• Attempt any five questions.
• All questions carry equal marks.
Find the real root of the equation x³ - 3x - 5 = 0 correct to four places of decimals by Newton Raphson method.
Evaluate Δ⁶(ax-1)(bx²-1)(cx³-1); h=1.
Using Newton's divided difference formula, find f(8) and f(15) from the given table.
Find the real root of the equation xe^x - 3 = 0 correct to three decimal places by Regula Falsi method.
Use Simpson's 1/3 and 3/8 rule to evaluate ∫₀¹ dx/(1+x²). Hence obtain the approximate value of π.
Compute the value of ∫₀·₂¹·⁴ (sin x - log_e x + e^x) dx by trapezoidal rule.
Solve the following system by Gauss Seidel iteration method: 27x+6y-z=85, 6x+15y+2z=72, x+y+54z=110.
Use Simpson's rule to find approximate value of ∫₁² dx/x.
Use Euler's method compute the solution of dy/dx = y² - x² with y(0)=1 at x=0.1.
Use Euler's Modified method to solve dy/dx = x + y, y(0)=1, h=0.2 compute y(1).
Use Laplace transform to solve the IVP: y' + 2y = 26 sin 3t, y(0) = 3.
Evaluate L(t cos at).
Evaluate L⁻¹[1/(1+s)³].
Evaluate L{t² e^(-3t)}.
Find mean of Poisson distribution.
Write Short note on Exponential Distribution.
