## Wednesday, 8 August 2012

### CBNST B tech previous year qus paper 2nd year

UTTARAKHAND TECHNICAL UNIVERSITY

B.TECH (SEM. Iii)

2011-2012

SUB: cbnst
time : 2hr]
Total marks :50

SECTION A
Q1:- Attempt any four of the following :
4x3=12
1.  If  Π = 22/7 is approximated as 3:14, find the absolute error, relative errors and percentage error.
2. Describe briefly the floating point representation of numbers.
3. Find a real root of the equation  2x – log10x =7 correct to four decimal places using iteration method.
4. Use Muller's method to find a root of the following equation.
x3-x-1=0
5. Define rate of convergence. Obtain rate of convergence of Newton Raphson method.
6. Calculate the value of (31)1/4 by Newton's Raphson method, correct to 3 decimal places.

SECTION B
Q2:- Attempt any two parts of the following:

6x2=12
1. Using Newton's divided difference formula, find the value of f(2), f(8) and f(15) from the following   table.
2. The following is the data from steam table.
Using Newton's formula, find the pressure of steam for a temperature of 142˚C.
3. Applying Lagrange's formula, find a cubic polynomial which approximate the following data.
SECTION C
Q3:- Attempt any two parts of the following:
6x2=12

1. Evaluate the integral given above by Simpson's rule with 4 strips and 8 strips respectively. Determine the error by direct integration.
2. Use the Runge-Kutta fourth order method to find the value of y when x = 1 given that y = 1 when    x = 0 and that dy/dx = (y - x)/(y + x).
3. (a) Solve dy/dx = x+y, Given y(1) = 0 find y(1,1) by Taylor's series method.
(b) Using Euler's method, solve the following differential equation.
dy/dx+ 2y=0, y(0)=1.

SECTION D
Q4:- Attempt any two parts of the following:
7x2=14

1. Fit a second degree parabola to the following data taking x as the independent variable.
2. For a bi variate distribution n=18,
Σx2=60, Σy2=96, Σx=12, Σy=18, Σxy=48.
3. Write shorts notes on the following.
(a) Frequency Chart.
(b) Multiple Regression.

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