SYJC Commerce Maths PractiseSums

Nirmala Memorial Foundation College of Commerce & Science

Std: S.Y.J.C (COMMERCE) Subject : Mathematical and Statistics

Practical 01. Mathematical Logic

Date :05/06/2015

1) Using Truth Table, verify that

[(p q) (q r)] [(~p q) ( q r) ] is a contingency, where p,q and r are

logical statements.

2) Using Truth Table, verify that { [ (p q) ~ p ] ~ q } (p q) is a contradiction

where p,q,r are logical statements.

3) Using Truth Table, verify that

p (~q r) p ~(q ~r) [p (q ~r)] Where p,q and r are logical statements.

4) Draw Venn Diagrams of the following Statements

a) All real numbers are complex numbers.

b) Some Indians are living in America.

c) Some government servants are not talented.

d) No government industries are co. operative firms.

e) Some rectangles are not squares.



Practical 02. Matrices

Date :08/06/2015

1) A = 414

3 30 14 3

,find A-1 using Adjoin method and hence show that A2 = .Hence find A200

& A201 .

2) If A = 233

3 32 33 2

show that A2 7A 8 = 0.Hence find A-1.

3) If A = 05

1 24 1

and B = 103

021 , find AB. Also find (AB)-1, if exists.

4) For A = 21

32 , B =

13

01 verify that (AB)-1 = B-1 A-1.



Practical 03. Matrices Date :08/06/2015

1) Solve the following equations by the inversion method:

3 + 3 - 4 = 2; - = 1and 2 = 1.

2) Express the following equations in matrix form & Solve them by method of reduction: 2

+ = 1, + 2 + 3 = 8 and 3 + - 4 = 1

3) Solve, using reduction method, the following system of equations :

log + + 2 = 3; log + 2

+ 32 = 6 and 2log + 3 42 = 1

4) The cost of 4 pencils, 3 pens and 2 erasers is ` 60. The cost of 2 pencils, 4 pens and 6

erasers is ` 90and cost of 6 pencils, 2 pens and 3 erasers is ` 70. Find the cost of each item,

by using matrices.



Practical 04. Correlation of Bivariate Ungrouped Data

Date :15/06/2015

1) The following data relates production cost (in Rs. 000) and profit (in Rs. 000) of a

company for last seven years.

Production Cost (in 000) 12 9 8 10 11 13 7

Profit (in 000) 14 8 6 9 11 12 3 Calculate Karl Persons correlation coefficient between production Cost & Profit.

2) The following information is available from the data on two variables & .

( - )2 = 900, ( - )(- ) = 108, = 3, = 0.4.Find the number of pairs of

observations.

3) From the information given below, calculate the value of correlation co efficient. ( - 10)

( 15) = 105, ( 10) = 35, ( 15) = 60, n = 12, ( 10)2 = 148, ( - 15)2 = 450.

4) The following Table gives marks obtained by 5 students in the oral Test () and written

Test ()

Marks in Oral Test () 1 2 3 4 5

Marks in written Test () 5 7 9 11 13 Find the value of coefficient of correlation between marks in orals and marks in written

Test state the type of correlation.



Practical 05. Spearmans Rank Correlation Co Efficient

Date :15/06/2015

1) The Rank given to 12 candidates by two judges A and B in a singing competition are as

follows:

A 1 2 3 4 5 6 7 8 9 10 11 12

B 12 9 6 10 3 5 4 7 8 2 11 1 Find spearmans rank correlation coefficient. Do the Judges have contrasting opinions?

2) The following data relate to marks in economics and marks in statistics of 10, students in a

Marks in Economics 29 55 52 82 72 65 15 88 26 68 Marks In Statistics 39 25 48 76 52 58 59 81 41 74 Compute spearmans coefficient of correlation.

3) The following data gives marks obtained by 10 students in English () and statistics ()

X 82 32 72 62 32 87 52 67 32 27 Y 72 89 87 81 79 69 59 64 59 34

Calculate spearmans rank correlation coefficient.

4) Two tests were conducted for a group of 6 students. Marks were given for the first test

while grades were allotted for the second test. Find spearmans rank correlation coefficient

between marks & grades.

Marks 35 35 80 60 35 75

Grades B+ A+ C B A+ A



Practical 06. Regression Analysis

Date :29/06/2015

1) The following data gives expenditure in Rs. 000 () & profit in Rs. 000 () of a firm in

years 2001 to 2006

Year 2001 2002 2003 2004 2005 2006

Expenditure () 1 2 3 4 5 6 Profit () 2 4 7 6 5 6

Find regression equation of on and predict the profit when expenditure allocated in Rs.

1,00,000.

2) The regression equations are 5 6 +90 = 0 and 15 8 - 130 = 0. Also = 1.

Find , , , & .

3) Find the regression equation showing the capacity utilization on production from the

following data.

Average Standard Deviation

Production(in lakh units) 35.06 10.05

Capacity utilization(in percentage) 84.08 8.5

Coefficient of Correlation r = 0.62

Estimate the production when the capacity utilization is 70 percent.

4) The following table gives indices of industrial production and number of registered

unemployed persons(in lakhs)

Index of Production () 100 102 104 107 105 112 103 99 No. of unemployed () 15 12 13 11 12 12 19 26



Practical 07. Linear In equations

Date :05/07/2015

1) Find the set of all points satisfying the In equitation +4

2 >0, 2. Represent the solution

set in (a) Interval from as well as (b) Graphically.

2) Find the common region bounded by the in equations 2 + 3 12,

+ 3, 4 and 3. Also represent this region graphically.

3) Solve: 2 3 3 + 5, R. Represent the solution set on number line. Also

represent the solution in XOY plane.

4) Find the common region representing the in equitation: 3 + 2 1800,

2 + 7 1400, 0 350, 0 150. Write the Co-ordinates of the corner points of

the region.



Practical 08. Linear Programming Problems

Date :12/07/2015

1) Solve graphically the following Linear Programming Problem:

Minimize = 3 + 2, subject to 5 + 10, 2 + 2 12, + 4 12, 0, 0

2) A carpenter manufactures chairs and tables. He sells them at a profit of Rs. 200 per chair

and Rs. 300 per table. Both the products are to be processed on the three machines M1, M2

and M3. The time required for each product in hours and the total time available in hours

for each machine are as per the following.

Machine Chair Table Available time in hours M1 3 3 36 M2 5 2 50 M3 2 6 60

Determine the number of chairs & tables to be manufactured so as to get maximum profit.

3) Solve following problem graphically. Maximise Z = 2.7182 1 +3.1416 2 ,

Subject to 1 + 22 4, 2 1 - 2 8 and 1 0, 2 0.



Practical 09. Measurements of Mortality

Date :19/07/2015

1) Obtain Crude death rates for Town A and Town B given below and compare them

Age Group

Town A Town B Population (in

000) No. of Deaths Population (in

000) No. of Deaths

0 20 150 3520 120 2080 20 40 210 7040 220 2030 40 60 230 2160 210 2420

Above 60 180 3880 170 3970

2) Find the missing value if CDR = 13.08. Also find age SDRs

Age (years) 0 20 20 40 40 75 Above 75 Population (in 000) 8 7 4 No. of Deaths 96 84 72 93

3) Find age specific Death Rates for population A and B given by the following table.

Age Group 0 30 30 60 60 and above Population A in thousand 50 90 30 Death in A 150 180 200 Population B in thousand 60 100 20 Death in B 120 160 250

4) Find CDR and age SDRs from the following information:

Age Group Population in thousand No. of Deaths 0 30 10 150

30 60 14 140 60 80 9 180

80 and above 7 210



Practical 10. Construction of Life Tables

Date :19/07/2015

1) Fill in the blanks in the following life table.

ex0

21 95513 ? ? ? ? ? ? 22 94931 94626 3853229 ?

2) Construct the life table with columns , , , and for

0 1 2 3 4 5 l 60 40 35 20 10 0

3) For the following table find the terms marked by ?

ex0

5 90 ? ? ? ? 290 ? 6 80



Practical 11.Assignment Problems

Date :26/07/2015

1) A company has to assign four workers A,B,C and D to four jobs W, X, Y, and Z the cost

matrix is given below :

Jobs (cost in Rs.) W X Y Z

Workers

A 1000 1200 400 900 B 600 500 300 800 C 200 300 400 500 D 600 700 300 1000

Obtain an optimum assignment schedule and total cost required.

2) Four salesmen are to be assigned to four districts. Estimates of the sale revenue in

hundred of rupees for each sale are as follows.

District Salesman A B C D

1 320 350 400 280 2 400 250 300 220 3 420 270 340 300 4 250 390 410 350

Give the assignment pattern that will maximize the sale revenue. 3) Solve the following unbalanced assignment problem of minimizing total time for doing all the jobs.

Job Operator 1 2 3 4 5

1 6 2 5 2 6 2 2 5 8 7 7 3 7 8 6 9 8 4 6 2 3 4 5 5 9 3 8 9 7 6 4 7 4 6 8

4) Suggest optimum solution to the following assignment problem.

Services Time (in hrs) Salesman

Counter A B C D

W 41 72 39 52

X 22 29 49 65 Y 27 39 60 51 Z 45 50 48 52



Practical 12.Sequencing

Date :03/06/2015

1) Five jobs are to be processed. Each job must go through two machines A and B in order AB. The

time required for processing (in minutes) these jobs is given in the following table.

Job 1 2 3 4 5 A 6 2 10 4 11 B 3 7 8 9 5

Determine a sequence for these jobs which will minimize total required. Also find the idle

time for each machine.

2) Find the optimal sequence which minimizes total required for completing five jobs which

have to be processed on each of the machines M1, M2, M3 in that order. The processing

time for each Job on machine is given below. Also find the total elapsed time and idle time

for each machine.

Jobs 1 2 3 4 5

M1 6 7 5 11 5 M2 4 3 2 5 1 M3 3 8 7 4 9

3) Find the sequence that minimized the total time required in performing the following

jobs on three machines in the order X Y Z.

Jobs Machine

Processing time (in minutes)

1 2 3 4 5 6

X 8 3 7 2 5 1 Y 3 4 5 2 1 6 Z 8 7 6 9 10 9

4) The time (in hours) required to perfume the printing and binding operations in that

order for each book is given in the following table :

Book I II III III IV Printing Machine M1 3 7 4 5 7 Printing Machine M2 6 2 7 3 4

Find the sequence that minimizes the total elapsed time (in hours) to complete the work. Also

find the minimum elapsed time T and times for two machines



5) Five jobs are to be processed on three machines X, Y, Z in the order YXZ. The time

schedule for the entire task is as follows:

Machines Jobs P Q R S T

X 5 6 2 3 4 Y 4 9 8 6 5 Z 8 10 6 7 11

Determine the optimal sequence, state the total elapsed time and optain the idle times for

machines, X, Y, Z.

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SYJC Commerce Maths PractiseSums