Exam Papers

Numerical Analysis 2021 – BSc Computer Science Part 2

Total No. of Questions : 8] [Total No. of Printed Pages : 4

 

Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2021
Paper No. 1.3
NUMERICAL ANALYSIS

Time: 1\tfrac{1}{2} Hours] [Maximum Marks: 50

 

Note: Attempt all sections as directed.

Section-A

1. Attempt any two questions :15 each

   (a) Evaluate :

\bigtriangleup ^{2}\left [ \frac{5x+12}{x^{2}+5x+6} \right ]

   (b) Find f(6) given that f(0) = -3, f(1) = 6, f(2) = 8, f(3) = 12, the third difference being constant.

2. (a) Use Newton formula for interpolation to find the net premium at the age 25 from the table given below :

AgeAnnual New Premium
200.01427
240.01581
280.01772
320.01996

    (b) By means of Lagrange’s formula, prove that y_{1} = y_{3}-0.3\left ( y_{5}-y_{-3} \right )+0.2\left ( y_{-3}-y_{-5}\right ) approximately.

3. (a) Solve by Gauss’s elimination method the following :

 6x + 3y + 3z = 6

6x + 4y + 3z = 0

20x + 15y + 12z = 0

    (b) Solve the following systems by Gauss Seidel method.

 10x + 2y + z = 9

 2x + 20y -2z = -44

 -2x + 3y + 10z = 22

4. (a) Find the derivative of f(x) at x = 0.4 from the following table :

x0.10.20.30.4
f(x)1.105171.221401.349861.49182

    (b) Evaluate :

\int_{0}^{4}\frac{dx}{1+x^{2}}

     by using Weddle’s rule.

Section-B

Note : Attempt any one question.20 each

5. Evaluate:

\int_{0}^{4}e^{x}dx

    by Simpson’s rule, given that

e=2.72, e^{2}=7.39, e^{3}=20.09, e^{4}=54.60

    and compare it with the actual value.

6. (a) Use Newton-Raphson method to find root of the equation x2 + 4 sinx = 0 correct to four places of decimals.

    (b) Find a Polynomial satisfied by (-4, 1245), (-1, 33), (0, 5), (2, 9) and (5, 1335), by the use of Newton’s interpolation formula with divided difference.

7. (a) Given \frac{dy}{dx}= \frac{y-x}{y+x} with y=1 for x=0. Find approximately for x=0.1 by Euler’s method. (Five Steps).

    (b) Use Runge-Kutta method to solve the equation \frac{dy}{dx}=1+y^{2} for x=0.2 to x=0.6 with h=0.2. Given the initially at x=0, y=0. 

8. (a) Obtain the missing terms in the following table :

x:12345678
f(x):18?64?216343512

    (b) Show that :

\left ( n+1 \right )\bigtriangleup^{n}\bigcirc ^{n} = 2\left [ \bigtriangleup ^{n-1}\bigcirc^{n}+ \bigtriangleup ^{n}\bigcirc^{n} \right ]

……..End……..

Lokesh Kumar

Being EASTER SCIENCE's founder, Lokesh Kumar wants to share his knowledge and ideas. His motive is "We assist you to choose the best", He believes in different thinking.

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