b)

0)
a)

b)

0)

1192004 Pages:3

Solve using Runge - Kutta method of order 4:

‎85—20x+ 12x°—2x*,y(0)= 1 for x = 0.5. [Choose h = 0.5]‏ = ا
‎Evaluate ம்‌ xe*dx using Simpson’s 1/3™ rule with n = 8.‏

‎A gambler has rupees 2 and he plays a betting game where he wins Rs. 1, if a tail shows up
and loses Rs. | if a head shows up in the tossing of a fair coin. He stops playing this game
if he wins Rs 2 or loses Rs 2. Find (i) the transition probability matrix of the Markov chain
(ii) the probability that the gambler lost his money at the end of 2 plays.(iii) the probability
that the gambler ends the game in 2 plays.

‎Using Lagrange’s interpolation method to find the value of f(2) from the following data:

‎Find a positive root of the equation >° + x ‏ع‎ 1 = 0 using Newton-Raphson method correct

‎to 4 decimal places.

‎Page 3 of 3

‎(7)

‎(6)

‎(10)

‎(5)

‎(5)