12 STD BUSINESS MATHEMATICS · PDF file12/3/2012 · 12 std business mathematics 10 mark faq’s: chapter : 1. application of matrices and determinants 1. ¸if

12 STD BUSINESS MATHEMATICS

10 MARK FAQ’S:

CHAPTER : 1. APPLICATION OF MATRICES AND DETERMINANTS

1. If

312

321

111

A verify that .IAAAdjAAdjAA (M’10)

2. Show that the equations 2x – y + z = 7, 3x + y – 5z = 13, x + y + z = 0 are consistent and have

unique solution. (O’09)

3. NON – TEXTUAL: Solve by matrix method the equations 3x – y – z = -2; x + y + z = 6 ; x – 2y + 4z = 9

(J’09)

4. Solve by using matrix inversion method: ,5582 zyx ,2 zyx .22 zyx (J’07 ; M’09)

5. Solve by matrix method the equations .1z2yx2;3z4yx3;1z3y2x (M’06 ; J’08 ; O’10)

6. Solve by Cramer’s rule : ,122 zyx ,0 zyx .1323 zyx (J’06 ; M’07 ; M’08 ; O’08; J’11; M’12)

7. Solve by Cramer’s rule : ,2 yx ,6 zy .4 xz (O’07) 8. Solve the equations x + 2y + 5z = 23 ; 3x + y + 4z = 26 ; 6x + y + 7z = 47 by determinant method.

(J’10 ; M’11; O’11) 9. A salesman has the following record of sales during three months for three items A, B and C which

have different rates of commission.

Month Sales of Units Total commission

drawn (in Rs.) A B C January 90 100 20 800

February 130 50 40 900 March 60 100 30 850

Find out the rates of commission on the items A, B and C, Solve by Cramer’s rule. (O’06) 10. The data below are about an economy of two industries P and Q. The values are in lakhs of rupees.

Find the technology matrix and test whether the system is viable as per Hawkins – Simon

conditions.(O’08) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM – 8 ; PH : 94899 69230

Producer User Final

demand

Total

output P Q

P

Q

16

12

12

8

12

4

40

24

www.Padasalai.Net1

PADASALAI

11. In an economy there are two industries P and Q and the following table gives the supply and demand

positions in crores of rupees:

Determine the outputs when the final demand changes to 35 for P and 42 for Q.

(J’07 ; M’08 ; J’08 ; M’10 ; O’10 ; J’11 ; M’12) 12. In an economy of two industries P and Q the following table gives the supply and demand positions

in crores of rupees:

Find the outputs when the final demand changes to 18 for P and 44 for Q. (J’06 ; O’06 ; J’09) 13. The data below are about an economy of two industries P and Q. The values are in crores of rupees:

Find the outputs when the final demand changes to 300 for P and 600 for Q. (M’07 ; J’10) 14. In an economy of two industries P and Q the following table gives the supply and demand positions

in millions of rupees.

Find the outputs when the final demand changes to 20 for P and 30 for Q. (O’09)

15. Suppose that the inter-relationship between the production of two industries P and Q in a year (in

millions of rupees)

Find the outputs when the final demand changes (i) 12 for P and 18 for Q

(ii) 8 for P and 12 for Q. (O’11)

K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM – 8 ; PH : 94899 69230

Producer User Final

demand

Total

output P Q

P 10 25 15 50

Q 20 30 10 60

Producer User

Final demand Total output P Q

P

Q

16

8

20

40

4

32

40

80

Producer User

Final demand Total output P Q

P

Q

50

100

75

50

75

50

200

200

Producer User

Final Demand Total Output P Q

P 14 6 8 28

Q 7 18 11 36

Producer User

Final Demand Total Output P Q

P 16 20 4 40

Q 8 40 32 80

www.Padasalai.Net2

PADASALAI

16. Two products A and B currently share the market with shares 60% and 40% each respectively. Each

week some brand switching takes place. Of those who bought A the previous week, 70% buy it again

whereas 30% switch over to B. Of those who bought B the previous week, 80% buy it again whereas

20% switch over to A. Find their shares after one week and after two weeks. If the price war

continues, when is the equilibrium reached? (O’07)

17. Two products P and Q share the market currently with shares 70% and 30% each respectively. Each week some brand switching takes place. Of those who bought P in the previous week, 80% buy it again whereas 20% switch over to Q. Of those who bought Q in the previous week, 40% buy it again whereas 60% switch over to P. Find their shares after two weeks. If the price war continues, when is

the equilibrium reached? (M’06 ; M’09)

18. The newspapers A and B are published in a city. Their present market shares are 15% for A and 85% for B. Of those who bought A the previous year 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year 55% buy it again and 45% switch over to A. Find their

market shares after two years. (M’11)

CHAPTER : 2. ANALYTICAL GEOMETRY

1. Find the centre, vertices, eccentricity, foci and latus rectum and directrices of the ellipse .092y32x36y16x9 22 (M’08 ; J’10 ; J’11)

2. Find the centre, vertices, eccentricity, foci and latus rectum and directrices of the ellipse .079401447 22 yxyx (O’07 ; O’10)

3. Find the centre, eccentricity, foci and directrices of the ellipse

.05y8x6y4x3 22 (M’06 ; O’08 ; J’09)

4. Find the centre, eccentricity, foci and directrices of the hyperbola

.01273224412 22 yxyx (J’07)

5. Find the centre, eccentricity, foci and latusrectum of the hyperbola

.01996418169 22 yxyx (O’06 ; J’08)

6. Find the equation to the hyperbola which has the lines x + 4y – 5 = 0 and 2x – 3y + 1 = 0 for its

asymptotes and which passes through the point (1,2). (M’11)

7. Find the equation to the hyperbola which has 3x – 4y + 7 = 0 and 4x + 3y + 1 = 0 for asymptotes and

which passes through the origin. (M’12) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM – 8 ; PH : 94899 69230

www.Padasalai.Net3

PADASALAI

8. Find the equations of the asymptotes of the hyperbola

.04711252 22 yxyxyx (J’06 ; M’07 ; M’09)


.02423108 22 yxyxyx (M’10 ; O’11)


.01417253 22 yxyxyx (O’09)

CHAPTER : 3. APPLICATION OF DIFFERENTIATION - I

1. A firm produces x tones of output at a total cost .82542

1.)( 23

xxxRsxC Find (i) Average cost

(ii) Average Variable Cost (iii) Average Fixed Cost. Also find the value of each of the above when the

output level is 10 tonnes. (O’10)

2. Find the elasticity of demand, when the demand is 1

20

pq and p = 3. Interpret the result. (M’10)

3. If AR and MR denote the average and marginal revenues at any output level, show that elasticity of

demand is equal to .MRAR

AR

Verify this for the linear demand law ,bxap where p is price and x is

the quantity. (M’07 ; J’08 ; J’11)

4. Prove that for the cost function ,2100 2xxC where x is the output,

the slope of AC curve = .1

ACMCx

(MC is the marginal cost and AC is the average cost) (O’07)

5. Determine the coefficients a and b so that the curve y = ax2 – 6x + b may pass through the point (0,2)

and have its tangent parallel to the x-axis at x = 1.5. (J’09)

6. Find the equation of the tangent and normal to the demand curve 22 xxy at .6x (O’06)

7. Prove that the curves y = x2 – 3x + 1 and x(y + 3) = 4 intersect at right angles at the point (2,-1).(J’06)

8. Find the equations of the tangent and normal to the curve 07x3x2xy at the point where it

cuts the x-axis. (M’06 ; M’09 ; M’11 ; O’11 ; M’12)

9. Find the equations of the tangent and normal at the point tanb,seca on the hyperbola

.1b

y

a

x2

2

2

2

(M’08 ; O’08)


www.Padasalai.Net4

PADASALAI

10. Find the point on the curve y = (x – 1)(x – 2) at which the tangent makes an angle 135 with the positive

direction of x – axis. (J’10)

11. At what points on the circle x2 + y

2 – 2x - 4y + 1 = 0, the tangent is parallel to (i) x-axis (ii) y-axis.

(J’07 ; O’09)

CHAPTER : 4. APPLICATION OF DIFFERENTIATION - II

1. Find the maximum and minimum values of the function .1596 23 xxx (O’06)

2. Investigate the maxima and minima of the function .10x36x3x2 23 (M’08 ; O’10)

3. Find the maximum and minimum values of the function .1524152 23 xxx (M’06 ; J’11)

4. NON – TEXTUAL: Investigate the maxima and minima of the function .151292 23 xxx (O’09)

5. Show that the maximum value of the function 108x27x)x(f 3 is 108 more than the minimum

value. (J’08)

6. For the cost function C = 2000 + 1800x - 75x2 + x3 find when the total cost (C) is increasing and when it is

decreasing . Also discuss the behavior of the marginal cost (MC) (J’09)

7. A certain manufacturing concern has total cost function C = 15 + 9x – 6x2 + x

3. Find x, when the total cost

is minimum. (M’10)

8. A firm produces x tonnes of output at a total cost .510510

1 23 xxxC At what level of output will

the marginal cost and the average variable cost attain their respective minimum? (J’07)

9. R = 21x – x2 and 16x9x3

3

xC 2

3

are respectively the sales revenue and cost function of x units

sold. Find the following:

(i) At what output is the revenue maximum? What is the total revenue at this point?

(ii) What is the marginal cost at a minimum?

(iii) What output will maximise the profit? (M’09 ; M’11)

10. A Radio manufacturer finds that he can sell x radios per week at Rs.p each, where .4

1002

xp His

cost of production of x radios per week is Rs. .2

1202

xx Show that his profit is maximum when the

production is 40 radios per week. Find also his maximum profit per week. (O’08)


www.Padasalai.Net5

PADASALAI

11. The total cost and total revenue of a firm are given by C = x3 – 12x

2 + 48x + 11 and R = 83x – 4x

2 – 21.

Find the output (i) when the revenue is maximum (ii) when the profit is maximum? (J’10)

12. Find EOQ for the data given below. Also verify that carrying costs is equal to ordering costs at EOQ.

(J’06)

Item Monthly

Requirements

Ordering

cost per

order

Carrying

cost per

unit

A 9000 Rs.200 Rs.3.60

B 25000 Rs.648 Rs.10.00

C 8000 RS.100 Rs.0.60

13. A manufacturer has to supply his customer with 600 units of his products per year. Shortages are not

allowed and storage cost amounts to 60 paise per unit per year. When the set up cost is Rs. 80

find, (i) The economic order quantity (ii) The minimum average yearly cost (O’07)

14. Calculate EOQ in units and total variable cost for the following item, assuming an ordering cost of Rs.5

and a holding cost of 10%.

Item A

Annual demand 460 units

Unit price Re. 1 (M’12)

15. The annual demand for an item is 3200 units. The unit cost is Rs.6 and inventory carrying charges 25%

per annum. If the cost of one procurement Rs.150, determine (i) Economic order quantity (ii) Time

between two consecutive orders. (M’07)

16. If ,zyxlogu 222 then prove that .zyx

1

z

u

y

u

x

u2222

2

2

2

2

2

(J’08 ; O’08 ; O10)

17. If

yx

yxtanu

221

then prove that u2sin2

1

y

uy

x

ux

by Euler’s theorem. (M’08)

18. If ,33 yxez then prove that .log3 zz

y

zy

x

zx

(Use Euler’s theorem). (M’10 ; J’10 ;O’11)

19. NON – TEXTUAL: Prove using Euler’s theorem if

yx

yxu 1cos then

.0cot2

1

u

y

uy

x

ux (O’06)

20. NON – TEXTUAL: Prove using Euler’s theorem if yx

yxu

33

then .2

5u

y

uy

x

ux

(J’07)

21. The demand for a commodity A is .6240 212

2

11 ppppq Find the partial elasticities

1

1

Ep

Eqand

2

1

Ep

Eq when p1 = 5 and p2 = 4.(M’06 ; J’06 ; M’07 ; O’09 ; M’11; O’11 ; M’12)


www.Padasalai.Net6

PADASALAI

22. The demand for a commodity A is .p2p316q2

211 Find (i) the partial elasticities 1

1

Ep

Eqand

2

1

Ep

Eq

(ii) the partial elasticities when 2p1 and 1p2 .(O’07 ; M’08 ; J’09)

23. The demand for a commodity A is .12 21

2

11 pppq Find (i) the partial elasticities 1

1

Ep

Eqand

2

1

Ep

Eq

(ii) the partial elasticities when 101 p and 42 p .(J’11)

CHAPTER : 5. APPLICATIONS OF INTEGRATION

1. Evaluate:

3

6

.xtan1

dx

(J’06 ; M’09 ; J’10 ; M’11;J’11;O’11)

2. Evaluate:

3

6

.cot1

x

dx (M’07 ; M’08 ; O’10)

3. Evaluate:

2

033

3

.dxxcosxsin

xsin

(M’06)

4. Evaluate:

2

0cossin

cossin

dxxx

xbxa (J’07 ; O’08)

4. Evaluate:

2

0

.2

dxxx

x (J’09 ; M’12)

5. NON – TEXTUAL: Evaluate:

3

0

.3

dxxx

x (M’10)

6. Evaluate:

0

2 .sin xdxx (O’09)

7. NON – TEXTUAL: Find the area of one loop of the curve 222 9 xxy between 0x and

.3x (J’08)

8. NON – TEXTUAL: Find the area of one loop of the curve 22222 xaxya between 0x and

.ax (O’08)

9. NON – TEXTUAL: Find the area of one loop of the curve 222 4 xxy between 0x and

.2x (O’06)

10. Find the area of the ellipse .12

2

2

2

b

y

a

x (J’09)

11. The elasticity of demand (x) with respect to price p is .3,3

xx

x Find the demand function and the

revenue function when the price is 2 and the demand is 1. (M’11)

12. Find the consumers’ surplus for the demand function p = 25 – x – x2 when p0 = 19. (O’08)


www.Padasalai.Net7

PADASALAI

13. Find the consumers’ surplus and producers’ surplus under market equilibrium if the demand

function is 2320 xxpd and the supply function is .1 xps (M’06 ; O’07;J’11)

14. The demand and supply curves are 4x

16pd

and .

2

xps Find the consumers’ surplus and

producers’ surplus at market equilibrium price. (J’08)

15. The demand and supply function for a commodity are given by xpd 15 and .23.0 xps Find the

consumers’ surplus and producers’ surplus at market equilibrium price. (M’07)

16. The demand and supply law under a pure competition are given by pd = 23 – x2 and ps = 2x

2 – 4. Find

the consumers’ surplus and producers’ surplus at the market equilibrium price. (O’06 ; O’10)

17. Under pure competition The demand and supply laws for commodity and pd = 56 – x2 and

.3

82x

ps Find the consumers’ surplus and producers’ surplus at the market equilibrium price.

(J’07;O’11)

18. In a perfect competition The demand and supply curves of a commodity are given by pd = 40 – x2 and

.883 2 xxps Find the consumers’ surplus and producers’ surplus at the market equilibrium price.

(O’09 ; J’10) .

The demand and supply functions under pure competition are 2

d x16p and .4x2p 2

s Find the

consumers’ surplus and producers’ surplus at market equilibrium price. (J’06 ; M’08 ; M’09 ; M’10 ;

M’12)

CHAPTER : 6. DIFFERENTIAL EQUATIONS

1. The net profit p and quantity x satisfy the differential equation .xp3

xp2

dx

dp2

33 Find the relationship

between net profit and demand given that 20p when .10x (M’06)

2. Solve : .

yx

xy

dx

dy22

(M’09 ; M’10)

3. Solve : .

2

22

2

xyx

xyy

dx

dy

(O’10)

4. Solve : .2

2

x

y

x

y

dx

dy (O’11)


www.Padasalai.Net8

PADASALAI

5. The rate of increase in the cost c of ordering and holding as the size q of the order increases is given by

the differential equation .2

22

cq

qc

dq

dC Find the relationship between c and q, if c = 4 and q = 2.

(J’11)

6. Suppose that 2

2

2530dt

Pd

dt

dPPQd and ,36 PQs where P denotes price. Find the

equilibrium price for market clearance. (J’06 ; M’07 ; J’ 07 ; M’08 ; O’08 ; M’12)

7. Suppose that 2

2

4442dt

Pd

dt

dPPQd and ,86 PQs where P denotes price. Find the

equilibrium price for market clearance. (J’09 ; M’11)

8. Solve : .51213 22 xx eeyDD (O’06 ; O’09 ; J’10)

9. Solve : .3125 22 xx eeyDD (J’08)

10. Solve : .34914 72 xeyDD (O’07)

CHAPTER : 7. INTERPOLATION AND FITTING A STRAIGHT LINE

1. From the following data calculate the value of e1.75 (O’09) x: 1.7 1.8 1.9 2.0 2.1

ex: 5.474 6.050 6.686 7.389 8.166

2. From the following data, find the number of students whose height in between 80 cm and 90 cm: (M’08)

3. Find the number of men getting wages between Rs.30 and Rs.35 from the following table. (O’11)

4. Find y when 2.0x given that (O’10) x: 0 1 2 3 4

y: 176 185 194 202 212


Height in cm x: 40 – 60 60 - 80 80 – 100 100 - 120 120 - 140

No. of students y: 250 120 100 70 50

Wages x: 20 – 30 30 – 40 40 – 50 50 – 60

No. of men y: 9 30 35 42

www.Padasalai.Net9

PADASALAI

5. Using Gregory-Newton’s formula, find y(22.4) (M’11) X: 19 20 21 22 23

Y: 91 100 110 120 131

6. Using Lagrange’s formula find y when x = 4 from the following table (J’08 ; M’10) x: 0 3 5 6 8

y: 276 460 414 343 110

7. Fit a straight line to the following data: (J’06 ; O’06 ; O’07 ; J’11 ; M’12)

x: 4 8 12 16 20 24

y: 7 9 13 17 21 25

8. Fit a straight line baxy to the following data by the method of least squares: (M’06)

9. Fit a straight line baxy to the following data by the method of least squares: (M’07 ; J’07)

10. Fit a straight line to the data given below. Also estimate the value of y at x = 3.5 : (M’09 ; J’10)

11. A group of 5 students took tests before and after training and obtained the following scores. (O’08)

Find by the method of least squares the line of best fit.

CHAPTER : 8. PROBABILITY DISTRIBUTION

1. Given the p.d.f of a continuous random variable X as follows otherwise

xforxkxxf

10

0

)1()(

Find k and c.d.f. (J’09)


x: 100 200 300 400 500 600

y: 90.2 92.3 94.2 96.3 98.2 100.3

x: 0 1 3 6 8

y: 1 3 2 5 4

x: 0 1 2 3 4

y: 1 1.8 3.3 4.5 6.3

Scores before training 3 4 4 6 8

Scores after training 4 5 6 8 10

www.Padasalai.Net10

PADASALAI

2. Suppose that the life in hours of a certain part of radio tube is a continuous random variable X with

p.d.f given by elsewhere

xwhenxxf

100

0

;100

)( 2

(i) What is the probability that all of three such tubes in a given radio set will have to be replaced during the first of 150 hours of operation?

(ii) What is the probability that none of three of the original tubes will have to be replaced during

that first 50 hours of operation? (M’10)

3. A random variable X has the following probability probability distribution. x: 0 1 2 3 4 5 6 7 8

P(x) a 3a 5a 7a 9a 11a 13a 15a 17a (i) Determine the value of a

(ii) Find P(X < 3) , P(X > 3) and P(0 < X < 5) (J’07 ; O’09)

4.

A continuous random variable has the following p.d.f:

0

,kx)x(f

2

otherwise

10x0

Determine k and evaluate (i) 5.0x2.0P (ii) .3xP (M’08)

5. Let X be a continuous random variable with p.d.f otherwise

xxf

11

0

,2

1

)(

Find (i) E(X) (ii) E(X2) (iii) Var(X) (O’06 ; O’10)

6. Find the mean and variance for the probability distribution:

0

,e2)x(f

x2

0x

0x

(M’06 ; J’06 ; O’08 ; M’09 ; M’11 ; J’11)

NON – TEXTUAL: Find the mean and variance for the probability distribution

otherwise

xxxf

10

,0

,2

1

)(

(O’07)

7. NON – TEXTUAL: In a continuous distribution, whose probability density function is given

byotherwise

xxxxf

20,

,0

)2(4

3

)(

Show that the arithmetic mean of the distribution is 1 and the

variance is .5

1 (M’07)

8. Ten coins are thrown simultaneously. Find the probability of getting at least 7 heads. (M’06;O’10;O’11) 9. For a binomial distribution with parameters n = 5 and p = 0.3 find the probabilities of getting (i) at least

3 successes (ii) at most 3 successes. (J’10)


www.Padasalai.Net11

PADASALAI

10. Find the probability that at most 5 defective bolts will be found in a box of 200 bolts, If it is known that

2% of such bolts are expected to be defective. (e-4

= 0.01832) (M’10 ; M’12)

11. It is stated that 2% of razor blades supplied by a manufacturer are defective. A random sample of 200

blades is drawn from a lot. Find the probability that 3 or more blades are defective. (e-4

= 0.01832) (J’09)

12. NON – TEXTUAL: The number of accidents in a year attributed to taxi drivers in a city follows

Poisson distribution with mean 3.Out of 500 taxi drivers, find the approximate number of drivers with

(i) no accident in a year (ii) more than 2 accidents in a year. (e-3 = 0.04979) (M’11)

13. A sample of 1000 candidates the mean of certain test is 45 and S.D 15. Assuming the normality of the

distribution find the following: (i) How many candidates score between 40 and 60?

(ii) How many candidates score above 50?

(iii) How many candidates score below 30? (O’09 ; J’11)

14. The I.Q (intelligence quotient) of a group of 1000 children has mean 96 and the standard deviation 12.

Assuming the distribution as normal, find approximately the number of children having I.Q.

(i) less than 72. (ii) between 80 and 120. (M’07 ; J’07 ; M’08)

15. NON – TEXTUAL: The distribution of marks obtained by 1000 students in an examination is

normally distributed with mean 34 and S.D 16.

(i) Find the number of students scoring between 30 and 60 marks and

(ii) Find the number of students scoring above 70 marks. (J’06)

16. In a normal distribution 20% of items are less than 100 and 30% are over 200. Find the mean and S.D

of the distribution. (J’08 ; O’11 ; M’12)

Z 0.84 0.525 Area 0.3 0.2

17. The mean yield for one-acre plot is 663 kg with an S.D of 32 kg. Assuming normal distribution, how many one-acre plots in a batch 1000 plots would you expect to have yield (i) over 700 kg? (ii) below

650 kg? (M’09) 18. A large number of measurements is normally distributed with a mean of 65.5” and S.D of 6.2”. Find the

percentage of measurements that fall between 54.8” and 68.8”. (O’06 ; J’10) 19. The diameter of shafts produced in a factory conforms to normal distribution. 31% of the shafts

have a diameter less than 45 mm and 8% have more than 64 mm. Find the mean and standard

deviation of the diameter of shafts.(O’07 ; O’08)


www.Padasalai.Net12

PADASALAI

CHAPTER : 9. SAMPLING TECHNIQUES AND STATISTICAL INFERENCE 1. A sample of 100 students are drawn from a school. The mean weight and variance of the sample are

67.45 kg and 9 kg. respectively. Find (a) 95% and (b) 99% confidence intervals for estimating the mean

weight of the students. (J’07)

2. Out of 1000 TV viewers, 320 watched a particular programme. Find 95% confidence limits for

TV watched this programme.(O’07)

3. A sample of five measurements of the diameter of a sphere were recorded by a scientist as 6.33,

6.37, 6.32 , 6.36 and 6.37 mm. Determine the point estimate of (a) mean, (b) variance. (O’09 ; J’10)

4. The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825

hours with a standard deviation of 110 hours. If is the mean life time of all the bulbs produced by

the company, test the hypothesis that 900 hours at 5% level of significance. (M’07;M’09;O’11)

5. A company markets car tyres. Their lives are normally distributed with a mean of 50000 kilometers and

standard deviation of 2000 kilometers. A test sample of 64 tyres has a mean life of 51250 kms. Can you

conclude that the sample mean differs significantly from the population mean? (Test at 5% level)

(O’06)

6. A sample of 400 students is found to have a mean height of 171.38 cm. Can it reasonably be regarded

as a sample from a large population with mean height of 171.17 cm and standard deviation of 3.3 cm?

(Test at 5% level). (M’06 ; O’08 ; J’11)

7. To test the conjecture of the management that 60 percent employees favour a new bonus scheme, a

sample of 150 employees was drawn and their opinion was taken whether they favoured it or not. Only

55 employees out of 150 favoured the new bonus scheme. Test the conjecture at 1% level of

significance. (J’06 ; M’11)

8. The mean I.Q. of a sample of 1600 children was 99. Is it likely that this was a random sample from a

population with mean I.Q. 100 and standard deviation 15? ( Test at 5% level of significance ) (J’08 ; J’09 ; M’10 ; O’10 ; M’12)

9. The income distribution of the population of a village has a mean of Rs.6,000 and a variance of Rs.

32,400. Could a sample of 64 persons with a mean income of Rs. 5,950 belong to this population?

(Test at both 5% and 1% levels of significance) (M’08)


www.Padasalai.Net13

PADASALAI

CHAPTER : 10. APPLIED STATISTICS

1. Solve graphically:

Minimize 21 x40x20Z

Subject to 108x6x36 21 ; 36x12x3 21 ; 100x10x20 21 ; 0x,x 21 ( J’07 ; M’08) 2. Solve the following, using graphical method:

Maximize 21 43 xxZ

subject to the constraints 402 21 xx ; 18052 21 xx ; .0, 21 xx (J’06 ; J’10 ; O’11)

3. Solve the following, using graphical method:

Minimize 21 23 xxZ

subject to the constraints 105 21 xx ; 1222 21 xx ; 124 21 xx ; .0, 21 xx (O’09 ; J’11)

4. Solve the following, using graphical method:

Maximize 21 8045 xxZ

subject to the constraints 400205 21 xx ; 4501510 21 xx ; .0, 21 xx (O’10 ; M’12)

5. NON – TEXTUAL: Solve graphically:

Maximize 21 x3x5Z

Subject to 1000xx2 21 ; 400x0 1 ; 700x0 2 ; .0x,x 21 (M’09)

6. NON – TEXTUAL: Solve the following using graphical method:

Maximize 21 x6x5Z

Subject to the constraints, 120x2x3 21 ; 260x6x4 21 ; 0x,x 21 (M’06)

7. Find the co-efficient of correlation for the data given below: (O’06 ; J’08 ; J’09)

8. Obtain the two regression lines from the following: (M’10)


X : 10 12 18 24 23 27

Y : 13 18 12 25 30 10

X : 6 2 10 4 8

Y : 9 11 5 8 7

www.Padasalai.Net14

PADASALAI

9. From the data given below calculate Seasonal Indices. (O’09 ; J’10)

10. Calculate the seasonal indices by the method of simple average for the following data: (M’08)

Year Quarters

I II III IV

1985

1986

1987

65

68

68

60

55

60

61

66

63

63

61

67

11. Calculate the seasonal indices for the following data using average method: (M’06 ; M’11)

Year Quarters

I II III IV

1982

1983

1984

1985

1986

72

76

74

76

78

68

70

66

74

74

80

82

84

84

86

70

74

80

78

82

12. Calculate Fisher’s ideal index from the following data: (O’07)


Quarter Year

1984 1985 1986 1987 1988 I 40 42 41 45 44 II 35 37 35 36 38 III 38 39 38 36 38 IV 40 38 40 41 42

Commodity

Price Quantity

1985 1986 1985 1986

A

B

C

D

E

8

2

1

2

1

20

6

2

5

5

50

15

20

10

40

60

10

25

8

30

www.Padasalai.Net15

PADASALAI

13. Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s index numbers for the year 2000

from the following: (O’06 ; J’08)

14. From the following data calculate the price index number by (a) Laspeyre’s method,

(b) Paasche’s method and (c) Fisher’s method: (M’07) 15. From the following data calculate the price index number by (a) Laspeyre’s method,

(b) Paasche’s method and (c) Fisher’s method: (M’10)

16. From the following data calculate the price index number by (a) Laspeyre’s method,

(b) Paasche’s method and (c) Fisher’s method: (M’12)


Commodity

Price Quantity

1980 1990 1980 1990

A 2 4 8 6

B 5 6 10 5

C 4 5 14 10

D 2 2 19 13

Commodity

Base year Current Year

Price Quantity Price Quantity

A

B

C

D

5

10

3

6

25

5

40

30

6

15

2

8

30

4

50

35

Commodity



A

B

C

D

E

2

4

6

8

10

40

50

20

10

10

6

8

9

6

5

50

40

30

20

20

Commodity



A

B

C

D

2

4

6

10

40

50

20

10

6

8

9

5

50

40

30

20

www.Padasalai.Net16

PADASALAI

17. NON – TEXTUAL: Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s index numbers for the year

2000 from the following: (M’09)

18. From the following data, construct Fisher’s Ideal index and show that it satisfies factor Reversal test

and Time Reversal test: (J’06 ; J’11)


and Time Reversal test: (O’10)


and Time Reversal test: (J’07 ; O’08)


Commodity

Price Quantity

1990 2000 1990 2000

A 2 4 8 6

B 5 6 10 5

C 4 5 14 10

D 2 2 19 13

Commodity



A

B

C

D

E

F

10

8

12

20

5

2

10

12

12

15

8

10

12

8

15

25

8

4

8

13

8

10

8

6

Commodity



A

B

C

D

10

7

5

16

12

15

24

5

12

5

9

14

15

20

20

5

Commodity



A

B

C

D

E

6

2

4

10

8

10

2

6

12

12

50

100

60

30

40

56

120

60

24

36

www.Padasalai.Net17

PADASALAI

21. Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s index numbers for the following data: (O’11)

22. Calculate the cost of living Index Number using Family Budget method: (J’09) Commodity A B C D E F G H

Quantity in base year (unit)

20 50 50 20 40 50 60 40

Price in Base year(Rs.)

10 30 40 200 25 100 20 150

Price in current year(Rs.)

12 35 50 300 50 150 25 180

23. The following data shows the value of sample mean X and the range R for ten samples of size 6 each.

Calculate the values for central line and control limits for mean chart and range chart and determine

whether the process is in control. (M’07)

(Given for n = 6 , A2 = 0.483 , D3 = 0 , D4 = 2.004 )

24. The following data shows the value of sample mean X and the range R for ten samples of size 5

each. Calculate the values for central line and control limits for mean chart and range chart and

determine whether the process is in control. (O’07 ; O’08 ; M’11) Sample No. 1 2 3 4 5 6 7 8 9 10

Mean X

11.2 11.8 10.8 11.6 11.0 9.6 10.4 9.6 10.6 10.0

Range R 7 4 8 5 7 4 8 4 7 9

(Given for n = 5 , A2 = 0.577 , D3 = 0 , D4 = 2.115 )


Commodity

Price Quantity

Base year Current

year Base year

Current

year

A

B

C

D

6

2

4

10

10

2

6

12

50

100

60

30

50

120

60

25

Sample No. 1 2 3 4 5 6 7 8 9 10

Mean X 681 586 651 641 680 639 665 604 569 629

Range R 118 167 134 171 490 200 236 188 309 257

www.Padasalai.Net18

PADASALAI

Documents

12 STD BUSINESS MATHEMATICS · PDF file12/3/2012 · 12 std business mathematics 10 mark faq’s: chapter : 1. application of matrices and determinants 1. ¸if