**UTTARAKHAND TECHNICAL UNIVERSITY**

**B.TECH (SEM. Iii)**

**2011-2012**

**SUB: cbnst****time : 2hr]**

Total marks :

**50****Note:**Attempt all questions. Be precise in your answer.

**SECTION A**

Q1:- Attempt any

**four**of the following :**4x3=12**

- If
**Π**=**22/7**is approximated as**3:14**, find the absolute error, relative errors and percentage error. - Describe briefly the floating point representation of numbers.
- Find a real root of the equation
correct to four decimal places using iteration method.*2x – log*_{10}x =7 - Use Muller's method to find a root of the following equation.
*x*^{3}-x-1=0 - Define rate of convergence. Obtain rate of convergence of Newton Raphson method.
- Calculate the value of
by Newton's Raphson method, correct to 3 decimal places.**(31)**^{1/4}

**SECTION**

**B**

**two**parts of the following:

**6x2=12**

- Using Newton's divided difference formula, find the value of
**f(2)**,**f(8)**and**f(15)**from the following table.

- The following is the data from steam table.

Using Newton's formula, find the pressure of steam for a temperature of^{142}^{˚}^{C.}^{} - Applying Lagrange's formula, find a cubic polynomial which approximate the following data.

**SECTION C**

**two**parts of the following:

**6x2=12**

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

(b) Using Euler's method, solve the following differential equation.**dy/dx+ 2y=0, y(0)=1**.

**SECTION D**

**two**parts of the following:

**7x2=14**

- Fit a second degree parabola to the following data taking
*x*as the independent variable.

- For a bi variate distribution
*n*=**18,**ΣΣ*x*^{2}=60,Σ*y*^{2}=96,Σ*x=12,*Σ*y=18,**xy=48.* - Write shorts notes on the following.

(a) Frequency Chart.

(b) Multiple Regression.

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