ASSIGNMENT BOOKLET

Bachelor’s Degree Programme

(B.Sc./B.A./B.Com.)

MATHEMATICAL METHODS

Valid from 1st January, 2016 to 31st December, 2016

• It is compulsory to submit the Assignment before filling in the

Term-End Examination Form.

• It is mandatory to register for a course before appearing in the Term-End Examination of the course. Otherwise, your result will not be declared.

For B.Sc. Students Only

• You can take electives (56 or 64 credits) from a minimum of TWO and a

maximum of FOUR science disciplines, viz. Physics, Chemistry, Life

Sciences and Mathematics.

• You can opt for elective courses worth a MINIMUM OF 8 CREDITS and a

MAXIMUM OF 48 CREDITS from any of these four disciplines.

• At least 25% of the total credits that you register for in the elective

courses from Life Sciences, Chemistry and Physics disciplines must be

from the laboratory courses. For example, if you opt for a total of 24

credits of electives in these 3 disciplines, then at least 6 credits out of

those 24 credits should be from lab courses.

School of Sciences

Indira Gandhi National Open University

Maidan Garhi, New Delhi-110068

(2016)

MTE-03

2

Dear Student,

Please read the section on assignments in the Programme Guide for Elective Courses that we sent you

after your enrolment. A weightage of 30 per cent, as you are aware, has been earmarked for continuous

evaluation, which would consist of one tutor-marked assignment for this course. The assignment is in

this booklet.

Instructions for Formating Your Assignments

Before attempting the assignment please read the following instructions carefully:

1) On top of the first page of your answer sheet, please write the details exactly in the following format:

ROLL NO.:……………………………………………

NAME :……………………………………………

ADDRESS :……………………………………………

……………………………………………

……………………………………………

COURSE CODE : …………………………….

COURSE TITLE : …………………………….

ASSIGNMENT NO.: ………………………….…

STUDY CENTRE : ………………………..….. DATE :……………………….………………...

PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION AND

TO AVOID DELAY.

2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers.

3) Leave 4 cm margin on the left, top and bottom of your answer sheet.

4) Your answers should be precise.

5) While solving problems, clearly indicate which part of which question is being solved.

6) This assignment is to be submitted to the Study Centre as per the schedule made by the study centre.

Answer sheets received after the due date shall not be accepted.

We strongly suggest that you retain a copy of your answer sheets.

7) This assignment is valid only upto December, 2016. If you have failed in this assignment or fail to

submit it by December, 2016, then you need to get the assignment for the year 2017 and submit it as

per the instructions given in the programme guide.

8) You cannot fill the Exam Form for this course till you have submitted this assignment. So solve it

and submit it to your study centre at the earliest.

We wish you good luck.

3

Assignment

Course Code: MTE-03

Assignment Code: MTE-03/TMA/2016

Maximum Marks: 100

1. State whether the following statements are true or false. Give reasons for your answer.

i) The rule given below is a function

7)3(,7)2(,4)2(:}7,4{}3,2{: ===→ ffff

ii) For two non-negative integers r and n s.t., nr ≤

r

n

r

n

r

n CCC 1

1

+

−=+

iii) The normal curve for

∞<<∞−=

−

xefx

;2

1 2

2

1

π

attains its maximum at 0=x .

iv) The magnitude of a vector product vu× is equal to the area of a triangle having u and v as

two of its sides.

v) If X has the uniform distribution on ],[ ba , then mean of X is 2

ab −. (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 5)98( using Binomial theorem. (3)

c) Evaluate

+−

−

→ 65

2lim

2

23

2 xx

xx

x. (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 18

th hour? (3)

3. a) Find the equation of the sphere which passes through the points

)0,3,1(),2,5,1(),3,4,1( −−− and whose centre lies on the plane 0=++ zyx . (5)

b) Solve the differential equation

0)()1(1tan2

=−++−

−

dx

dyexy y

. (5)

4. a) What value assigned to )(xf at 2=x will make the function f defined by

4

6)(

2

2

−

−+=

x

xxxf continuous? (3)

b) Let kjiCkjBkjiA 3315,5,5 −+−=−=+−= be three vectors. Which pair of

vectors are i) perpendicular? ii) parallel? (3)

4

c) Find dx

df for

3 1

1)(

+

+=

x

xxf . (4)

5. a) Find the asymptotes for the function 1−

=

x

xy . (2)

b) For the function 1093 3+− xx , find the value of x 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 ∫+

2/

0cos2

1π

dxx

. (4)

6. a) For what value of x will the angle between the lines with direction ratios )4,2,(x and

)1,0,1( be o45 ? (2)

b) Find the coordinates of the foot of the perpendicular from )2,3( − on the line

0154 =−+ yx . (3)

c) A ball drops from 180 metres and rebounds one-third of its previous height on each bounce.

i) Find the total distance it travels before it comes to rest.

ii) Find the total distance traveled uptill the time the ball strikes the ground fifth time. (5)

7. a) A bag contains 8 white balls and 4 red balls. One ball is drawn from the bag and it is replaced after noting its colour. In the second draw again one ball is drawn and its color is

noted. Find the probability that both the balls drawn are of different colours? (4)

b) From the frequency distribution given below find

i) the mean ii) the median iii) the mode.

Also plot the histogram and sketch the cumulative frequency curve. (6)

8. a) A sample of size 36 is picked at random from a population of adult males. If the standard

deviation of the distribution of their heights is known to be 3 cms, find the standard error of

the mean if

i) the population consists of 1000 males.

ii) the population is extremely large. (3)

b) Suppose the gene ‘A’ stands for tall and gene ‘a’ stands for short, and ‘A’ is dominant over ‘a’. Suppose the parents are of genotype aa and Aa.

i) In a family like this what is the probability of having a short child?

ii) In a family like this if there are four children, what is the probability that two children

are tall and two children are short?

iii) If you survey a large number of such families having four children, what is the average

number of tall children to be expected in a family?

iv) If you survey 256 families of this type, each having four children, how many families are expected to have all tall children? (7)

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

Frequency 5 10 21 8 6

5

9. a) The genetic features of a group of adult mice are such that the probability of an offspring

being albino is 0.2. If 50 offsprings are born to a group of such mice, find the probability that 15 or more of them are albinos. (4)

b) The urinary secretion rate (mg./24 hours) of patients suffering from disease A is normally

distributed with mean 5 variance 1, while the corresponding rate for disease B is normally

distributed with mean 7 variance 4. A patient is classified as suffering from disease A and disease B if his rate is more than 5.5 and up to 5.5 respectively. What is the probability of

misclassification if disease A is twice as common as disease B? (6)

10. a) In an area %5.0 of the livestock dies of foot-and-mouth disease. A farmer in that area has

200 livestock. What is the probability that there will be no death. (2)

b) Three varieties A, B, C of a crop arae tested in fifteen plots as designed below. Each variety

was replicated five times. The crop yield in each plot is written inside the corresponding plot.

Analyse the data to find out if there is any significant difference in the yields of these three

varieties at %5 level of significance. (8)

A

6

C

5

A

8

B

9

C

7

C

8

A

4

B

6

C

9

B

6

B

7

B

6

C

10

A

6

A

8