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EYS-162
B. Tech. (New Scheme) Examination, 2024
(Fourth Semester)
NUMERICAL ANALYSIS
EL-401
Time : 3 Hours
[Maximum Marks : 60]
Note : All questions are compulsory and carry equal marks. Attempt any two parts from each question.
(a) Find the positive root of f(x) = x³ - x - 1 correct to four decimal places by Bisection method.
(b) Using Newton-Raphson method find the root between 0 and 1 of f(x) = x³ - 6x + 4 correct to 5 decimal places.
(c) Using Lagrange's Interpolation formula, find y(10) from the following table :
x : 5 6 9 11
y : 12 13 14 16
(a) Evaluate the integral :
I = ∫5.24 loge x dx
using Trapezoidal and Simpson's ⅓ as well as Simpson's ⅜ rule.
(b) Find, by Gaussian elimination method the inverse of :
A = [3 -1 1-15 6 -55 -2 2]
(c) Solve the following system by Gauss-Jacobi method :
10x - 5y - 2z = 3;
x + 6y + 10z = -3;
4x - 10y + 3z = -3;
(a) Solve :
dy/dx = x + y
given y(1) = 0 and get y(1.1), y(1.2) by Taylor series method.
(b) Apply the fourth order Runge-Kutta method to find y(0.2) given that y' = x + y, y(0) = 1.
(c) Solve :
dy/dx = 2x/y
given y(0.1) = 1, taking h = 0.1 and using Modified Euler's method.
(a) Explain Binomial Distribution. Hence find the probability of getting 4 heads in 6 tosses of a fair coin.
(b) If the variance of the Poisson distribution is 2, find the probabilities for r = 1, 2, 3, 4 from the recurrence relation of the Poisson distribution. Also find P(r ≥ 4).
(a) Prove that :
L[cosh at] = s / (s2 - a2)
(b) Find the Laplace transform of the periodic function (sawtooth wave) 
(c) State and prove convolution theorem.