Download AKTU B-Tech 2nd Sem 2016-17 Computer Based Numerical And Statistical Techniques Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU)) B-Tech 2nd Semester (Second Semester) 2016-17 Computer Based Numerical And Statistical Techniques Question Paper

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MCA
THEORY EXAMINATION (SEM?II) 2016-17
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Max. Marks: 70
RCA201
Note .' Be precise in your answer. In case ofnumericalproblem assume data wherever not provided.
b)
g)
h)
SECTION-A
Attempt all questions : 7 x2 = 14
Explain Pitfalls of ?oating-point Representation in detail.
1 2 62
Prove thatA= 56 + 6 1 + 7
Suppose 1.414 is used as an approximation tox/2. Find the absolute and relative errors.
Write down Gauss?s forward interpolation formula.
Prove that x4 = ?[3T0 (x) + 4T2 (x) + T4 (36)]
What do you mean by Histograms?
Explain Null hypothesis.
SECTION-B
Attempt any ?ve of the following : 7 x5 = 35
Find a real root of the equation 3x + sinx ? ex = 0 by the method of Regula falsi position
correct to four decimal places.
Find the missing term in the following table:
x 2 2.1 2.2
2.3 2.4 2.5 2.6
y 0.135 -?? 0.111 0.100 0.082 0.074
Given yzo = 24, y24 = 32, yzg = 35 and y32 = 40 find y25 by Bessel?s interpolation formula.
Given :?: = y ? x, y(0) = 2. Find y(0. 1) and y(0.2) correct to four decimal places using Runge?
Kutta method.
By the method of least squares, find the curve y = ax + bx2 that best fits the following data :
x 1 2 3 4 5
y 1.8 5.1 8.9 14.1 19.8
Apply Gauss?Seidel iteration method to solve the following equation (three iteration only)
20x + y ? 2: = 17
3x + 20y?: = -18
2x- 3y+20:=25
Find the cubic Lagrange?s interpolating polynomial from the following data :
x 0 1 2 5
f(x) 2 3
12 147
For 10 observations on price(x) and supply(y), the following data were obtained (in appropriate
units) :

2x = 130, 2y = 220, 2x2 = 2288, 23/2 = 5506 and ny = 3467
Obtain the two lines of regression.
SECTION-C
Attempt any two of the following : 10.5 x2 = 21
3. Find y(2) if y(x) is the solution 0% = g(x + y) where y(0) = 2, y(0.5) = 2.636, y(1) =
3.595,y(1.5) = 4.968 using Milne?s method.
4. Given that:?: = logm (x + y)with the initial condition that y = 1 when x = 0, find y for x = 0.2
and x = 0.5 using Euler?s modified formula.
5. Derive the Newton?divided difference formula, calculate the value 0ff(6) from the following
data
x 1 2 7 8
f(x) 1 5 5 4