• Attempt any five questions.
• All questions carry equal marks.
Using Newton-Raphson method find the real root of 3x = cos x + 1 correct to five decimal places.
Find f(g) from the given table.
Apply Simpson's 3/8 rule to evaluate ∫₁·₀¹·³ √x dx for six digits.
Solve the system using Gauss-Seidel method: 27x+6y-z=85, 6x+15y+2z=72, x+y+54z=110.
Using Runge-Kutta 4th order solve dy/dx=(y²-x²)/(y²+x²), y(0)=1 at x=0.4, step 0.2.
Find y(2.2) using Euler's method for dy/dx = -xy² where y(2)=1.
Find the Inverse Laplace transform of 1/[p³(p²+a²)].
Using Laplace transform solve y'''+2y''-y'-2y=0 with y(0)=1, y'(0)=2, y''(0)=2.
Fit a Poisson distribution to the given data.
Calculate the mean and standard deviation of Binomial Distribution.
Find dy/dx at x=1.5 from the given table.
Evaluate ∫₀^∞ e^(-t)·sin t / t dt.
Show that Newton Raphson method is quadratic convergent.
Derive Newton forward interpolation formula and estimate f(1.25) from the given table.
Solve the system using Gauss elimination: 3x+y-z=3, 2x-8y+z=-5, x-2y+9z=8.
Find Fourier sine transform of 1/x.
