# Probability Distributions,Transforms And Numerical Methods KTU B.Tech Important S4 Question Papers [ PDTM ] MA202 | Question Bank

**Probability Distributions,Transforms And Numerical Methods KTU B.Tech Important S4 Question Papers**

__Modules V and VI__
38) Use Newton-Raphson method to find a root of the equation X^3 - 2X - 5 = 0.

39) Set up a Newton iteration for computing the square root x of a given positive number c and using it find the square root of 2 exact to six decimal places.(Perform 4 iterations)

40) Find the positive solution of 2sinx = x using Newton-Raphson method

41) Use Newton-Raphson method to estimate the root of f(x) = e^-x -x employing an initial guess of X0 = 0

42) Find Lagrange’s interpolation polynomial fitting the points f(1) = -3, f(3)=0, f(4)=30, f(6)=132.Hence find f(5).

43) Using Newton’s Forward Difference formula estimate the value of from the following data

**x : 10 20 30 40 50**

**f(x) : 46 66 81 93 101**

44) Using Newton’s backward Difference Interpolation formula, estimate the value of from the following data.

**x : 20 25 30 35 40 45**

**f(x) : 35.4 33.2 29.1 26.0 23.1 20.4**

Temperature : 15 20 25 30 35 (in degree c)

Solubility : 20.51 21.47 23.52 24.57 25.85

Estimate the solubility at 33*c using Newton’s backward difference interpolation.

52) The population of a certain city are as follows.

Year :1921 1931 1941 1951 1961 1971

Population(in lakhs) : 12 15 20 27 39 52

Estimate the population in the year 1965 using Newton’s backward difference interpolation.

53) Solve the following system of equations by Gauss elimination method with partial pivoting.

54) Solve the following linear system by Gauss elimination with partial pivoting

55) Solve the following system of equations (correct to 3 decimal places) with Gauss- Seidel iteration method.

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