Determine y for x = 4 and x = 12. State the formulae used

B) Use Gauss - Seidel Method to solve 10x + 2y + z = 9, 2x + 20y - 2z -44, -2x + 3y + 10z = 22

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L A) Given: X: y: A) 2 B) 0 5 10 15 0 0.0875 0.1763 0.2639 B) Determine y for x=4 and x=12. State the formulae used. Use Gauss - Seidel Method to solve 10x + 2y +z = 9, 2x + 20y – 2z = -44, -2x + 3y + 10z = 22 5 1 B) A) State and prove the Orthogonally property of Bessel function. n B) Prove that: i) J'(x) = n(x) − In+1(x) B B) Advance Mathematics π/2 Evaluate numerically 2² √cose de using 1/3rd and 3/8th formula. dy Find approximately y for x=0.2 for = x + y², y=1 when x=0 (take h-0.1) by modified Euler's method. dx x 2n | ii) Jn+1(x) = ²n Jn (x) — In-1 (x) x A) A bag contains 10 white and 15 black balls. Two balls are drawn in succession. Find the probability that one of them is black and other white. X: f: 0 13 Fit a binomial probability distribution to the following frequency distribution: 1 24 2 12 20 0.3640 2 52 3 59 3 16 25 0.4663 4 32 4 28 A) Given the data: X: 1 5 7 y: 10 25 41 Find the co-efficient of correlation between x and y. Obtain also the equations of the two regression lines. Establish the following Z-transforms: 5 16 6 36 az i) Z[na"] = {2} ii) z]-{log _²} = z-a 6 4 L A) Given: X: y: A) 2 B) 0 5 10 15 0 0.0875 0.1763 0.2639 B) Determine y for x=4 and x=12. State the formulae used. Use Gauss - Seidel Method to solve 10x + 2y +z = 9, 2x + 20y – 2z = -44, -2x + 3y + 10z = 22 5 1 B) A) State and prove the Orthogonally property of Bessel function. n B) Prove that: i) J'(x) = n(x) − In+1(x) B B) Advance Mathematics π/2 Evaluate numerically 2² √cose de using 1/3rd and 3/8th formula. dy Find approximately y for x=0.2 for = x + y², y=1 when x=0 (take h-0.1) by modified Euler's method. dx x 2n | ii) Jn+1(x) = ²n Jn (x) — In-1 (x) x A) A bag contains 10 white and 15 black balls. Two balls are drawn in succession. Find the probability that one of them is black and other white. X: f: 0 13 Fit a binomial probability distribution to the following frequency distribution: 1 24 2 12 20 0.3640 2 52 3 59 3 16 25 0.4663 4 32 4 28 A) Given the data: X: 1 5 7 y: 10 25 41 Find the co-efficient of correlation between x and y. Obtain also the equations of the two regression lines. Establish the following Z-transforms: 5 16 6 36 az i) Z[na"] = {2} ii) z]-{log _²} = z-a 6 4