No. of Printed Pages : 5

CS-711

BACHELOR OF COMPUTER APPLICATIONS (BCA) (Pre-Revised) Term-End Examination 02

13 5 3

June, 2015

CS-71 : COMPUTER ORIENTED NUMERICAL TECHNIQUES Maximum Marks : 75

Time : 3 hours

Note : Question number 1 is compulsory. Attempt any three from questions number 2 to 5. Scientific *calculator is permitted. 1.

(a)

(i) Round the following numbers to two decimal places : 48.21416, 2.3742, 52.275, 2.375, 2.385, 81.255 (ii) Round-off the following numbers to four significant figures : 38.46235, 0.70029, 0.0022218, 19.235101, 2.36425

(b) Let x = 0.345 x 100, y = 0.245 x 10-3 and z = 0.432 x 10-3 . Using 3-digit decimal arithmetic with rounding, find whether (a + b) + c = a + (b + c), or not. 5 CS-71

1

P.T.O.

(c)

(d)

(e)

(f)

Find a real root of the equation by using Bisection method x3 - x - 1 = 0.

5

Use the method of iteration to find a positive root between 0 and 1 of the equation x ex = 1.

5

Use the Newton-Raphson method to find a root of the equation x 3 - 2x - 5 = 0.

5

For each of the following numbers, find the number of significant digits and express it in scientific notation : (i)

0.00682

(ii)

1.072

(iii) 300.2

2.

(iv)

400.0

(v)

1070

(a) Using Runge-Kutta fourth order method, find the value of y(0.1) and y(0.2) correct to four decimal places.

Given

dy = y - x, dx

where y(0) = 2. (b) Use Newton-Raphson method to obtain a root of the equation x 2 - 5x + 6 = 0 lying between 1.0 and 2.5, correct to three decimal places. CS-71

2

5

5

(c) The population of a town in the decennial census was as given below. Estimate the population for the year 1895. Year : x

1891 1901 1911 1921 1931

Population : y (in thousands)

46

66

81

93

101

3. (a) The function y = sin x is tabulated below :

(b)

CS-71

0

y=sinx

0

rr/4

rc/2

0.70711 1.000

Using Lagrange's interpolation formula, find the value of sin (7r/6).

5

Using the following table, find f(x) as a polynomial in x by using Newton's interpolation formula. Hence compute ff6.5).

5

x fix) (c)

x

-1 3

0 -6

3 39

6 822

7 1611

Prove the following where the operators have their usual meaning : (i) AmEN7 (ii) E =1 + A 3

P.T.O.

4.

(a) Find the missing term in the following table by using interpolation method :

(b)

x

0

1

2

3

4

Y

1

3

9

?

81

Solve the following equations by Cramer's rule :

5

5

3x + y + 2z = 3 2x - 3y - z = - 3 x + 2y + z = 4 (c)

Solve the following equations by Jacobi Iteration :

5

5x 1 + x2 + 2x3 = 19 x1 + 4x2 - 2x3 = -2 + 3x2 + 8x3 = 39

5.

(a) Solve the following equations by Gauss-Seidel method :

5

3x 1 + 2x2 + x3 - 7 -

x 1 + 3x2 + 2x3 = 4 2x 1 + x2 + 3x3 = 7 (b) Find by the method of Regula-Falsi a real root of the equation x3 + x2 - 3x - 3 = 0 lying between 1 and 2. CS-71

4

5

(c)

Solve by Euler's method, the equation dy = x +y. dx Given y(0) = 0. Choose h = 0.2 and compute y(0.4) and y(0.6).

CS-71

5

5

5,000

BACHELOR OF COMPUTER APPLICATIONS (BCA) (Pre-Revised ...

Jun 3, 2015 - arithmetic with rounding, find whether. (a + b) + c = a + (b + c), or not. 5 ... Solve the following equations by Cramer's rule : 5. 3x + y + 2z = 3.

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