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

Tuesday, 22 January 2013 03:55Web

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.

**(**What is the difference ranging from secant method and False Position method?

**a)****(**What is transcendental equation?

**b)****(**elaborate the characteristics of iterative methods?

**c)****(**obtain the interval in which the real root of the subsequent formula lie

**d)**x3 β 4x - 9

**(**What is partial pivoting?

**e)****(**Compare and contrast homogeneous and non-homogeneous system of linear equations.

**f)**(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

**(**provide a few advantages of the difference tables.

**i)**(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:

x3β 2x β 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 = ΒΌ

**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 metho

**d.**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. |