12 STD BUSINESS MATHEMATICS

Transcription

1 STD BUSINESS MATHEMATICS 0 MARK FAQ S: CHAPTER :. APPLICATION OF MATRICES AND DETERMINANTS. If A verify that AAdjA AdjA A AI. (M 0). Show that the equations y + z = 7, + y 5z =, + y + z = 0 are consistent and have unique solution. (O 09). NON TEXTUAL: Solve by matri method the equations y z = -; + y + z = 6 ; y + 4z = 9 (J 09) 4. Solve by using matri inversion method: 8y 5z 5, y z, y z. (J 07 ; M 09) 5. Solve by matri method the equations y z ; y 4z ; y z. (M 06 ; J 08 ; O 0) 6. Solve by Cramer s rule : y z, y z 0, y z. (J 06 ; M 07 ; M 08 ; O 08; J ; M ) 7. Solve by Cramer s rule : y, y z 6, z 4. (O 07) 8. Solve the equations + y + 5z = ; + y + 4z = 6 ; 6 + y + 7z = 47 by determinant method. (J 0 ; M ; O ) 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 A B C drawn (in Rs.) January February March Find out the rates of commission on the items A, B and C, Solve by Cramer s rule. (O 06) 0. The data below are about an economy of two industries P and Q. The values are in lakhs of rupees. Producer User Final Total P Q demand output P 6 40 Q Find the technology matri 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 :

2 . In an economy there are two industries P and Q and the following table gives the supply and demand positions in crores of rupees: Producer User Final Total P Q demand output P Q Determine the outputs when the final demand changes to 5 for P and 4 for Q. (J 07 ; M 08 ; J 08 ; M 0 ; O 0 ; J ; M ). In an economy of two industries P and Q the following table gives the supply and demand positions in crores of rupees: Producer P Q P 6 8 User Q 0 40 Final demand Total output Find the outputs when the final demand changes to 8 for P and 44 for Q. (J 06 ; O 06 ; J 09). The data below are about an economy of two industries P and Q. The values are in crores of rupees: Producer P Q User P Q Final demand Total output Find the outputs when the final demand changes to 00 for P and 600 for Q. (M 07 ; J 0) 4. In an economy of two industries P and Q the following table gives the supply and demand positions in millions of rupees. Producer User P Q Final Demand Total Output P Q Find the outputs when the final demand changes to 0 for P and 0 for Q. (O 09) 5. Suppose that the inter-relationship between the production of two industries P and Q in a year (in millions of rupees) Producer User P Q Final Demand Total Output P Q Find the outputs when the final demand changes (i) for P and 8 for Q (ii) 8 for P and for Q. (O ) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

3 6. 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 0% switch over to B. Of those who bought B the previous week, 80% buy it again whereas 0% 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) 7. Two products P and Q share the market currently with shares 70% and 0% each respectively. Each week some brand switching takes place. Of those who bought P in the previous week, 80% buy it again whereas 0% 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) 8. The newspapers A and B are published in a city. Their present market shares are 5% for A and 85% for B. Of those who bought A the previous year 65% continue to buy it again while 5% 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 ) CHAPTER :. ANALYTICAL GEOMETRY. Find the centre, vertices, eccentricity, foci and latus rectum and directrices of the ellipse 9 6 y 6 y 9 0. (M 08 ; J 0 ; J ). Find the centre, vertices, eccentricity, foci and latus rectum and directrices of the ellipse 7 4y 4 40 y (O 07 ; O 0). Find the centre, eccentricity, foci and directrices of the ellipse 4 y 6 8 y 5 0. (M 06 ; O 08 ; J 09) 4. Find the centre, eccentricity, foci and directrices of the hyperbola 4y 4 y 7 0. (J 07) 5. Find the centre, eccentricity, foci and latusrectum of the hyperbola 9 6 y 8 64 y (O 06 ; J 08) 6. Find the equation to the hyperbola which has the lines + 4y 5 = 0 and y + = 0 for its asymptotes and which passes through the point (,). (M ) 7. Find the equation to the hyperbola which has 4y + 7 = 0 and 4 + y + = 0 for asymptotes and which passes through the origin. (M ) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

4 8. Find the equations of the asymptotes of the hyperbola 5y y 7y 4 0. (J 06 ; M 07 ; M 09) 9. Find the equations of the asymptotes of the hyperbola 8 0 y y 4y 0. (M 0 ; O ) 0. Find the equations of the asymptotes of the hyperbola 5y y 7 y 4 0. (O 09) CHAPTER :. APPLICATION OF DIFFERENTIATION - I. A firm produces tones of output at a total cost C ( ) Rs Find (i) Average cost (ii) Average Variable Cost (iii) Average Fied Cost. Also find the value of each of the above when the output level is 0 tonnes. (O 0) 0. Find the elasticity of demand, when the demand is q and p =. Interpret the result. (M 0) p. If AR and MR denote the average and marginal revenues at any output level, show that elasticity of AR demand is equal to. Verify this for the linear demand law p a b, where p is price and is AR MR the quantity. (M 07 ; J 08 ; J ) 4. Prove that for the cost function C 00, where is the output, the slope of AC curve = MC AC. (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 = a 6 + b may pass through the point (0,) and have its tangent parallel to the -ais at =.5. (J 09) 6. Find the equation of the tangent and normal to the demand curve y at 6. (O 06) 7. Prove that the curves y = + and (y + ) = 4 intersect at right angles at the point (,-).(J 06) 8. Find the equations of the tangent and normal to the curve y 7 0 cuts the -ais. (M 06 ; M 09 ; M ; O ; M ) 9. Find the equations of the tangent and normal at the point a sec,btan a y b. (M 08 ; O 08) on the hyperbola at the point where it K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

5 0. Find the point on the curve y = ( )( ) at which the tangent makes an angle 5 with the positive direction of ais. (J 0) At what points on the circle + y - 4y + = 0, the tangent is parallel to (i) -ais (ii) y-ais. (J 07 ; O 09) CHAPTER : 4. APPLICATION OF DIFFERENTIATION - II. Find the maimum and minimum values of the function (O 06). Investigate the maima and minima of the function 6 0. (M 08 ; O 0). Find the maimum and minimum values of the function (M 06 ; J ) 4. NON TEXTUAL: Investigate the maima and minima of the function 9 5. (O 09) 5. Show that the maimum value of the function f ( ) 7 08 is 08 more than the minimum value. (J 08) 6. For the cost function C = 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 = Find, when the total cost is minimum. (M 0) 8. A firm produces tonnes of output at a total cost C At what level of output will 0 the marginal cost and the average variable cost attain their respective minimum? (J 07) 9. R = and C 9 6 are respectively the sales revenue and cost function of units sold. Find the following: (i) At what output is the revenue maimum? What is the total revenue at this point? (ii) What is the marginal cost at a minimum? (iii) What output will maimise the profit? (M 09 ; M ) 0. A Radio manufacturer finds that he can sell radios per week at Rs.p each, where p 00. His 4 cost of production of radios per week is Rs. 0. Show that his profit is maimum when the production is 40 radios per week. Find also his maimum profit per week. (O 08) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

6 . The total cost and total revenue of a firm are given by C = and R = 8 4. Find the output (i) when the revenue is maimum (ii) when the profit is maimum? (J 0). 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.00 Rs..60 B 5000 Rs.648 Rs.0.00 C 8000 RS.00 Rs 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) 4. Calculate EOQ in units and total variable cost for the following item, assuming an ordering cost of Rs.5 and a holding cost of 0%. Item A Annual demand 460 units Unit price Re. (M ) 5. The annual demand for an item is 00 units. The unit cost is Rs.6 and inventory carrying charges 5% per annum. If the cost of one procurement Rs.50, determine (i) Economic order quantity (ii) Time between two consecutive orders. (M 07) u u u 6. If u log y z, then prove that. (J 08 ; O 08 ; O0) y z y z y 7. If u tan then prove that y u u y y sin u by Euler s theorem. (M 08) y z z 8. If z e, then prove that y z log z. (Use Euler s theorem). (M 0 ; J 0 ;O ) y 9. NON TEXTUAL: Prove using Euler s theorem if u u y cotu 0. (O 06) y 0. NON TEXTUAL: Prove using Euler s theorem if u cos u y then y y u u 5 then y u.(j 07) y y. The demand for a commodity A is q 40 p 6 p p p. Find the partial elasticities Eq Eq and when p = 5 and p = 4.(M 06 ; J 06 ; M 07 ; O 09 ; M ; O ; M ) Ep Ep K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

7 . The demand for a commodity A is q 6 p p. Find (i) the partial elasticities (ii) the partial elasticities when p and p.(o 07 ; M 08 ; J 09). The demand for a commodity A is q p p p. Find (i) the partial elasticities (ii) the partial elasticities when p 0 and p 4.(J ) Eq Eq and Ep Ep Eq Eq and Ep Ep. Evaluate: 6. Evaluate: 6. Evaluate: 0 sin d. tan d. cot sin CHAPTER : 5. APPLICATIONS OF INTEGRATION (J 06 ; M 09 ; J 0 ; M ;J ;O ) (M 07 ; M 08 ; O 0) cos d. (M 06) a sin bcos 4. Evaluate: d (J 07 ; O 08) sin cos 0 4. Evaluate: d. 0 (J 09 ; M ) 5. NON TEXTUAL: Evaluate: d. 6. Evaluate: sin d. (O 09) 0 0 (M 0) 7. NON TEXTUAL: Find the area of one loop of the curve y 9. (J 08) between 0 and 8. NON TEXTUAL: Find the area of one loop of the curve a y a a. (O 08) 9. NON TEXTUAL: Find the area of one loop of the curve y 4. (O 06) between 0 and between 0 and y 0. Find the area of the ellipse. b a (J 09). The elasticity of demand () with respect to price p is,. revenue function when the price is and the demand is. (M ) Find the demand function and the. Find the consumers surplus for the demand function p = 5 when p 0 = 9. (O 08) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

8 . Find the consumers surplus and producers surplus under market equilibrium if the demand function is p d 0 and the supply function is p s. (M 06 ; O 07;J ) 6 4. The demand and supply curves are p d and p s. Find the consumers surplus and 4 producers surplus at market equilibrium price. (J 08) 5. The demand and supply function for a commodity are given by 5 and 0.. Find the consumers surplus and producers surplus at market equilibrium price. (M 07) p d p s 6. The demand and supply law under a pure competition are given by p d = and p s = 4. Find the consumers surplus and producers surplus at the market equilibrium price. (O 06 ; O 0) 7. Under pure competition The demand and supply laws for commodity and p d = 56 and p s 8. Find the consumers surplus and producers surplus at the market equilibrium price. (J 07;O ) 8. In a perfect competition The demand and supply curves of a commodity are given by p d = 40 and p s 8 8. Find the consumers surplus and producers surplus at the market equilibrium price. (O 09 ; J 0). The demand and supply functions under pure competition are p d 6 and ps 4. Find the consumers surplus and producers surplus at market equilibrium price. (J 06 ; M 08 ; M 09 ; M 0 ; M ) CHAPTER : 6. DIFFERENTIAL EQUATIONS dp p. The net profit p and quantity satisfy the differential equation. Find the relationship d p between net profit and demand given that p 0 when 0. (M 06). Solve : dy y d y. (M 09 ; M 0). Solve : dy y y. (O 0) d y dy y y 4. Solve :. (O ) d K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

9 5. The rate of increase in the cost c of ordering and holding as the size q of the order increases is given by dc c q the differential equation. Find the relationship between c and q, if c = 4 and q =. dq cq (J ) dp d P 6. Suppose that Q d 0 5P and Q 6 P, s where P denotes price. Find the dt dt equilibrium price for market clearance. (J 06 ; M 07 ; J 07 ; M 08 ; O 08 ; M ) dp d P 7. Suppose that Q d 4 4P 4 and Q 6 8P, s where P denotes price. Find the dt dt equilibrium price for market clearance. (J 09 ; M ) 8. Solve : D D y e 5e. (O 06 ; O 09 ; J 0) 9. Solve : D 5D y e e. (J 08) 7 0. Solve : D 4 D 49 y e. (O 07) CHAPTER : 7. INTERPOLATION AND FITTING A STRAIGHT LINE. From the following data calculate the value of e.75 (O 09) : e : From the following data, find the number of students whose height in between 80 cm and 90 cm: (M 08) Height in cm : No. of students y: Find the number of men getting wages between Rs.0 and Rs.5 from the following table. (O ) Wages : No. of men y: Find y when 0. given that (O 0) : 0 4 y: K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

10 5. Using Gregory-Newton s formula, find y(.4) (M ) X: 9 0 Y: Using Lagrange s formula find y when = 4 from the following table (J 08 ; M 0) : y: Fit a straight line to the following data: (J 06 ; O 06 ; O 07 ; J ; M ) : y: Fit a straight line y a b to the following data by the method of least squares: (M 06) : y: Fit a straight line y a b to the following data by the method of least squares: (M 07 ; J 07) : y: Fit a straight line to the data given below. Also estimate the value of y at =.5 : (M 09 ; J 0) : 0 4 y: A group of 5 students took tests before and after training and obtained the following scores. (O 08) Scores before training Scores after training Find by the method of least squares the line of best fit. CHAPTER : 8. PROBABILITY DISTRIBUTION. Given the p.d.f of a continuous random variable X as follows Find k and c.d.f. (J 09) k( ) f ( ) 0 for0 otherwise K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

11 . Suppose that the life in hours of a certain part of radio tube is a continuous random variable X with 00 ; when 00 p.d.f given by f ( ) 0 elsewhere (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 50 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 0). A random variable X has the following probability probability distribution. : P() a a 5a 7a 9a a a 5a 7a (i) Determine the value of a (ii) Find P(X < ), P(X > ) and P(0 < X < 5) (J 07 ; O 09) 4. k, 0 0 A continuous random variable has the following p.d.f: f ( ) 0 otherwise P (ii) P. (M 08) Determine k and evaluate (i), 5. Let X be a continuous random variable with p.d.f f ( ) 0 otherwise Find (i) E(X) (ii) E(X ) (iii) Var(X) (O 06 ; O 0) 6. Find the mean and variance for the probability distribution: (M 06 ; J 06 ; O 08 ; M 09 ; M ; J ) f ( e ) 0, 0 0 NON TEXTUAL: Find the mean and variance for the probability distribution, 0 f ( ) (O 07) otherwise 0, 7. NON TEXTUAL: In a continuous distribution, whose probability density function is given ( ) 0 by f ( ) 4, Show that the arithmetic mean of the distribution is and the 0, otherwise variance is. (M 07) 5 8. Ten coins are thrown simultaneously. Find the probability of getting at least 7 heads. (M 06;O 0;O ) 9. For a binomial distribution with parameters n = 5 and p = 0. find the probabilities of getting (i) at least successes (ii) at most successes. (J 0) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

12 0. Find the probability that at most 5 defective bolts will be found in a bo of 00 bolts, If it is known that % of such bolts are epected to be defective. (e -4 = 0.08) (M 0 ; M ). It is stated that % of razor blades supplied by a manufacturer are defective. A random sample of 00 blades is drawn from a lot. Find the probability that or more blades are defective. (e -4 = 0.08) (J 09). NON TEXTUAL: The number of accidents in a year attributed to tai drivers in a city follows Poisson distribution with mean.out of 500 tai drivers, find the approimate number of drivers with (i) no accident in a year (ii) more than accidents in a year. (e - = ) (M ). A sample of 000 candidates the mean of certain test is 45 and S.D 5. 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 0? (O 09 ; J ) 4. The I.Q (intelligence quotient) of a group of 000 children has mean 96 and the standard deviation. Assuming the distribution as normal, find approimately the number of children having I.Q. (i) less than 7. (ii) between 80 and 0. (M 07 ; J 07 ; M 08) 5. NON TEXTUAL: The distribution of marks obtained by 000 students in an eamination is normally distributed with mean 4 and S.D 6. (i) Find the number of students scoring between 0 and 60 marks and (ii) Find the number of students scoring above 70 marks. (J 06) 6. In a normal distribution 0% of items are less than 00 and 0% are over 00. Find the mean and S.D of the distribution. (J 08 ; O ; M ) Z Area The mean yield for one-acre plot is 66 kg with an S.D of kg. Assuming normal distribution, how many one-acre plots in a batch 000 plots would you epect to have yield (i) over 700 kg? (ii) below 650 kg? (M 09) 8. A large number of measurements is normally distributed with a mean of 65.5 and S.D of 6.. Find the percentage of measurements that fall between 54.8 and (O 06 ; J 0) 9. The diameter of shafts produced in a factory conforms to normal distribution. % 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) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

13 CHAPTER : 9. SAMPLING TECHNIQUES AND STATISTICAL INFERENCE. A sample of 00 students are drawn from a school. The mean weight and variance of the sample are kg and 9 kg. respectively. Find (a) 95% and (b) 99% confidence intervals for estimating the mean weight of the students. (J 07). Out of 000 TV viewers, 0 watched a particular programme. Find 95% confidence limits for TV watched this programme.(o 07). A sample of five measurements of the diameter of a sphere were recorded by a scientist as 6., 6.7, 6., 6.6 and 6.7 mm. Determine the point estimate of (a) mean, (b) variance. (O 09 ; J 0) 4. The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 85 hours with a standard deviation of 0 hours. If is the mean life time of all the bulbs produced by the company, test the hypothesis that 900hours at 5% level of significance. (M 07;M 09;O ) 5. A company markets car tyres. Their lives are normally distributed with a mean of kilometers and standard deviation of 000 kilometers. A test sample of 64 tyres has a mean life of 550 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 7.8 cm. Can it reasonably be regarded as a sample from a large population with mean height of 7.7 cm and standard deviation of. cm? (Test at 5% level). (M 06 ; O 08 ; J ) 7. To test the conjecture of the management that 60 percent employees favour a new bonus scheme, a sample of 50 employees was drawn and their opinion was taken whether they favoured it or not. Only 55 employees out of 50 favoured the new bonus scheme. Test the conjecture at % level of significance. (J 06 ; M ) 8. The mean I.Q. of a sample of 600 children was 99. Is it likely that this was a random sample from a population with mean I.Q. 00 and standard deviation 5? ( Test at 5% level of significance ) (J 08 ; J 09 ; M 0 ; O 0 ; M ) 9. The income distribution of the population of a village has a mean of Rs.6,000 and a variance of Rs.,400. Could a sample of 64 persons with a mean income of Rs. 5,950 belong to this population? (Test at both 5% and % levels of significance) (M 08) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

14 CHAPTER : 0. APPLIED STATISTICS. Solve graphically: Minimize Z 0 40 Subject to ; 6 ; ;, 0 ( J 07 ; M 08). Solve the following, using graphical method: Maimize Z 4 subject to the constraints 40 ; 5 80 ; 0. (J 06 ; J 0 ; O ),. Solve the following, using graphical method: Minimize Z subject to the constraints 0 ; ; ; 0. (O 09 ; J ) 5 4, 4. Solve the following, using graphical method: Maimize Z subject to the constraints ; ;, 0. (O 0 ; M ) 5. NON TEXTUAL: Solve graphically: Maimize Z 5 Subject to 000 ; ; ;, 0. (M 09) 6. NON TEXTUAL: Solve the following using graphical method: Maimize Z 5 6 Subject to the constraints, 0 ; ;, 0 (M 06) 7. Find the co-efficient of correlation for the data given below: (O 06 ; J 08 ; J 09) X : Y : Obtain the two regression lines from the following: (M 0) X : Y : K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

15 9. From the data given below calculate Seasonal Indices. (O 09 ; J 0) Quarter Year I II III IV Calculate the seasonal indices by the method of simple average for the following data: (M 08) Year Quarters I II III IV Calculate the seasonal indices for the following data using average method: (M 06 ; M ) Year Quarters I II III IV Calculate Fisher s ideal inde from the following data: (O 07) Commodity A B C D E Price Quantity K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

16 . Compute (i) Laspeyre s (ii) Paasche s (iii) Fisher s inde numbers for the year 000 from the following: (O 06 ; J 08) Price Quantity Commodity A B C D 9 4. From the following data calculate the price inde number by (a) Laspeyre s method, (b) Paasche s method and (c) Fisher s method: (M 07) Commodity A B C D Base year Current Year Price Quantity Price Quantity From the following data calculate the price inde number by (a) Laspeyre s method, (b) Paasche s method and (c) Fisher s method: (M 0) Commodity A B C D E Base year Current Year Price Quantity Price Quantity From the following data calculate the price inde number by (a) Laspeyre s method, (b) Paasche s method and (c) Fisher s method: (M ) Commodity A B C D Base year Current Year Price Quantity Price Quantity K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

17 7. NON TEXTUAL: Compute (i) Laspeyre s (ii) Paasche s (iii) Fisher s inde numbers for the year 000 from the following: (M 09) Commodity Price Quantity A B C D 9 8. From the following data, construct Fisher s Ideal inde and show that it satisfies factor Reversal test and Time Reversal test: (J 06 ; J ) Commodity A B C D E F Base year Current Year Price Quantity Price Quantity From the following data, construct Fisher s Ideal inde and show that it satisfies factor Reversal test and Time Reversal test: (O 0) Commodity A B C D Base year Current Year Price Quantity Price Quantity From the following data, construct Fisher s Ideal inde and show that it satisfies factor Reversal test and Time Reversal test: (J 07 ; O 08) Commodity A B C D E Base year Current Year Price Quantity Price Quantity K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :

18 . Compute (i) Laspeyre s (ii) Paasche s (iii) Fisher s inde numbers for the following data: (O ) Commodity A B C D Base year Price Current year 0 6 Base year Quantity Current year Calculate the cost of living Inde Number using Family Budget method: (J 09) Commodity A B C D E F G H Quantity in base year (unit) Price in Base year(rs.) Price in current year(rs.) 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) Sample No Mean X Range R (Given for n = 6, A = 0.48, D = 0, D 4 =.004 ) 4. 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 ) Sample No Mean X Range R (Given for n = 5, A = 0.577, D = 0, D4 =.5 ) K. MANIMARAN. M.Sc.,B.Ed., GOLDEN GATES MHSS, SALEM 8 ; PH :