Himachal Pradesh University (HPU) 2010 Model NACP - Question Paper

NUMERICAL ANALYSIS third Sem CSE/ECE/EEE
HPU. Shimla
Max marks 60

Note: part A is compulsory. Attempt any 4 ques. from part B and 2 from part C. Use of scientific calculator is allowed.

part A Marks two every

1.
(a) What is the difference ranging from secant method and False Position method?
(b) What is transcendental equation?
(c) elaborate the characteristics of iterative methods?
(d) obtain the interval in which the real root of the subsequent formula lie
x3 – 4x - 9
(e) What is partial pivoting?
(f) Compare and contrast homogeneous and non-homogeneous system of linear equations.
(g) What is the difference ranging from initial value issue and boundary value problem?
(h) Write forward differences table if :

x= 10 20 30 40
y= 1.1 2.0 4.4 7.9

(i) provide a few advantages of the difference tables.
(j) What improvement is done in replaced Euler's method?

part B Marks five every

2. obtain a root of the subsequent formula using the Bisection method:

x3– 2x – five =0.

3. The distance(s) covered by a car in a provided time (t) is provided in the subsequent table

Time (minutes) 10 12 14 16 18
Distance (km) 12 15 20 27 37

obtain the acceleration of the car at t = 13 minutes.

4.Evaluate (please see the attachment) using Trapezoidal rule taking h = ¼

5. By the method of lowest square, obtain the straight line that best fits the subsequent data:

x= 0 five 10 15
y= 1.8 1.45 1.18 1.0

6. Derive the formula for Simpson's 3/8 rule.

part C Marks 10 every

7. Solve the subsequent system of equations using Gauss elimination method
2x1+x2+x3=10

3x1+2x2+3x3=18

x1+4x2+9x3=16

8. obtain the rate of convergence of Newton-Raphson method. Derive it.

9. Using Picard's method obtain the solution accurate to 3 decimal positions, of the 1st order formula dy/dx = x + y2 for x = 0.1 when y(0) = 1.

Earning:   Approval pending.