problem. #### Discuss the Doolittle LU decomposition method for matrix factorization. #### How can  Horner’s rule be used to evaluate the f(x) and f(x) of a polynomial at a given point? Explain. Write an algorithm and program to calculate a real root of a polynomial using Horner’s rule. #### Construct Newton’s forward difference table for the given data points and approximate the value of f(x) at x = 15. #### Describe processes involved in the fabrication of integrated circuits include epitaxial growth, oxidation, oxide removal and pattern definition, doping (impurities in the Si), and interconnection of components. #### Find expression for force on a current-carrying wire in a magnetic field to find the force experienced by a single charge.  