Reference no: EM132758864

Question 1) Express f (x) = |x|, -Π < x < Π, as Fourier Series.

Question 2) If L (sint/t) = tan^-1 1/s, find L( sin at/t ).

Question 3) Solve the partial differential equation p - q = log(x + y).

Question 4) Find p such that the function f(z) = r² cos 2θ + tr² sin pθ is analytic function.

Question 5) Solve the system of linear equations: x + y - 6z = -12, x + 4y - z = -5, 3x - y - z = 4 using Gauss Elimination method.

Question 6) Solve y' = -y; y(0) = 1 using Euler's method for y(0.6) taking h = 0.2.

Question 7) Six dice are thrown 500 times. How many times do you expect at least three dice to show a 2 or 3?

Question 8) In two independent samples of sizes 9 and 20, the sum of squares of deviation of the sample values from the respective sample means are 60.6 and 109.2. Test whether the difference of variance of the populations is significant or not.