LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – CHEMISTRY

CV 09

THIRD SEMESTER – APRIL 2007

MT 3101 – ALLIED MATHEMATICS FOR CHEMISTRY

 

 

 

Date & Time: 28/04/2007 / 9:00 – 12:00   Dept. No.                                          Max. : 100 Marks

 

 

SECTION A

Answer ALL questions:                                                                                  10 ´ 2 = 20

1. Find the angle which the tangent at (2, 4) to the curve y = 6 + x – makes with the x-axis.
2. Differentiate with respect to .
3. Evaluate .
4. Solve (+ D + 1)y = 0.
5. Sum the series to .
6. Solve .
7. Write down the value of in powers of .
8. Prove that cosh(x – y) = coshx coshy – sinhx sinhy.
9. What is the chance that a leap year selected at a random will contain 53 Sundays?
10. Let X be a random variable with the following distribution

X	–3	6	9
P(X)

Find the expectation of X.

 

 

SECTION B

Answer any FIVE questions:                                                                          5 ´ 8 = 40

11. What is the maximum value of .
12. Evaluate .
13. Sum the series to
14. (a) Solve z = px + qy + 2.

(b) Obtain a partial differential equation by eliminating a, b from. (4 + 4)

15. Expand in a series of sines of multiples of .
16. Prove that (a) sinh 3x = 3sinh x + 4.

(b) .                  (4 + 4)

17. A problem in statistics is given to 5 students whose chances of solving are respectively. What is the probability that the problem will be solved if all of them try independently?
18. The mean yield for one-acre plot is 662 kilos with a S. D 32 kilo. Assuming normal distribution, how many one-acre plots in a batch of 1000 plots would you expect to have yield       (i) Over 700 kilos

(ii) Below 650 kilos

given that, , .

 

 

SECTION C

Answer any TWO questions:                                                                          2 ´ 20 = 40

19. (a) Differentiate (i) , (ii)

(b) Show that the parabolas  and  cut orthogonally. (5 + 5 + 10)

20. (a) Solve.

(b) Prove that.                       (8 + 12)

21. (a) Sum the series to .

(b) Find the eigen values and eigen vectors of .  (8 + 12)

21. (a) Obtain the Fourier series for the function and

deduce that .

(b) Find the mean of the Binomial distribution.   (15 + 5)

 

 

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