Gujarat University 2009-2nd Year B.C.A Computer Application Scientific and Statistical Computing - Question Paper

1

Answer the following.

14

(A)

Attempt (Any two)

4

1

There are 3 notes of Rs. 50 and 4 notes of Rs. 100 in a bag. Three notes are taken atrandom froim it, find the expectes number of notes of Rs. 50.

2

10,000 tickets are sold in a lottery in which there is a first prize of Rs. 5,000. two second prizes of Rs. 1,000 each and ten consolation prizes of Rs. 100 each. One ticket cost Rs. 10. Find the expected net gain or loss if you buy a ticket.

3

A random variable X has the following probability distribution :

(B)

Attempt (any two).

6

1

Calculate co-efficient of correlationfor the followding data :

2

The coefficient of rank correlation between marks in statics and mark in mathematics by a certain group of students is 0.8. If the sum of the squares of the sifference in ranks is given to be 33, find the number of students in the group.

3

Folowing observations were obtainedfor velocity of the carbon dioxide in a given volume of water of different temperature t.

Obtain the relation of the form V = a +bt, which best fits these observation.

(C)

With the help of the following data :

4

Obtain

 (1) Two regression lines.

 (2) The robable vlue of x when y =8.

 (3) The robable vlue of y when x =11.

2

Answer the following

14

(A)

Attempt any four :

12

1

From a pack of cards, one card is selected at random. What is the probbility that the card is a spade, an honour card or a jack ? [Ace, King and Queen are called honour card].

2

A and B throw altenately with a single die, A having the first throw. One who gets '5' firs wins. What are thier respective chances of winning ?

3

There are 40 electric bulbs in a box. Of them 25% are defective. If two bulbs are drawn one by one at random (i) with replacement (ii) without replacement, find the probability that both bulbs are defective.

4

There are 3 red, 3 white and 4 black balls in a bag. 3 balls are taken at random from it. Find the probability that

 (i) all are of the same colour.

 (ii) all are of the different colour.

5

Three groups of children contain respectively 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One cild is selected at ramdom from each group. Find the probability that the three selected children will have (i) 1 girl and 2 boys, (ii) all girls.

(B)

Attempt any two :

12

1

What is the rang of probability ?

2

Define the term "Sample Space".

3

Write an Axiomatic definition of probability.

3

Answer the following

14

(A)

Attempt any four :

12

1

Find the root of equation cos x - 3x + 1 = 0 correct to three decimal places using method of linear interpolation.

2

Find the root of equation x³ - 5x + 3 = 0 correct to three decimal places using iteration method.

3

Find the positive root of equation x⁴ - x - 10 = 0 correct to three decimal places using iteration method.

4

Find the value of to six places of decimal using Network-Raphson method.

(B)

Attempt any two :

2

1

What is the formuls to find approximate number of iteratioms; when the prescribed levsel of tolerance Eand the length of interval within which root lies is given ?

2

What is the rate of convergence of Secant method ?

3

Is it true that "Iteration mehod is also known as fixed point iteration method" ?

4

Answer the following.

14

(A)

Attempt any two.

8

1

Derive Newton's Backward difference Interpolation Formula for n-equally spaced pointes.

2

Using Newton's Divided Difference Interpolation, find the polynomial satisfying the data.

3

Give the set of values (1,4), (3,12), (4,19). Find the value of x corresponding to y = 7 using Langrange's formula for inverse interpolation.

(B)

Attempt any two

6

1

The growth rate of bacteria (n) in a culture after t seconds is given below. Fit a curve of the form n = ab^tand estimate n when t = 2.5 seconds.

2

Fit a second degree parabola to the following data :

3

Using Newton's Forword difference interpolation formula find the value for y when x = 102

5

Answer the following.

14

(A)

Attempt (any two).

6

1

Give a number 0.05578. compute absolutle error and relative error, if
 (i) rounded-off to three decimal digits.
 (ii) truncated to three decimal digits.

2

Explain normalized floating point representation with illustration. Give the range of exponent and mantissa.

3

Give the solution of a problem as x_a = 35.25 with relative error in the solution at most 2%. Find, to four decimal digits, the range of values within which the exact value of the solution must lie.

(B)

Attempt any two

8

1

Calculate Mean and Medan for the following distribution :

2

In the following frequency distribution, two clas frequencies are missing.

Ti is however known that the total frequency is 900 and the madian is 100.048, find the two missing frequencies.

3

Goals scored by two terms A and B in a football season werw as follows. Find out which team is more consistent.