LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – CHEMISTRY

THIRD SEMESTER – APRIL 2012

MT 3103 – MATHEMATICS FOR CHEMISTRY

 

 

Date : 28-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

 

Part A. Answer all the questions. Each question carries two marks.                               (10 x 2 = 20)

1. Find  for x = a(+sin ); y = a(1-cos),
2. Find  if
3. Evaluate
4. Evaluate
5. Prove that
6. If
7. If, show that the angle  is 3^o approximately
8. Prove that sinh 3x = 3 sinh x + 4 sinh³ x

 

1. If the probability of defective bolt is 0.1; find the mean and standard deviation for the distribution of defective bolts in a total of 500.

 

1. What are the significance of normal distribution.

 

Part B. Any 5 questions only. Each question carries 8 marks.                                          (5 x 8=40)

 

1. Find the equation of the tangent and normal for y²= 4ax at (at²,2at).

 

1. Prove that the tangents to the curve y = x² -5x + 6 at the points (2,0) and (3,0) cut at right angles.

 

1. Solve (3D²– 4D + 5) y = 3 e^2x
2. Prove that
3. If x is large, prove that  nearly.
4. Prove that
5. Find the standard deviation for the following data:

Age (x)	20-25	25-30	30-35	35-40	40-45	45-50
No of frequencies (f)	170	110	80	45	40	35

 

1. Ten percent of the tools produced in a certain manufacturing process turn out to be defective. Find the probability that in a sample of 10 tools chosen at random, exactly two will be defective by using (a) Binomial distribution and (b) the Poisson approximation to the binomial distribution.

 

 

 

 

 

 

Part C. Any two questions only. Each question carries 20 marks.                                   (2 x20 = 40)

• a) Prove that

19) b)  Solve xp + yq = x

 

20)a) Evaluate

20)b) Evaluate

 

21) Find the Fourier series to the function f(x) = in the interval (0,2).

 

 

• a) Find the maximum or minimum values of xy + 1/x +1/

 

22) b) A family has six children. Find the probability P that there are (a) three boys and three girls and (b) fewer boys than girls.

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – CHEMISTRY

FIRST SEMESTER – NOVEMBER 2012

MT 1102 – MATHEMATICS FOR CHEMISTRY

 

 

Date : 03/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

Part A

 

 

Answer ALL questions:                                                                   (10 x 2 =20)

 

1. Differentiate with respect to .
2. Find the slope of the tangent at to the curve
3. Change the limits of as lower limit to  and upper limit to .
4. Solve .
5. State Binomial theorem.
6. Solve the partial differential equation .
7. State DeMoivre’s theorem.
8. Show that
9. From a well-shuffled pack of 52 cards, one card is drawn at random. What is the probability that it will be (i) a jack (ii) a spade?
10. Define Normal distribution.

Part B

Answer any 5 questions:                                                                   (5 x8 = 40)

 

11. Find the angle of intersection of the cardioids and

.

12. If  , then show that .
13. Evaluate: (i), using Bernoulli’s formula.

(ii) Evaluate: .                                        (4+4)

1. Solve the differential equation .

15. Find the sum of the series
16. If , then show that
17. Obtain the expansion of .
18. Find the maxima and minima of the function .

 

Part C

Answer any TWO questions:                                                                       (2 x 20 = 40)

 

19. (i) Evaluate:

(ii) Prove that .                                          (10+10)

 

20. (i)Obtain the characteristic roots and the associated characteristic vectors of the

matrix  .

(ii) Solve the partial differential equation with usual notations.     (15+5)

 

21. Given that in the interval 0 to . Find the Fourier coefficients  and .Hence deduce that .

 

22. (i)Expand in series of cosines of multiples of .

(ii)The mean mark of  students were found to be 40. Later it was observed that a score of 53 was misread as 83. Find the correct mean using the correct score.

(14+6)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – CHEMISTRY

THIRD SEMESTER – NOVEMBER 2012

MT 3103 – MATHEMATICS FOR CHEMISTRY

 

 

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

 

Section A

 

Answer ALL the questions:                                                                           (10 ´ 2 = 20)

 

1. Differentiate with respect to x.
2. If , find .
3. Evaluate .
4. Solve .
5. Write the binomial expansion for
6. Prove that .
7. Solve .
8. Prove that .

1. Show that .

10. What is the chance that the leap year selected at random will contain 53 Sundays?

 

Section B

Answer any FIVE questions:                                                                           (5 ´ 8 = 40)

 

11. (a) If , find .

(b) Find the differential coefficient of  .

 

1. Find the angle of intersection of the cardioids

and .

 

13. Evaluate .

 

14. Prove that .
15. Sum the series to infinity
16. Express in series of powers of

 

17. Solve .

 

18. A car hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate the proportion of days on which (i) neither car is used, and (ii) the proportion of days on which some demand is refused.

 

Section C

 

Answer any TWO questions:                                                                               (2 ´ 20 = 40)

 

19. a) Find the equation of the tangent and normal to the curve , at .

 

1. b) Find the maxima and minima of the function .

(10 + 10)

 

20. a) Integrate with respect to x.

 

1. b) Solve .                                                                            (12 + 8)

 

21.a)       Expand   in a series of cosines multiples of

.

 

1. b) Show that

(10 + 10)

 

22. a) Show that   in the interval  . Also deduce that

 

1. b) An insurance company insures 4,000 people against loss of both eyes in a car accident. Based on previous data, the rates were computed on the assumption that on the average 10 persons in 1,00,000 will have car accident each year that result in this type of injury. What is the probability that more than 3 of the insured will collect on their policy in a given year?

( 12 + 8)

 

 

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