# IGNOU B.Sc / Mathematics MTE-03 Assignments 2010

ASSIGNMENT BOOKLET
Bachelor’s Degree Programme
MATHEMATICAL METHODS
Last date for submission: 31st March 2010
Special Instructions Only for B.Sc. Students
• You can take electives (56 to 64 credits) from a minimum of TWO and a maximum of Four science disciplines, viz. Physics, Chemistry, Life Sciences and Mathematics.

Dear Student,

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Assignment

(To be done after studying the course material)

Course Code: MTE-03

Assignment Code: MTE-03/TMA/2009

Maximum Marks: 100

1. Which of the following statements are true? Give reasons for your answers.

i) Set of letters needed to spell ‘CATARACT’ and the set of letters needed to spell ‘TRACT’ are equal.

ii) The function is monotone in the interval .

iii) The tangent to a straight line does not exist.

iv) The arithmetic mean is the best measure of central tendency.

v) If two variables deviate in opposite directions then they are uncorrelated. (10)

2. a) A committee of 5 persons is to be constituted from a group of 4 men and 3 women. In how many ways can this be done? How many of these committees would consist of 3 men and 2 women? (2)

b) Compute using Binomial theorem. (3)

c) Evaluate . (2)

d) The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 18th hour? (3)

3. a) Find the equation of the sphere which passes through the points and whose centre lies on the plane . (5)

b) Solve the differential equation

. (5)

4. a) What value assigned to at will make the function defined by continuous? (3)

b) Let be three vectors. Which pair of vectors are

i) perpendicular? ii) parallel? (3)

c) Find for . (4)

5. a) Find the asymptotes for the function . (2)

b) For the function , find the value of for which the curve is i) rising ii) falling

iii) concave up iv) concave down. Also find the point of inflexion. (4)

c) Evaluate the integral . (4)

6. a) Let be the size of certain population of predators and the size of the population of prey upon which they feed. As function of time and . Let be the number of prey to each predator. Find the rate of change of . (4)

b) A study was conducted to test the effects of growth hormone on the rate of growth of 10 children.

Subject Before treatment After treatment

1

2

3

4

5

6

7

8

9

10 3.4

3.6

4.8

3.4

4.8

5.8

4.2

5.7

4.1

4.3 4.5

5.2

6.5

5.2

7.4

8.9

8.4

8.5

7.5

8.2

Growth rates were measured before and after the subjects were given growth hormones three times a week for a year. Based on the data given above, does the sample show a significant difference in the growth rate at 5% level of significance? (6)

7. a) From the frequency distribution table given below find i) the mean ii) the median iii) mode

iv) variance v) standard deviation.

50 – 52 53 – 55 56 – 58 59 – 61 62 – 64

5 10 21 8 6

b) A fair coin is tossed five times. Find the possibilities that a head appears

i) exactly three times

ii) at least two times

iii) at the most four times. (3)

c) In a certain Poisson frequency distribution the frequency corresponding to 3 successes is one third the frequency corresponding to 4 successes. Find its mean and standard deviation. (2)

8. a) There are five children in a family of parents . The children of such parents must have genotype or genotype . Find the probability that two of the children have genotype and three others have genotype . (3)

b) Suppose the diameter of a rod has normal distribution . If the diameter satisfies , then it is non-defective. Find the probability that the rod is non-defective. (4)

c) A bag contains 6 white and 4 red balls. One ball is drawn at random and put aside without noticing its colour. Now another ball is drawn from the bag at random. What is the probability that the second ball is white? (3)

9. a) The following data were obtained in a study of the relationship between the resistance (ohms) and the failure time (minutes) of certain overloaded resistors

Resistance 48 28 33 40 36 39 46 40 30 42 44 48 39 34 47

Failure time 45 35 39 45 36 35 36 45 34 39 51 41 38 32 45

Find the coefficient of correlation. (5)

b) Suppose that the temperature is normally distributed with expectation and variance . What is the probability that the temperature will be between and ? What is the probability that ? (5)

10. a) A continuous random variable has the p.d.f.

Calculate the mean and standard deviation of . Construct the distribution function and hence evaluate . (6)

b) The probability that a certain plant will die within hours in a certain environment is estimated to be . Determine the probabilities that the plant will die within 2 hours and that it will survive more than 3 hours. Find the corresponding density function. (4)

Reference: http://www.ignou.ac.in/Assignments/bsc/July_09/Maths%20July%20%202009/BSc/mte-03n.doc