D192003 Pages:3

b) Prove that binomial distribution with parameters n and p can be approximated to (8)
Poisson distribution when n is large and ‏م‎ is small with np = 1, a constant.

PART B (MODULES III AND IV)
Answer two full questions.

a ⋅
) 20 COSXW+ WSINXW 0 if <2 >

Use Fourier integral to show that ர்‌ That do 24 7/2 ifx=0 (7)
° 7९ ~ ifx>0

b) ॐ if0O0
Find the Fourier Sine and Cosine Transform of f(x) = { 0 if ged

a) Find the Laplace Transform of :
(i) e © sin 36 cos 26
(ii) {2 coswt (7)
(1) t?u(t-1)

b) Find the inverse Laplace Transform of :

⋅ 1-75
(i) (5-3)(5-1)(5--2)

s-a (8)
(1) 1൩ =

7 0735
(111) 6-3

2) Find the Fourier Sine Transform of f(x) = 27१1, Hence evaluate 1 ard (2)

b) Solve by using Laplace Transform: ‏"بر‎ + 2y’ — 3) = 6e~7",y(0) = 2, )'(0) = -14 (8)

PART C (MODULES V AND VI)
Answer two full questions.

a)
Find the positive solution of 2sinx = x using Newton Raphson (method correct to (6)
five decimal places).

b) (7)

Find the value of tan 33° by using Lagrange‘s formula for interpolation

30° 320 350 380

० A second degree polynomial passes through the points (1,-1) (2,-1) (3, 1) (4, 5).
Find the polynomial f (x), Also find f (1.2). (7)

a) A river is 80 metre wide. The depth y in metres at a distance x metres from one

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