Test Papers / Previous Question Papers of IGNOU CS08 Numerical and Statistical Computing December 2001

ADCA / MCA (II Yr)
Term-End Examination

December, 2001

CS08 : Numerical and Statistical Computing

Time: 3 hours
Maximum Marks: 75

1. (a)  Which of the variable names given below are invalid in Fortran ? Give reasons in support of your answer : - 3 marks
	( i )	TEMP_X
	( ii )	ROLL2
	( iii )	PROGRAM
    
    (b)	Which are valid real constants in exponent form:					3

	( i )	0.01540E05
	( ii )	- 0.148E - 5
	( iii )	125.8E

    (c)	Write a Fortran statement for each of the following mathematical expressions : 		3

	( i )	x sup (1/3) - y sup (-2)
	( ii )	a (x + y / z) sup 3.5
	( iii )	| sin X | + log sqrt( 3x sup 2 + 5 y sup 2

    (d)	Suppose the variables A,B and C respectively contain the valuse 3,4 and 5. 		3
	Find the value of each of the following logical expressions : 

	( i )	( A + C) . EQ . 2 * B. AND . 2 * ( C - A) . EQ . B
	( ii )	. NOT . ( 3 . EQ . C - 2 . AND . A . LE . C )
	( iii )	. NOT . C . GT . A . OR . B . LT . 5

    (e)	Write each of the following statements in Fortran : 					3

	( i )	If R = 2S + T, go to statement labelled 87
	( ii )	If S not equal to 11, go to statement labelled 44
	( iii )	if 3S > 4T, stop

    (f)	Draw a Pie - chart of the monthly expenses of a hostler, 				3
	whose expenses per month are as follows:
	
	item				Amount in ruppes
	
	Food				2000
	room rent 			1000
	transport			 500
	books/stationery			 500
	maintenance			1000

   (g)	Explain the concepts of 'skewness' and 'kurtosis' along with their significance 		4
	in the study of 	distributions of mass of data.

   (h)	A computer while calculating correlation coefficient between 20 pairs of 			5
	two variables x and y obtain the following results : 
	n = 20, x = 100 , y = 80,
	x = 520, y = 360, xy = 420
	It was later discovered at the time of cheching that he had copied down two pairs as
				x		y	
				
				6		4
				8		6
	while the correct values were
				x		y
				8		12
				6		8
	obtain the correct value of correlation coefficient.

    ( i )	Two dice are thrown. Find the probability that sum of the numbers on two		3
	dice is 9 given that first dice shows 6.

2 (a).	Write a fortran 90 program that reads an n-digit number (for a positive integer n ) 		8
	and reverses the digits of the number to obtain a new number (eg. if number 24379
	 is read then the 	new number obtained by reversing the digits is 97342). 
	The program then prints the result with a 	suitable message.

   (b). 	Write a fortran program that goes on reading values for an integer variable N until 	7
	the value read is zero or negative. For each positive value of N read, the program tests
	whether N is a prime number of not. Also it should print appropriate messages.

3 (a).	Write a fortran program that goes on reading sets of three real values until at least one	7
	of the values in any set of values is zero or negative. The three values in a set denote 
	lengths of the sides of a triangle. The program tests whether the triangle represented by 
	the values is an equilateral triangle. If te triable is equilateral then it computes the area 
	of the triangle. If the triangle represented is not equilateral then it finds the perimeter of 
	the triangle. Program prints suitable messages also.

   (b).	Calculate the variance for the class-frequency distribution given below :			4
		Marks obtained			number of students
		0 - 10				15
		10 - 20				20
		20 - 30				25
		30 - 40				17
		40 - 50				12

    (c).	The income of 80 families are given below :						4
		Income (in Rs)			Number of families
		4000 - 6000			8
		6000 - 8000			24
		8000 -10000	  		32
		10000 - 12000			16
	Find the mode.

4 (a).	A five-figure number is formed by the digits 0,1,2,3,4 ( without repetition). Find the 	6
	probability that the number formed in divisible by 4.	

   (b).	The average number of radioactive particles through a counter during 			4
	1 milli second in a laboratory experiment is 3. What is the probability that five 
	particles enter the counter in a given milli second ?

   (c). 	The probability of a college student being male is 1/3 and that being female is 2/3. 	5
	The probability that a male student completes the course is 3/4 and that a female 
	student does it is 1/2. A student is selected at random and is found to have completed 
	course. What is the probability that the student is a male ?

5(a). 	Fit a straight line trend by the method of least squares to the following data:		7
	Year :		1951	52	53	54	55	56
	price index:	107	110	114	112	115	113

   (b). 	The following table gives the average wholesale prices of four grains for the 		8
	years 1998 to 2001. Compute chain base index number.
	Grain	1998	1999	2000	2001
	Rice	12	18	24	12
	Wheat	18	36	54	24
	Gram	12	36	60	24
	Barley	15	21	54	33

6(a).	Compute the approximate value of the integral					7
		I = ( 1 + x + x ) dx
	using simpson's rule by taking interval size h as 1.

   (b).	Find the value of cosh = d/dx (sinhx) at x = 1.52 from the following table : 		8
		x			sinhx
		1.5			2.129279
		1.6			2.375568
		1.7			2.645632
		1.8			2.942174
		1.9			3.268163
		2.0			3.626860