• Attempt any five questions.
• All questions carry equal marks.
Find the real root of f(x)=x³-x-10 by Newton Raphson method correct up to 4 decimal places.
Find solution y(301) using Newton Divided difference interpolation formula.
Evaluate the integral using Simpson's 3/8 rule from the given table.
Solve the system by Gauss elimination: x+y+z=4, x+4y+3z=8, x+6y+2z=6.
Using modified Euler's method, find y at x=0.3 given dy/dx=x+y, y=1 when x=0.
Find y(1.05) using 4th order Runge-Kutta for dy/dx=x²+y², y(1)=1.2.
Find the inverse Laplace transform of F(s)=1/[(s+1)(s²+1)].
Find Laplace transform of y(t) satisfying y''-2y'-y=1, y(0)=-1, y'(0)=1.
Find probability that car speed >100 km/hr for N(90,10²).
Find binomial distribution with mean 100 and SD 5.
Find mean and SD of normal distribution where 10.03% items under 25 kg and 89.97% under 70 kg.
Find solution using Lagrange's Interpolation formula.
Find L(t² e^(-t) cosh 2t) and L(e^(3t) sin² 4t).
Using Milne's method find y(4.4) given 5xy+y²-2=0 and four starting values.
Find mean of Poisson distribution.
Write short note on Exponential distribution.
