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Posted By: shalat Member Level: Gold Posted Date: 13 Jun 2008
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2008 Bangalore University B.C.A NUMERICAL AND STTISTICAL METHODS Question paper
II SEMESTER B.C.A EXAMINATION ,JUNE 2008
(Y2K7 SCHEME)(2007-08 AND ONWARDS)
COMPUTER SCIENCE
BCA:NUMERICAL AND STATISTICAL METHODS
MAX MARKS:80
TIME:3 HOURS
INSTUSTION:ANSWER BOTH THE SECTIONS
SECTION-A
ANSWER ANTY EIGHT (MARKS:8*3=24)
1.Define algebraic and transcendental equation ?give an example for each
2.What is partial pivoting?Explain the steps involved in partia; pivoting
3.Construct a backward difference table for the following data
X 5 10 15 20 25 30
Y 23 103 233 413 643 923
3
4.Integrate 1/1+x2 dx by Simpsons`s 3/8 rule using following data
0
x 0 1 2 3
Y(x) 1 1/2 1/5 1/10
5.Write the normal equation for the curve of the form y=abbx
6.Find the median and mode for the following series
12,14,10,12,18,16,13,14,17,19.
7.An analysis of result of two section A and B of BCA 2nd semester is given below
SECTION A SECTION B
No. of students 50 40
Average percentage 65 75
Variance in percentage 25 36
From the above data which section is more stable in giving the results
8.What is conditional probability?
9.The ddensity function of a random variable X is given by
F(X)= 1/4x 0 0 otherwise
10.Define exponential distribution
SECTION-B
ANSWER ANY FOUR (MARKS :4*14=56)
11.a)Find the root of hte equation tan x=x near x=4.5.correct upto 4 decimal places (mark:7)
b)evaluate 5.2
log x dx using Romberg`s method method ,with h=0.2 (marks:7)
4
12.a)Use LU Decomposition method to solve the following set of equations (marks:8)
2x+y+z=4
X+2y+z=4
X+y+2z=4.
b)Use Gauss seidel iteration method to solve following set of euation .Perform 3 iteration (marks:6)
x+y+54z=110
27x+6y-z=85
6x+15y+2z=72
13. a)Fit an exponential curve of the form y=abx to the following data (marks:7)
x 1 2 3 4 5 6
y 2.98 4.26 5.21 6.10 6.80 7.5
b)Given the following data estimate(1.5) (marks:7)
x 1 2 3 4 5 6
f(x) 1 8 27 64 125 216
14.a)Find the mean foe the following frequency distribution (marks:6)
0-5 5-10 10-15 15-20 20-25 25-30 30-35
2 4 5 3 2 4 5
b)10 participants in asinging competition were ranked by3(three)Judges in the following order
Judge1 10 3 2 9 4 8 7 5 6 1
Judge2 10 2 1 8 3 9 5 7 4 6
Judge3 7 4 3 6 2 5 10 9 8 1
Determine which pair of judges have common taste for singimg completion (marks:8)
15.a)State and prove Baye`s theorem
b)In a bolt factory 25%,35% and 40% of the total bolts is manufactured by machines.A,B and C out of which 5%,4% and 2 % are defective
What is the probability that a bolt drawn at random is
i)a defective bolt
ii)manufactured by machine A knowing it is defective (marks:8)
16. a)Derive mean and variance for poisson distribution (marks:8)
b)If the height of 300 students are normally distributed with mean 68 inches
and standard deviation 3 inches ,how many students have height
i)greater than 72 inches (marks :6)
ii)Less than or equal to 64 inches
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