Maths Ii

OMTEX CLASSES MATHS II

Total marks 40

IST PRELIMINARY EXAMINATION Code: OM 2008 Q1. (A) Attempt any one of the following: i.

In a school, out of 200 students 150 are boys. In an examination conducted in this school, 120 students passed. If 10 girls failed, find the a. Number of boys failed in the examination. b. Number of girls passed in the examination. ii. In a group of 100 employees of a firm there were 80 males. The number of married employees was 60, of whom 30 were males. Examine whether the information is correct. (B) Attempt any one of the following. i.

If (A) = (B) =4, N = 8 and A, B are independent attributes, find the value of (AB) and (αB). ii. Find Yule’s coefficient of association from the following data: (A) = 60, (B) = 80, (AB) = 50, N = 100. (C) Attempt any one of the following. i.

Find both the regression coefficients and the measure of the acute angle between the regression lines from the following data. n=10, x=250, y=300, x2=6500, y2=10,000 and xy=7,900.

ii.

If 5x+y=21 and 4x+5y=42 are the two regression equations find x, y and rthe coeficient of correlation.

Q2. (A) Attempt any ONE of the following:

i. ii. iii.

Using Simpson’s 38th rule, evaluate 06ydxfrom the following table given

below. If f0= 5, f1= 6, f2= 10, f3= 15, 0 1 2 x 1 0.7 0.58 y If f0= 5, f1= 6, f2= 10, f3= 15, evaluate 03fxdxusing Trapesoidal Rule.

3 0.5

4 0.45

5 0.41

6 0.38

(B) Attempt any ONE of the following. i. Construct both the difference tables (i.e. backward and forward) for the sequence 8, 3, 0,-1, 0, 3. ii.Prove that ∆Efx=E[∆fx] (C) Attempt any one of the following. i. Six jobs go first over the machine M and then over the machine N, one at a time. The time schedule for the task is given below. Determine the sequence of the jobs, which will minimize the processing time. Also find the total elapsed time and the idle times for both the machines. ii.Find the optimal sequence that minimizes total time required to complete five jobs, which have to be processed on each of the three machines M1, M2, M3 if the processing time for each job on each machine is given below. Also find the total elapsed time and idle time for M2. Machines

Jobs A

B

C

D

E

F

OMTEX CLASSES MATHS II

Total marks 40

IST PRELIMINARY EXAMINATION Code: OM 2008 M 5 9 4 7 8 6 N 7 4 8 3 9 5 iii.Find the optimal sequence that minimizes total time required to complete five jobs, which have to be processed on each of the three machines M1, M2, M3 if the processing time for each job on each machine is given below. Also find the total elapsed time and idle time for M2.

OMTEX CLASSES MATHS II

Total marks 40

IST PRELIMINARY EXAMINATION Code: OM 2008 Machines M1 M2 M3

P 6 4 3

Jobs R 5 2 7

Q 7 3 8

S 11 5 4

T 5 1 9

Q3. (A) Attempt any ONE of the following: i. A company manufactures two models of cars: model A and model B. To stay in business it must produce at least 50 cars of model A per month. It has facilities to produce at most 200 cars of model A and 150 cars of Model B per month. The total demand for both models together is at most 300 cars per month. The profit per car is Rs. 4000 for model A and Rs. 3,000 for model B. It is required to determine the number of cars of each type to be manufactured so as to get maximum profit. Formulate this problem as a L.P.P. ii.Represent graphically, the common solution set of the inequalities 3x+y≤6,

x+y≤4, x+3y≥2, x≥0 & y≥0.Also find the co-ordinates of vertices of the feasible region so obtained. (B) Attempt any One of the following. i. If for a binomial distribution probability of success is ¼ and the mean is 12.5, find the remaining parameters of the distribution. ii.The probability that A wins a game of chess against B is23. Find the probability that A wins at least ‘one’ game out of the 4 games he plays against B. (C). Attempt any One of the following.

i. For the given data write the entries in the column of dx, qx, px, and lx of thelife table, where notations have their usual meanings. 0 1 2 3 4 5 x 4 3 1 20 4 0 l 0 x 000 000 000 0 ii.For the following table find the terms marked by “?”.

x lx

d x

5

?

6

9 0 8 0

Q4. (A) Attempt any One of the following.

q x

p x

L x

Tx

?

?

29 0 ?

e x 0 ?

OMTEX CLASSES MATHS II

Total marks 40

IST PRELIMINARY EXAMINATION Code: OM 2008 i. If X is a Poisson random variable such that P(X= 3) = P(X = 4), find the mean and standard deviation of the distribution. ii.If X is a Poisson variate with mean 3, find x≥2). [Given:e-3=0.0498]

OMTEX CLASSES MATHS II

Total marks 40

IST PRELIMINARY EXAMINATION Code: OM 2008 (B) Attempt any One of the following. i. Construct cost of living index number for the following data. ii.The cost of living index numbers for the year 2001 and 2007 are 150 and 200 respectively. A person earned Rs. 18,000 per month in the year 2001. What should be his earnings per month in the year 2007, so as to maintain his former (i.e. the year 2001) standard of living? Group

Base Year P ric e

Quant ity

Current year Price

Food and 40 3 70 Clothing Fuel and 30 5 60 lighting House Rent 50 2 50 Miscellaneous 60 3 90 iii.The cost of living index numbers for the year 2001 and 2007 are 150 and 200 respectively. A person earned Rs. 18,000 per month in the year 2001. What should be his earnings per month in the year 2007, so as to maintain his former (i.e. the year 2001) standard of living? (C) Attempt any One of the following.

i. ii.

Find f(3.5)using Newton’s Backward Interpolation formula from the following table. Find f(6), using Lagrange’s Interpolations formula, given that f1=4, f7=5, f8= 4.

x fx

iii.

0 1 3 6

2 3 4 1 1 2 1 8 7 Find f(6), using Lagrange’s Interpolations formula, given that f1=4, f7=5, f8= 4.

Q5. (A) Attempt any ONE of the following. i.

ii.

Find the missing price, if Laspeyre’s price index numbe is equal to Paasche’s Price index number for the following data. If p0q0=150, p0q1=250, p1q1=371 and Laspeyre's price index number is

140, Commod ity A B

Base year Pric Quanti e ty 1 1

10 5

Current year Pric Quanti e ty 2 -

5 2

OMTEX CLASSES MATHS II

Total marks 40

IST PRELIMINARY EXAMINATION Code: OM 2008 iii. If p0q0=150, p0q1=250, p1q1=371 and Laspeyre's price index number is 140, Find Marshall – Edgeworth’s Index number. (B) Attempt any ONE of the following.

i.

If the total population under study is 45,000 and the age S.D.R. for age group (60 and above) is 25, find the C.D.R. and the values of x, y from the following data. Age group 0 – 30 30 – 60 600 and above

ii.

Populati on 4,000

x y

Taking the population of town B as standard population, compare the S.T.D.R. for the populations of towns A and B from the data given below. Age group

Town A Age S.D.R.

Town B Populati Number of on Deaths

0 – 10 7 10 – 40 4.5 40 and 18 above (C) Attempt any ONE of the following:

i.

3000 10000 7000

32 100 84

A chartered Accountants’ firm has accepted ‘five’ new cases. The estimated number of days required by each of their ‘five’ employees for each case are given below, where ‘_’ means that the particular employee can not be assigned the particular case. Determine the optimal assignment of cases to the employees so that the total number of days required completing these ‘five’ cases will be minimum. Also find the minimum number of days. Employe Cases I I II I V es I I V

E1 E2 E3 E4 E5 ii.

Number of Deaths 100 150 650

5 3 6 4 3

2 4 3 2 6

4 4 2 4

2 5 1 3 7

6 7 2 5 3

The cost (in hundreds of Rs.) of sending material to ‘five’ terminals by ‘four’ trucks, incurred by a company is as given below. Find the assignment of trucks to terminals which will minimise the cost. [‘One’ truck is assigned to only ‘one’

OMTEX CLASSES MATHS II

Total marks 40

IST PRELIMINARY EXAMINATION Code: OM 2008 terminal.] Which terminal will ‘not’ receive material from the truck company? What is the minimum cost? Termin als

T1 T2 T3 T4 T5

Trucks A B C D 3 7 3 5 5

6 1 8 2 7

2 4 5 4 6

6 4 8 3 2